id sid tid token lemma pos american_scientific_journal-2747 1 1 257 257 NUM american_scientific_journal-2747 1 2 american american ADJ american_scientific_journal-2747 1 3 scientific scientific ADJ american_scientific_journal-2747 1 4 research research NOUN american_scientific_journal-2747 1 5 journal journal NOUN american_scientific_journal-2747 1 6 for for ADP american_scientific_journal-2747 1 7 engineering engineering NOUN american_scientific_journal-2747 1 8 , , PUNCT american_scientific_journal-2747 1 9 technology technology NOUN american_scientific_journal-2747 1 10 , , PUNCT american_scientific_journal-2747 1 11 and and CCONJ american_scientific_journal-2747 1 12 sciences science NOUN american_scientific_journal-2747 1 13 ( ( PUNCT american_scientific_journal-2747 1 14 asrjets asrjet NOUN american_scientific_journal-2747 1 15 ) ) PUNCT american_scientific_journal-2747 1 16 issn issn PROPN american_scientific_journal-2747 1 17 ( ( PUNCT american_scientific_journal-2747 1 18 print print NOUN american_scientific_journal-2747 1 19 ) ) PUNCT american_scientific_journal-2747 1 20 2313 2313 NUM american_scientific_journal-2747 1 21 - - SYM american_scientific_journal-2747 1 22 4410 4410 NUM american_scientific_journal-2747 1 23 , , PUNCT american_scientific_journal-2747 1 24 issn issn PROPN american_scientific_journal-2747 1 25 ( ( PUNCT american_scientific_journal-2747 1 26 online online ADJ american_scientific_journal-2747 1 27 ) ) PUNCT american_scientific_journal-2747 1 28 2313 2313 NUM american_scientific_journal-2747 1 29 - - SYM american_scientific_journal-2747 1 30 4402 4402 NUM american_scientific_journal-2747 1 31 Β© Β© PROPN american_scientific_journal-2747 1 32 global global ADJ american_scientific_journal-2747 1 33 society society NOUN american_scientific_journal-2747 1 34 of of ADP american_scientific_journal-2747 1 35 scientific scientific ADJ american_scientific_journal-2747 1 36 research research NOUN american_scientific_journal-2747 1 37 and and CCONJ american_scientific_journal-2747 1 38 researchers researcher NOUN american_scientific_journal-2747 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ NOUN american_scientific_journal-2747 1 40 cryptanalysis cryptanalysis NOUN american_scientific_journal-2747 1 41 and and CCONJ american_scientific_journal-2747 1 42 modification modification NOUN american_scientific_journal-2747 1 43 of of ADP american_scientific_journal-2747 1 44 an an DET american_scientific_journal-2747 1 45 improved improve VERB american_scientific_journal-2747 1 46 selfcertified selfcertifie VERB american_scientific_journal-2747 1 47 digital digital ADJ american_scientific_journal-2747 1 48 signature signature NOUN american_scientific_journal-2747 1 49 scheme scheme NOUN american_scientific_journal-2747 1 50 with with ADP american_scientific_journal-2747 1 51 message message NOUN american_scientific_journal-2747 1 52 recovery recovery NOUN american_scientific_journal-2747 1 53 mahshid mahshid PROPN american_scientific_journal-2747 1 54 sadeghpour sadeghpour ADJ american_scientific_journal-2747 1 55 * * PROPN american_scientific_journal-2747 1 56 iran iran PROPN american_scientific_journal-2747 1 57 university university PROPN american_scientific_journal-2747 1 58 of of ADP american_scientific_journal-2747 1 59 science science NOUN american_scientific_journal-2747 1 60 and and CCONJ american_scientific_journal-2747 1 61 technology technology NOUN american_scientific_journal-2747 1 62 , , PUNCT american_scientific_journal-2747 1 63 tehran tehran PROPN american_scientific_journal-2747 1 64 , , PUNCT american_scientific_journal-2747 1 65 iran iran PROPN american_scientific_journal-2747 1 66 email email NOUN american_scientific_journal-2747 1 67 : : PUNCT american_scientific_journal-2747 1 68 m_sadeghpour@ieee.org m_sadeghpour@ieee.org NUM american_scientific_journal-2747 1 69 abstract abstract ADJ american_scientific_journal-2747 1 70 digital digital ADJ american_scientific_journal-2747 1 71 signature signature NOUN american_scientific_journal-2747 1 72 plays play VERB american_scientific_journal-2747 1 73 a a DET american_scientific_journal-2747 1 74 key key ADJ american_scientific_journal-2747 1 75 role role NOUN american_scientific_journal-2747 1 76 in in ADP american_scientific_journal-2747 1 77 bringing bring VERB american_scientific_journal-2747 1 78 authenticity authenticity NOUN american_scientific_journal-2747 1 79 to to ADP american_scientific_journal-2747 1 80 cryptographic cryptographic ADJ american_scientific_journal-2747 1 81 communications communication NOUN american_scientific_journal-2747 1 82 . . PUNCT american_scientific_journal-2747 2 1 a a DET american_scientific_journal-2747 2 2 signature signature NOUN american_scientific_journal-2747 2 3 scheme scheme NOUN american_scientific_journal-2747 2 4 with with ADP american_scientific_journal-2747 2 5 message message NOUN american_scientific_journal-2747 2 6 recovery recovery NOUN american_scientific_journal-2747 2 7 has have VERB american_scientific_journal-2747 2 8 two two NUM american_scientific_journal-2747 2 9 characteristics characteristic NOUN american_scientific_journal-2747 2 10 . . PUNCT american_scientific_journal-2747 3 1 the the DET american_scientific_journal-2747 3 2 public public ADJ american_scientific_journal-2747 3 3 key key NOUN american_scientific_journal-2747 3 4 of of ADP american_scientific_journal-2747 3 5 the the DET american_scientific_journal-2747 3 6 signer signer NOUN american_scientific_journal-2747 3 7 can can AUX american_scientific_journal-2747 3 8 be be AUX american_scientific_journal-2747 3 9 authenticated authenticate VERB american_scientific_journal-2747 3 10 while while SCONJ american_scientific_journal-2747 3 11 verifying verify VERB american_scientific_journal-2747 3 12 the the DET american_scientific_journal-2747 3 13 signature signature NOUN american_scientific_journal-2747 3 14 ; ; PUNCT american_scientific_journal-2747 3 15 and and CCONJ american_scientific_journal-2747 3 16 the the DET american_scientific_journal-2747 3 17 receiver receiver NOUN american_scientific_journal-2747 3 18 is be AUX american_scientific_journal-2747 3 19 able able ADJ american_scientific_journal-2747 3 20 to to PART american_scientific_journal-2747 3 21 obtain obtain VERB american_scientific_journal-2747 3 22 the the DET american_scientific_journal-2747 3 23 message message NOUN american_scientific_journal-2747 3 24 . . PUNCT american_scientific_journal-2747 4 1 in in ADP american_scientific_journal-2747 4 2 2013 2013 NUM american_scientific_journal-2747 4 3 , , PUNCT american_scientific_journal-2747 4 4 wu wu PROPN american_scientific_journal-2747 4 5 and and CCONJ american_scientific_journal-2747 4 6 xu xu PROPN american_scientific_journal-2747 4 7 presented present VERB american_scientific_journal-2747 4 8 a a DET american_scientific_journal-2747 4 9 self self NOUN american_scientific_journal-2747 4 10 - - PUNCT american_scientific_journal-2747 4 11 certified certify VERB american_scientific_journal-2747 4 12 digital digital ADJ american_scientific_journal-2747 4 13 signature signature NOUN american_scientific_journal-2747 4 14 scheme scheme NOUN american_scientific_journal-2747 4 15 with with ADP american_scientific_journal-2747 4 16 message message NOUN american_scientific_journal-2747 4 17 recovery recovery NOUN american_scientific_journal-2747 4 18 by by ADP american_scientific_journal-2747 4 19 combining combine VERB american_scientific_journal-2747 4 20 the the DET american_scientific_journal-2747 4 21 two two NUM american_scientific_journal-2747 4 22 concepts concept NOUN american_scientific_journal-2747 4 23 of of ADP american_scientific_journal-2747 4 24 digital digital ADJ american_scientific_journal-2747 4 25 signature signature NOUN american_scientific_journal-2747 4 26 with with ADP american_scientific_journal-2747 4 27 message message NOUN american_scientific_journal-2747 4 28 recovery recovery NOUN american_scientific_journal-2747 4 29 and and CCONJ american_scientific_journal-2747 4 30 self self NOUN american_scientific_journal-2747 4 31 - - PUNCT american_scientific_journal-2747 4 32 certified certify VERB american_scientific_journal-2747 4 33 public public ADJ american_scientific_journal-2747 4 34 key key NOUN american_scientific_journal-2747 4 35 . . PUNCT american_scientific_journal-2747 5 1 they they PRON american_scientific_journal-2747 5 2 also also ADV american_scientific_journal-2747 5 3 claimed claim VERB american_scientific_journal-2747 5 4 that that SCONJ american_scientific_journal-2747 5 5 their their PRON american_scientific_journal-2747 5 6 scheme scheme NOUN american_scientific_journal-2747 5 7 provides provide VERB american_scientific_journal-2747 5 8 provable provable ADJ american_scientific_journal-2747 5 9 security security NOUN american_scientific_journal-2747 5 10 against against ADP american_scientific_journal-2747 5 11 man man NOUN american_scientific_journal-2747 5 12 - - PUNCT american_scientific_journal-2747 5 13 in in ADP american_scientific_journal-2747 5 14 - - PUNCT american_scientific_journal-2747 5 15 the the DET american_scientific_journal-2747 5 16 - - PUNCT american_scientific_journal-2747 5 17 middle middle ADJ american_scientific_journal-2747 5 18 attack attack NOUN american_scientific_journal-2747 5 19 , , PUNCT american_scientific_journal-2747 5 20 forgery forgery NOUN american_scientific_journal-2747 5 21 attack attack NOUN american_scientific_journal-2747 5 22 , , PUNCT american_scientific_journal-2747 5 23 and and CCONJ american_scientific_journal-2747 5 24 message message NOUN american_scientific_journal-2747 5 25 leakage leakage NOUN american_scientific_journal-2747 5 26 . . PUNCT american_scientific_journal-2747 6 1 this this DET american_scientific_journal-2747 6 2 paper paper NOUN american_scientific_journal-2747 6 3 first first ADV american_scientific_journal-2747 6 4 reviews review VERB american_scientific_journal-2747 6 5 the the DET american_scientific_journal-2747 6 6 scheme scheme NOUN american_scientific_journal-2747 6 7 of of ADP american_scientific_journal-2747 6 8 wu wu PROPN american_scientific_journal-2747 6 9 and and CCONJ american_scientific_journal-2747 6 10 xu xu PROPN american_scientific_journal-2747 6 11 , , PUNCT american_scientific_journal-2747 6 12 and and CCONJ american_scientific_journal-2747 6 13 then then ADV american_scientific_journal-2747 6 14 presents present VERB american_scientific_journal-2747 6 15 an an DET american_scientific_journal-2747 6 16 insider insider NOUN american_scientific_journal-2747 6 17 forgery forgery NOUN american_scientific_journal-2747 6 18 attack attack NOUN american_scientific_journal-2747 6 19 to to ADP american_scientific_journal-2747 6 20 this this DET american_scientific_journal-2747 6 21 scheme scheme NOUN american_scientific_journal-2747 6 22 . . PUNCT american_scientific_journal-2747 7 1 it it PRON american_scientific_journal-2747 7 2 will will AUX american_scientific_journal-2747 7 3 be be AUX american_scientific_journal-2747 7 4 shown show VERB american_scientific_journal-2747 7 5 that that SCONJ american_scientific_journal-2747 7 6 this this DET american_scientific_journal-2747 7 7 scheme scheme NOUN american_scientific_journal-2747 7 8 is be AUX american_scientific_journal-2747 7 9 not not PART american_scientific_journal-2747 7 10 secure secure ADJ american_scientific_journal-2747 7 11 against against ADP american_scientific_journal-2747 7 12 insider insider NOUN american_scientific_journal-2747 7 13 forgery forgery NOUN american_scientific_journal-2747 7 14 attack attack NOUN american_scientific_journal-2747 7 15 . . PUNCT american_scientific_journal-2747 8 1 a a DET american_scientific_journal-2747 8 2 modification modification NOUN american_scientific_journal-2747 8 3 is be AUX american_scientific_journal-2747 8 4 proposed propose VERB american_scientific_journal-2747 8 5 in in ADP american_scientific_journal-2747 8 6 order order NOUN american_scientific_journal-2747 8 7 to to PART american_scientific_journal-2747 8 8 overcome overcome VERB american_scientific_journal-2747 8 9 this this DET american_scientific_journal-2747 8 10 weakness weakness NOUN american_scientific_journal-2747 8 11 . . PUNCT american_scientific_journal-2747 9 1 keywords keyword NOUN american_scientific_journal-2747 9 2 : : PUNCT american_scientific_journal-2747 9 3 authenticated authenticate VERB american_scientific_journal-2747 9 4 encryption encryption NOUN american_scientific_journal-2747 9 5 ; ; PUNCT american_scientific_journal-2747 9 6 digital digital ADJ american_scientific_journal-2747 9 7 signature signature NOUN american_scientific_journal-2747 9 8 ; ; PUNCT american_scientific_journal-2747 9 9 message message NOUN american_scientific_journal-2747 9 10 recovery recovery NOUN american_scientific_journal-2747 9 11 ; ; PUNCT american_scientific_journal-2747 9 12 self self NOUN american_scientific_journal-2747 9 13 - - PUNCT american_scientific_journal-2747 9 14 certified certify VERB american_scientific_journal-2747 9 15 public public ADJ american_scientific_journal-2747 9 16 key key NOUN american_scientific_journal-2747 9 17 . . PUNCT american_scientific_journal-2747 10 1 1 1 X american_scientific_journal-2747 10 2 . . X american_scientific_journal-2747 10 3 introduction introduction NOUN american_scientific_journal-2747 10 4 in in ADP american_scientific_journal-2747 10 5 cryptographic cryptographic ADJ american_scientific_journal-2747 10 6 cryptosystems cryptosystem NOUN american_scientific_journal-2747 10 7 , , PUNCT american_scientific_journal-2747 10 8 digital digital ADJ american_scientific_journal-2747 10 9 signature signature NOUN american_scientific_journal-2747 10 10 is be AUX american_scientific_journal-2747 10 11 of of ADP american_scientific_journal-2747 10 12 paramount paramount ADJ american_scientific_journal-2747 10 13 importance importance NOUN american_scientific_journal-2747 10 14 . . PUNCT american_scientific_journal-2747 11 1 it it PRON american_scientific_journal-2747 11 2 can can AUX american_scientific_journal-2747 11 3 provide provide VERB american_scientific_journal-2747 11 4 integrity integrity NOUN american_scientific_journal-2747 11 5 , , PUNCT american_scientific_journal-2747 11 6 authenticity authenticity NOUN american_scientific_journal-2747 11 7 , , PUNCT american_scientific_journal-2747 11 8 and and CCONJ american_scientific_journal-2747 11 9 non non NOUN american_scientific_journal-2747 11 10 - - NOUN american_scientific_journal-2747 11 11 repudiation repudiation NOUN american_scientific_journal-2747 11 12 . . PUNCT american_scientific_journal-2747 12 1 in in ADP american_scientific_journal-2747 12 2 public public ADJ american_scientific_journal-2747 12 3 key key ADJ american_scientific_journal-2747 12 4 cryptosystems cryptosystem NOUN american_scientific_journal-2747 12 5 , , PUNCT american_scientific_journal-2747 12 6 the the DET american_scientific_journal-2747 12 7 integrity integrity NOUN american_scientific_journal-2747 12 8 of of ADP american_scientific_journal-2747 12 9 the the DET american_scientific_journal-2747 12 10 public public ADJ american_scientific_journal-2747 12 11 keys key NOUN american_scientific_journal-2747 12 12 must must AUX american_scientific_journal-2747 12 13 be be AUX american_scientific_journal-2747 12 14 kept keep VERB american_scientific_journal-2747 12 15 . . PUNCT american_scientific_journal-2747 13 1 in in ADP american_scientific_journal-2747 13 2 classical classical ADJ american_scientific_journal-2747 13 3 digital digital ADJ american_scientific_journal-2747 13 4 signature signature NOUN american_scientific_journal-2747 13 5 schemes scheme NOUN american_scientific_journal-2747 13 6 , , PUNCT american_scientific_journal-2747 13 7 the the DET american_scientific_journal-2747 13 8 system system NOUN american_scientific_journal-2747 13 9 authority authority NOUN american_scientific_journal-2747 13 10 𝑺𝑺𝑺𝑺 𝑺𝑺𝑺𝑺 PROPN american_scientific_journal-2747 13 11 is be AUX american_scientific_journal-2747 13 12 used use VERB american_scientific_journal-2747 13 13 to to PART american_scientific_journal-2747 13 14 bind bind VERB american_scientific_journal-2747 13 15 users user NOUN american_scientific_journal-2747 13 16 to to ADP american_scientific_journal-2747 13 17 their their PRON american_scientific_journal-2747 13 18 own own ADJ american_scientific_journal-2747 13 19 public public ADJ american_scientific_journal-2747 13 20 keys key NOUN american_scientific_journal-2747 13 21 . . PUNCT american_scientific_journal-2747 14 1 however however ADV american_scientific_journal-2747 14 2 , , PUNCT american_scientific_journal-2747 14 3 the the DET american_scientific_journal-2747 14 4 management management NOUN american_scientific_journal-2747 14 5 of of ADP american_scientific_journal-2747 14 6 the the DET american_scientific_journal-2747 14 7 certificates certificate NOUN american_scientific_journal-2747 14 8 of of ADP american_scientific_journal-2747 14 9 public public ADJ american_scientific_journal-2747 14 10 keys key NOUN american_scientific_journal-2747 14 11 costs cost VERB american_scientific_journal-2747 14 12 a a DET american_scientific_journal-2747 14 13 lot lot NOUN american_scientific_journal-2747 14 14 . . PUNCT american_scientific_journal-2747 15 1 in in ADP american_scientific_journal-2747 15 2 1991 1991 NUM american_scientific_journal-2747 15 3 , , PUNCT american_scientific_journal-2747 15 4 girault girault VERB american_scientific_journal-2747 15 5 [ [ X american_scientific_journal-2747 15 6 1 1 X american_scientific_journal-2747 15 7 ] ] PUNCT american_scientific_journal-2747 15 8 introduced introduce VERB american_scientific_journal-2747 15 9 the the DET american_scientific_journal-2747 15 10 notion notion NOUN american_scientific_journal-2747 15 11 of of ADP american_scientific_journal-2747 15 12 self self NOUN american_scientific_journal-2747 15 13 - - PUNCT american_scientific_journal-2747 15 14 certified certify VERB american_scientific_journal-2747 15 15 public public ADJ american_scientific_journal-2747 15 16 key key ADJ american_scientific_journal-2747 15 17 cryptosystem cryptosystem NOUN american_scientific_journal-2747 15 18 . . PUNCT american_scientific_journal-2747 16 1 in in ADP american_scientific_journal-2747 16 2 his his PRON american_scientific_journal-2747 16 3 scheme scheme NOUN american_scientific_journal-2747 16 4 , , PUNCT american_scientific_journal-2747 16 5 the the DET american_scientific_journal-2747 16 6 features feature NOUN american_scientific_journal-2747 16 7 of of ADP american_scientific_journal-2747 16 8 discrete discrete ADJ american_scientific_journal-2747 16 9 logarithm logarithm NOUN american_scientific_journal-2747 16 10 problem problem NOUN american_scientific_journal-2747 16 11 and and CCONJ american_scientific_journal-2747 16 12 factoring factoring NOUN american_scientific_journal-2747 16 13 problem problem NOUN american_scientific_journal-2747 16 14 are be AUX american_scientific_journal-2747 16 15 combined combine VERB american_scientific_journal-2747 16 16 . . PUNCT american_scientific_journal-2747 17 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-2747 18 1 * * PUNCT american_scientific_journal-2747 18 2 corresponding correspond VERB american_scientific_journal-2747 18 3 author author NOUN american_scientific_journal-2747 18 4 . . PUNCT american_scientific_journal-2747 19 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-2747 19 2 american american PROPN american_scientific_journal-2747 19 3 scientific scientific PROPN american_scientific_journal-2747 19 4 research research NOUN american_scientific_journal-2747 19 5 journal journal NOUN american_scientific_journal-2747 19 6 for for ADP american_scientific_journal-2747 19 7 engineering engineering NOUN american_scientific_journal-2747 19 8 , , PUNCT american_scientific_journal-2747 19 9 technology technology NOUN american_scientific_journal-2747 19 10 , , PUNCT american_scientific_journal-2747 19 11 and and CCONJ american_scientific_journal-2747 19 12 sciences science NOUN american_scientific_journal-2747 19 13 ( ( PUNCT american_scientific_journal-2747 19 14 asrjets asrjet NOUN american_scientific_journal-2747 19 15 ) ) PUNCT american_scientific_journal-2747 19 16 ( ( PUNCT american_scientific_journal-2747 19 17 2017 2017 NUM american_scientific_journal-2747 19 18 ) ) PUNCT american_scientific_journal-2747 19 19 volume volume NOUN american_scientific_journal-2747 19 20 28 28 NUM american_scientific_journal-2747 19 21 , , PUNCT american_scientific_journal-2747 19 22 no no DET american_scientific_journal-2747 19 23 1 1 NUM american_scientific_journal-2747 19 24 , , PUNCT american_scientific_journal-2747 19 25 pp pp ADV american_scientific_journal-2747 19 26 257 257 NUM american_scientific_journal-2747 19 27 - - SYM american_scientific_journal-2747 19 28 265 265 NUM american_scientific_journal-2747 19 29 258 258 NUM american_scientific_journal-2747 19 30 each each DET american_scientific_journal-2747 19 31 user user NOUN american_scientific_journal-2747 19 32 is be AUX american_scientific_journal-2747 19 33 able able ADJ american_scientific_journal-2747 19 34 to to PART american_scientific_journal-2747 19 35 choose choose VERB american_scientific_journal-2747 19 36 his his PRON american_scientific_journal-2747 19 37 own own ADJ american_scientific_journal-2747 19 38 private private ADJ american_scientific_journal-2747 19 39 key key NOUN american_scientific_journal-2747 19 40 , , PUNCT american_scientific_journal-2747 19 41 and and CCONJ american_scientific_journal-2747 19 42 the the DET american_scientific_journal-2747 19 43 user user NOUN american_scientific_journal-2747 19 44 ’s ’s PART american_scientific_journal-2747 19 45 public public ADJ american_scientific_journal-2747 19 46 key key NOUN american_scientific_journal-2747 19 47 is be AUX american_scientific_journal-2747 19 48 derived derive VERB american_scientific_journal-2747 19 49 from from ADP american_scientific_journal-2747 19 50 user user NOUN american_scientific_journal-2747 19 51 ’s ’s PART american_scientific_journal-2747 19 52 identity identity NOUN american_scientific_journal-2747 19 53 and and CCONJ american_scientific_journal-2747 19 54 his his PRON american_scientific_journal-2747 19 55 own own ADJ american_scientific_journal-2747 19 56 private private ADJ american_scientific_journal-2747 19 57 key key NOUN american_scientific_journal-2747 19 58 . . PUNCT american_scientific_journal-2747 20 1 in in ADP american_scientific_journal-2747 20 2 this this DET american_scientific_journal-2747 20 3 kind kind NOUN american_scientific_journal-2747 20 4 of of ADP american_scientific_journal-2747 20 5 cryptosystem cryptosystem NOUN american_scientific_journal-2747 20 6 , , PUNCT american_scientific_journal-2747 20 7 the the DET american_scientific_journal-2747 20 8 user user NOUN american_scientific_journal-2747 20 9 ’s ’s PART american_scientific_journal-2747 20 10 public public ADJ american_scientific_journal-2747 20 11 key key NOUN american_scientific_journal-2747 20 12 is be AUX american_scientific_journal-2747 20 13 generated generate VERB american_scientific_journal-2747 20 14 by by ADP american_scientific_journal-2747 20 15 𝑺𝑺𝑺𝑺 𝑺𝑺𝑺𝑺 PROPN american_scientific_journal-2747 20 16 whereas whereas SCONJ american_scientific_journal-2747 20 17 his his PRON american_scientific_journal-2747 20 18 private private ADJ american_scientific_journal-2747 20 19 key key NOUN american_scientific_journal-2747 20 20 is be AUX american_scientific_journal-2747 20 21 only only ADV american_scientific_journal-2747 20 22 known know VERB american_scientific_journal-2747 20 23 by by ADP american_scientific_journal-2747 20 24 user user NOUN american_scientific_journal-2747 20 25 himself himself PRON american_scientific_journal-2747 20 26 . . PUNCT american_scientific_journal-2747 21 1 the the DET american_scientific_journal-2747 21 2 user user NOUN american_scientific_journal-2747 21 3 ’s ’s PART american_scientific_journal-2747 21 4 public public ADJ american_scientific_journal-2747 21 5 key key NOUN american_scientific_journal-2747 21 6 and and CCONJ american_scientific_journal-2747 21 7 identity identity NOUN american_scientific_journal-2747 21 8 can can AUX american_scientific_journal-2747 21 9 be be AUX american_scientific_journal-2747 21 10 verified verify VERB american_scientific_journal-2747 21 11 implicitly implicitly ADV american_scientific_journal-2747 21 12 in in ADP american_scientific_journal-2747 21 13 self self NOUN american_scientific_journal-2747 21 14 - - PUNCT american_scientific_journal-2747 21 15 certified certify VERB american_scientific_journal-2747 21 16 public public ADJ american_scientific_journal-2747 21 17 key key ADJ american_scientific_journal-2747 21 18 cryptosystems cryptosystem NOUN american_scientific_journal-2747 21 19 . . PUNCT american_scientific_journal-2747 22 1 in in ADP american_scientific_journal-2747 22 2 1994 1994 NUM american_scientific_journal-2747 22 3 , , PUNCT american_scientific_journal-2747 22 4 neyberg neyberg NOUN american_scientific_journal-2747 22 5 and and CCONJ american_scientific_journal-2747 22 6 ruppel ruppel VERB american_scientific_journal-2747 22 7 [ [ X american_scientific_journal-2747 22 8 2 2 NUM american_scientific_journal-2747 22 9 ] ] PUNCT american_scientific_journal-2747 22 10 introduced introduce VERB american_scientific_journal-2747 22 11 a a DET american_scientific_journal-2747 22 12 novel novel ADJ american_scientific_journal-2747 22 13 digital digital ADJ american_scientific_journal-2747 22 14 signature signature NOUN american_scientific_journal-2747 22 15 scheme scheme NOUN american_scientific_journal-2747 22 16 that that PRON american_scientific_journal-2747 22 17 provides provide VERB american_scientific_journal-2747 22 18 the the DET american_scientific_journal-2747 22 19 property property NOUN american_scientific_journal-2747 22 20 of of ADP american_scientific_journal-2747 22 21 message message NOUN american_scientific_journal-2747 22 22 recovery recovery NOUN american_scientific_journal-2747 22 23 based base VERB american_scientific_journal-2747 22 24 on on ADP american_scientific_journal-2747 22 25 discrete discrete ADJ american_scientific_journal-2747 22 26 logarithm logarithm NOUN american_scientific_journal-2747 22 27 problem problem NOUN american_scientific_journal-2747 22 28 . . PUNCT american_scientific_journal-2747 23 1 later later ADV american_scientific_journal-2747 23 2 , , PUNCT american_scientific_journal-2747 23 3 at at ADP american_scientific_journal-2747 23 4 the the DET american_scientific_journal-2747 23 5 same same ADJ american_scientific_journal-2747 23 6 year year NOUN american_scientific_journal-2747 23 7 , , PUNCT american_scientific_journal-2747 23 8 horster horster NOUN american_scientific_journal-2747 23 9 and and CCONJ american_scientific_journal-2747 23 10 his his PRON american_scientific_journal-2747 23 11 colleagues colleague NOUN american_scientific_journal-2747 23 12 [ [ X american_scientific_journal-2747 23 13 3 3 X american_scientific_journal-2747 23 14 ] ] PUNCT american_scientific_journal-2747 23 15 proposed propose VERB american_scientific_journal-2747 23 16 a a DET american_scientific_journal-2747 23 17 modification modification NOUN american_scientific_journal-2747 23 18 of of ADP american_scientific_journal-2747 23 19 the the DET american_scientific_journal-2747 23 20 scheme scheme NOUN american_scientific_journal-2747 23 21 of of ADP american_scientific_journal-2747 23 22 neyberg neyberg NOUN american_scientific_journal-2747 23 23 and and CCONJ american_scientific_journal-2747 23 24 ruppel ruppel VERB american_scientific_journal-2747 23 25 and and CCONJ american_scientific_journal-2747 23 26 called call VERB american_scientific_journal-2747 23 27 it it PRON american_scientific_journal-2747 23 28 authenticated authenticate VERB american_scientific_journal-2747 23 29 encryption encryption NOUN american_scientific_journal-2747 23 30 scheme scheme NOUN american_scientific_journal-2747 23 31 . . PUNCT american_scientific_journal-2747 24 1 based base VERB american_scientific_journal-2747 24 2 on on ADP american_scientific_journal-2747 24 3 horster horster NOUN american_scientific_journal-2747 24 4 and and CCONJ american_scientific_journal-2747 24 5 his his PRON american_scientific_journal-2747 24 6 colleagues colleague NOUN american_scientific_journal-2747 24 7 ’ ' PUNCT american_scientific_journal-2747 24 8 scheme scheme NOUN american_scientific_journal-2747 24 9 , , PUNCT american_scientific_journal-2747 24 10 in in ADP american_scientific_journal-2747 24 11 2003 2003 NUM american_scientific_journal-2747 24 12 , , PUNCT american_scientific_journal-2747 24 13 tseng tseng PROPN american_scientific_journal-2747 24 14 and and CCONJ american_scientific_journal-2747 24 15 his his PRON american_scientific_journal-2747 24 16 colleagues colleague NOUN american_scientific_journal-2747 24 17 [ [ X american_scientific_journal-2747 24 18 4 4 X american_scientific_journal-2747 24 19 ] ] PUNCT american_scientific_journal-2747 24 20 designed design VERB american_scientific_journal-2747 24 21 an an DET american_scientific_journal-2747 24 22 authenticated authenticate VERB american_scientific_journal-2747 24 23 encryption encryption NOUN american_scientific_journal-2747 24 24 scheme scheme NOUN american_scientific_journal-2747 24 25 . . PUNCT american_scientific_journal-2747 25 1 they they PRON american_scientific_journal-2747 25 2 also also ADV american_scientific_journal-2747 25 3 introduced introduce VERB american_scientific_journal-2747 25 4 two two NUM american_scientific_journal-2747 25 5 variants variant NOUN american_scientific_journal-2747 25 6 of of ADP american_scientific_journal-2747 25 7 their their PRON american_scientific_journal-2747 25 8 scheme scheme NOUN american_scientific_journal-2747 25 9 . . PUNCT american_scientific_journal-2747 26 1 in in ADP american_scientific_journal-2747 26 2 2004 2004 NUM american_scientific_journal-2747 26 3 , , PUNCT american_scientific_journal-2747 26 4 shao shao PROPN american_scientific_journal-2747 26 5 [ [ X american_scientific_journal-2747 26 6 5 5 NUM american_scientific_journal-2747 26 7 ] ] PUNCT american_scientific_journal-2747 26 8 demonstrated demonstrate VERB american_scientific_journal-2747 26 9 that that SCONJ american_scientific_journal-2747 26 10 their their PRON american_scientific_journal-2747 26 11 scheme scheme NOUN american_scientific_journal-2747 26 12 is be AUX american_scientific_journal-2747 26 13 insecure insecure ADJ american_scientific_journal-2747 26 14 against against ADP american_scientific_journal-2747 26 15 insider insider NOUN american_scientific_journal-2747 26 16 forgery forgery NOUN american_scientific_journal-2747 26 17 attack attack NOUN american_scientific_journal-2747 26 18 , , PUNCT american_scientific_journal-2747 26 19 and and CCONJ american_scientific_journal-2747 26 20 proposed propose VERB american_scientific_journal-2747 26 21 an an DET american_scientific_journal-2747 26 22 improvement improvement NOUN american_scientific_journal-2747 26 23 of of ADP american_scientific_journal-2747 26 24 their their PRON american_scientific_journal-2747 26 25 scheme scheme NOUN american_scientific_journal-2747 26 26 . . PUNCT american_scientific_journal-2747 27 1 however however ADV american_scientific_journal-2747 27 2 , , PUNCT american_scientific_journal-2747 27 3 chen chen PROPN american_scientific_journal-2747 27 4 and and CCONJ american_scientific_journal-2747 27 5 jan jan PROPN american_scientific_journal-2747 28 1 [ [ X american_scientific_journal-2747 28 2 6 6 NUM american_scientific_journal-2747 28 3 ] ] PUNCT american_scientific_journal-2747 28 4 showed show VERB american_scientific_journal-2747 28 5 that that SCONJ american_scientific_journal-2747 28 6 the the DET american_scientific_journal-2747 28 7 scheme scheme NOUN american_scientific_journal-2747 28 8 of of ADP american_scientific_journal-2747 28 9 shao shao PROPN american_scientific_journal-2747 28 10 is be AUX american_scientific_journal-2747 28 11 still still ADV american_scientific_journal-2747 28 12 not not PART american_scientific_journal-2747 28 13 secure secure ADJ american_scientific_journal-2747 28 14 against against ADP american_scientific_journal-2747 28 15 insider insider NOUN american_scientific_journal-2747 28 16 forgery forgery NOUN american_scientific_journal-2747 28 17 attack attack NOUN american_scientific_journal-2747 28 18 . . PUNCT american_scientific_journal-2747 29 1 in in ADP american_scientific_journal-2747 29 2 2005 2005 NUM american_scientific_journal-2747 29 3 , , PUNCT american_scientific_journal-2747 29 4 chang chang PROPN american_scientific_journal-2747 29 5 and and CCONJ american_scientific_journal-2747 29 6 his his PRON american_scientific_journal-2747 29 7 colleagues colleague NOUN american_scientific_journal-2747 30 1 [ [ X american_scientific_journal-2747 30 2 7 7 X american_scientific_journal-2747 30 3 ] ] PUNCT american_scientific_journal-2747 30 4 proved prove VERB american_scientific_journal-2747 30 5 that that SCONJ american_scientific_journal-2747 30 6 the the DET american_scientific_journal-2747 30 7 scheme scheme NOUN american_scientific_journal-2747 30 8 of of ADP american_scientific_journal-2747 30 9 tseng tseng PROPN american_scientific_journal-2747 30 10 and and CCONJ american_scientific_journal-2747 30 11 his his PRON american_scientific_journal-2747 30 12 colleagues colleague NOUN american_scientific_journal-2747 30 13 can can AUX american_scientific_journal-2747 30 14 not not PART american_scientific_journal-2747 30 15 resist resist VERB american_scientific_journal-2747 30 16 𝑺𝑺𝑺𝑺 𝑺𝑺𝑺𝑺 PROPN american_scientific_journal-2747 30 17 ’s ’s PART american_scientific_journal-2747 30 18 forgery forgery NOUN american_scientific_journal-2747 30 19 attack attack NOUN american_scientific_journal-2747 30 20 . . PUNCT american_scientific_journal-2747 31 1 they they PRON american_scientific_journal-2747 31 2 also also ADV american_scientific_journal-2747 31 3 designed design VERB american_scientific_journal-2747 31 4 an an DET american_scientific_journal-2747 31 5 improvement improvement NOUN american_scientific_journal-2747 31 6 to to PART american_scientific_journal-2747 31 7 overcome overcome VERB american_scientific_journal-2747 31 8 this this DET american_scientific_journal-2747 31 9 flaw flaw NOUN american_scientific_journal-2747 31 10 . . PUNCT american_scientific_journal-2747 32 1 however however ADV american_scientific_journal-2747 32 2 , , PUNCT american_scientific_journal-2747 32 3 in in ADP american_scientific_journal-2747 32 4 2006 2006 NUM american_scientific_journal-2747 32 5 , , PUNCT american_scientific_journal-2747 32 6 yoon yoon PROPN american_scientific_journal-2747 32 7 and and CCONJ american_scientific_journal-2747 32 8 yoo yoo PROPN american_scientific_journal-2747 33 1 [ [ X american_scientific_journal-2747 33 2 8 8 NUM american_scientific_journal-2747 33 3 ] ] PUNCT american_scientific_journal-2747 33 4 showed show VERB american_scientific_journal-2747 33 5 that that SCONJ american_scientific_journal-2747 33 6 their their PRON american_scientific_journal-2747 33 7 proposed propose VERB american_scientific_journal-2747 33 8 improvement improvement NOUN american_scientific_journal-2747 33 9 is be AUX american_scientific_journal-2747 33 10 vulnerable vulnerable ADJ american_scientific_journal-2747 33 11 to to ADP american_scientific_journal-2747 33 12 known know VERB american_scientific_journal-2747 33 13 plaintext plaintext NOUN american_scientific_journal-2747 33 14 - - PUNCT american_scientific_journal-2747 33 15 ciphertext ciphertext NOUN american_scientific_journal-2747 33 16 attack attack NOUN american_scientific_journal-2747 33 17 . . PUNCT american_scientific_journal-2747 34 1 in in ADP american_scientific_journal-2747 34 2 their their PRON american_scientific_journal-2747 34 3 paper paper NOUN american_scientific_journal-2747 34 4 , , PUNCT american_scientific_journal-2747 34 5 they they PRON american_scientific_journal-2747 34 6 introduced introduce VERB american_scientific_journal-2747 34 7 a a DET american_scientific_journal-2747 34 8 new new ADJ american_scientific_journal-2747 34 9 signature signature NOUN american_scientific_journal-2747 34 10 scheme scheme NOUN american_scientific_journal-2747 34 11 which which PRON american_scientific_journal-2747 34 12 could could AUX american_scientific_journal-2747 34 13 resist resist VERB american_scientific_journal-2747 34 14 the the DET american_scientific_journal-2747 34 15 known know VERB american_scientific_journal-2747 34 16 plaintext plaintext NOUN american_scientific_journal-2747 34 17 - - PUNCT american_scientific_journal-2747 34 18 ciphertext ciphertext NOUN american_scientific_journal-2747 34 19 attack attack NOUN american_scientific_journal-2747 34 20 . . PUNCT american_scientific_journal-2747 35 1 in in ADP american_scientific_journal-2747 35 2 2013 2013 NUM american_scientific_journal-2747 35 3 , , PUNCT american_scientific_journal-2747 35 4 wu wu PROPN american_scientific_journal-2747 35 5 and and CCONJ american_scientific_journal-2747 35 6 xu xu PROPN american_scientific_journal-2747 36 1 [ [ X american_scientific_journal-2747 36 2 9 9 NUM american_scientific_journal-2747 36 3 ] ] PUNCT american_scientific_journal-2747 36 4 pointed point VERB american_scientific_journal-2747 36 5 out out ADP american_scientific_journal-2747 36 6 that that SCONJ american_scientific_journal-2747 36 7 the the DET american_scientific_journal-2747 36 8 scheme scheme NOUN american_scientific_journal-2747 36 9 of of ADP american_scientific_journal-2747 36 10 yoon yoon PROPN american_scientific_journal-2747 36 11 and and CCONJ american_scientific_journal-2747 36 12 his his PRON american_scientific_journal-2747 36 13 colleague colleague NOUN american_scientific_journal-2747 36 14 is be AUX american_scientific_journal-2747 36 15 vulnerable vulnerable ADJ american_scientific_journal-2747 36 16 to to ADP american_scientific_journal-2747 36 17 man man NOUN american_scientific_journal-2747 36 18 - - PUNCT american_scientific_journal-2747 36 19 in in ADP american_scientific_journal-2747 36 20 - - PUNCT american_scientific_journal-2747 36 21 the the DET american_scientific_journal-2747 36 22 - - PUNCT american_scientific_journal-2747 36 23 middle middle ADJ american_scientific_journal-2747 36 24 attack attack NOUN american_scientific_journal-2747 36 25 . . PUNCT american_scientific_journal-2747 37 1 they they PRON american_scientific_journal-2747 37 2 also also ADV american_scientific_journal-2747 37 3 proposed propose VERB american_scientific_journal-2747 37 4 a a DET american_scientific_journal-2747 37 5 new new ADJ american_scientific_journal-2747 37 6 self self NOUN american_scientific_journal-2747 37 7 - - PUNCT american_scientific_journal-2747 37 8 certified certify VERB american_scientific_journal-2747 37 9 digital digital ADJ american_scientific_journal-2747 37 10 signature signature NOUN american_scientific_journal-2747 37 11 scheme scheme NOUN american_scientific_journal-2747 37 12 with with ADP american_scientific_journal-2747 37 13 message message NOUN american_scientific_journal-2747 37 14 recovery recovery NOUN american_scientific_journal-2747 37 15 , , PUNCT american_scientific_journal-2747 37 16 and and CCONJ american_scientific_journal-2747 37 17 provided provide VERB american_scientific_journal-2747 37 18 its its PRON american_scientific_journal-2747 37 19 provable provable ADJ american_scientific_journal-2747 37 20 security security NOUN american_scientific_journal-2747 37 21 in in ADP american_scientific_journal-2747 37 22 eight eight NUM american_scientific_journal-2747 37 23 aspects aspect NOUN american_scientific_journal-2747 37 24 . . PUNCT american_scientific_journal-2747 38 1 in in ADP american_scientific_journal-2747 38 2 this this DET american_scientific_journal-2747 38 3 paper paper NOUN american_scientific_journal-2747 38 4 , , PUNCT american_scientific_journal-2747 38 5 it it PRON american_scientific_journal-2747 38 6 will will AUX american_scientific_journal-2747 38 7 be be AUX american_scientific_journal-2747 38 8 demonstrated demonstrate VERB american_scientific_journal-2747 38 9 that that SCONJ american_scientific_journal-2747 38 10 the the DET american_scientific_journal-2747 38 11 scheme scheme NOUN american_scientific_journal-2747 38 12 of of ADP american_scientific_journal-2747 38 13 wu wu PROPN american_scientific_journal-2747 38 14 and and CCONJ american_scientific_journal-2747 38 15 xu xu PROPN american_scientific_journal-2747 38 16 is be AUX american_scientific_journal-2747 38 17 vulnerable vulnerable ADJ american_scientific_journal-2747 38 18 to to ADP american_scientific_journal-2747 38 19 insider insider NOUN american_scientific_journal-2747 38 20 forgery forgery NOUN american_scientific_journal-2747 38 21 attack attack NOUN american_scientific_journal-2747 38 22 , , PUNCT american_scientific_journal-2747 38 23 and and CCONJ american_scientific_journal-2747 38 24 the the DET american_scientific_journal-2747 38 25 specified specify VERB american_scientific_journal-2747 38 26 verifier verifier NOUN american_scientific_journal-2747 38 27 is be AUX american_scientific_journal-2747 38 28 able able ADJ american_scientific_journal-2747 38 29 to to PART american_scientific_journal-2747 38 30 forge forge VERB american_scientific_journal-2747 38 31 the the DET american_scientific_journal-2747 38 32 signature signature NOUN american_scientific_journal-2747 38 33 if if SCONJ american_scientific_journal-2747 38 34 another another DET american_scientific_journal-2747 38 35 verifier verifier NOUN american_scientific_journal-2747 38 36 fully fully ADV american_scientific_journal-2747 38 37 collaborates collaborate VERB american_scientific_journal-2747 38 38 with with ADP american_scientific_journal-2747 38 39 him he PRON american_scientific_journal-2747 38 40 , , PUNCT american_scientific_journal-2747 38 41 in in ADP american_scientific_journal-2747 38 42 terms term NOUN american_scientific_journal-2747 38 43 of of ADP american_scientific_journal-2747 38 44 providing provide VERB american_scientific_journal-2747 38 45 the the DET american_scientific_journal-2747 38 46 specified specified ADJ american_scientific_journal-2747 38 47 receiver receiver NOUN american_scientific_journal-2747 38 48 with with ADP american_scientific_journal-2747 38 49 his his PRON american_scientific_journal-2747 38 50 own own ADJ american_scientific_journal-2747 38 51 private private ADJ american_scientific_journal-2747 38 52 key key NOUN american_scientific_journal-2747 38 53 . . PUNCT american_scientific_journal-2747 39 1 the the DET american_scientific_journal-2747 39 2 rest rest NOUN american_scientific_journal-2747 39 3 of of ADP american_scientific_journal-2747 39 4 the the DET american_scientific_journal-2747 39 5 paper paper NOUN american_scientific_journal-2747 39 6 is be AUX american_scientific_journal-2747 39 7 organized organize VERB american_scientific_journal-2747 39 8 as as SCONJ american_scientific_journal-2747 39 9 follows follow VERB american_scientific_journal-2747 39 10 . . PUNCT american_scientific_journal-2747 40 1 section section NOUN american_scientific_journal-2747 40 2 2 2 NUM american_scientific_journal-2747 40 3 is be AUX american_scientific_journal-2747 40 4 the the DET american_scientific_journal-2747 40 5 review review NOUN american_scientific_journal-2747 40 6 of of ADP american_scientific_journal-2747 40 7 the the DET american_scientific_journal-2747 40 8 scheme scheme NOUN american_scientific_journal-2747 40 9 of of ADP american_scientific_journal-2747 40 10 wu wu PROPN american_scientific_journal-2747 40 11 and and CCONJ american_scientific_journal-2747 40 12 xu xu PROPN american_scientific_journal-2747 40 13 . . PUNCT american_scientific_journal-2747 41 1 in in ADP american_scientific_journal-2747 41 2 section section NOUN american_scientific_journal-2747 41 3 3 3 NUM american_scientific_journal-2747 41 4 , , PUNCT american_scientific_journal-2747 41 5 it it PRON american_scientific_journal-2747 41 6 will will AUX american_scientific_journal-2747 41 7 be be AUX american_scientific_journal-2747 41 8 shown show VERB american_scientific_journal-2747 41 9 that that SCONJ american_scientific_journal-2747 41 10 this this DET american_scientific_journal-2747 41 11 scheme scheme NOUN american_scientific_journal-2747 41 12 is be AUX american_scientific_journal-2747 41 13 insecure insecure ADJ american_scientific_journal-2747 41 14 against against ADP american_scientific_journal-2747 41 15 insider insider NOUN american_scientific_journal-2747 41 16 forgery forgery NOUN american_scientific_journal-2747 41 17 attack attack NOUN american_scientific_journal-2747 41 18 . . PUNCT american_scientific_journal-2747 42 1 section section NOUN american_scientific_journal-2747 42 2 4 4 NUM american_scientific_journal-2747 42 3 is be AUX american_scientific_journal-2747 42 4 the the DET american_scientific_journal-2747 42 5 modification modification NOUN american_scientific_journal-2747 42 6 of of ADP american_scientific_journal-2747 42 7 the the DET american_scientific_journal-2747 42 8 scheme scheme NOUN american_scientific_journal-2747 42 9 of of ADP american_scientific_journal-2747 42 10 wu wu PROPN american_scientific_journal-2747 42 11 ad ad PROPN american_scientific_journal-2747 42 12 xu xu PROPN american_scientific_journal-2747 42 13 . . PUNCT american_scientific_journal-2747 43 1 finally finally ADV american_scientific_journal-2747 43 2 , , PUNCT american_scientific_journal-2747 43 3 the the DET american_scientific_journal-2747 43 4 conclusion conclusion NOUN american_scientific_journal-2747 43 5 is be AUX american_scientific_journal-2747 43 6 given give VERB american_scientific_journal-2747 43 7 in in ADP american_scientific_journal-2747 43 8 section section NOUN american_scientific_journal-2747 43 9 5 5 NUM american_scientific_journal-2747 43 10 . . NOUN american_scientific_journal-2747 43 11 2 2 NUM american_scientific_journal-2747 43 12 . . PUNCT american_scientific_journal-2747 44 1 the the DET american_scientific_journal-2747 44 2 scheme scheme NOUN american_scientific_journal-2747 44 3 of of ADP american_scientific_journal-2747 44 4 wu wu PROPN american_scientific_journal-2747 44 5 and and CCONJ american_scientific_journal-2747 44 6 xu xu PROPN american_scientific_journal-2747 45 1 this this DET american_scientific_journal-2747 45 2 scheme scheme NOUN american_scientific_journal-2747 45 3 consists consist VERB american_scientific_journal-2747 45 4 of of ADP american_scientific_journal-2747 45 5 four four NUM american_scientific_journal-2747 45 6 phases phase NOUN american_scientific_journal-2747 45 7 : : PUNCT american_scientific_journal-2747 45 8 system system NOUN american_scientific_journal-2747 45 9 initialization initialization NOUN american_scientific_journal-2747 45 10 phase phase NOUN american_scientific_journal-2747 45 11 , , PUNCT american_scientific_journal-2747 45 12 signature signature NOUN american_scientific_journal-2747 45 13 generation generation NOUN american_scientific_journal-2747 45 14 phase phase NOUN american_scientific_journal-2747 45 15 , , PUNCT american_scientific_journal-2747 45 16 message message NOUN american_scientific_journal-2747 45 17 recovery recovery NOUN american_scientific_journal-2747 45 18 phase phase NOUN american_scientific_journal-2747 45 19 , , PUNCT american_scientific_journal-2747 45 20 and and CCONJ american_scientific_journal-2747 45 21 signature signature NOUN american_scientific_journal-2747 45 22 conversion conversion NOUN american_scientific_journal-2747 45 23 phase phase NOUN american_scientific_journal-2747 45 24 . . PUNCT american_scientific_journal-2747 46 1 the the DET american_scientific_journal-2747 46 2 process process NOUN american_scientific_journal-2747 46 3 of of ADP american_scientific_journal-2747 46 4 the the DET american_scientific_journal-2747 46 5 signature signature NOUN american_scientific_journal-2747 46 6 is be AUX american_scientific_journal-2747 46 7 given give VERB american_scientific_journal-2747 46 8 in in ADP american_scientific_journal-2747 46 9 figure figure NOUN american_scientific_journal-2747 46 10 1 1 NUM american_scientific_journal-2747 46 11 . . ADP american_scientific_journal-2747 46 12 2.1 2.1 NUM american_scientific_journal-2747 46 13 . . PUNCT american_scientific_journal-2747 46 14 system system NOUN american_scientific_journal-2747 46 15 initialization initialization NOUN american_scientific_journal-2747 46 16 phase phase NOUN american_scientific_journal-2747 46 17 in in ADP american_scientific_journal-2747 46 18 the the DET american_scientific_journal-2747 46 19 system system NOUN american_scientific_journal-2747 46 20 initialization initialization NOUN american_scientific_journal-2747 46 21 phase phase NOUN american_scientific_journal-2747 46 22 , , PUNCT american_scientific_journal-2747 46 23 there there PRON american_scientific_journal-2747 46 24 exists exist VERB american_scientific_journal-2747 46 25 a a DET american_scientific_journal-2747 46 26 system system NOUN american_scientific_journal-2747 46 27 authority authority NOUN american_scientific_journal-2747 46 28 ( ( PUNCT american_scientific_journal-2747 46 29 𝑺𝑺𝑺𝑺 𝑺𝑺𝑺𝑺 PROPN american_scientific_journal-2747 46 30 ) ) PUNCT american_scientific_journal-2747 46 31 that that PRON american_scientific_journal-2747 46 32 is be AUX american_scientific_journal-2747 46 33 responsible responsible ADJ american_scientific_journal-2747 46 34 for for ADP american_scientific_journal-2747 46 35 generating generate VERB american_scientific_journal-2747 46 36 system system NOUN american_scientific_journal-2747 46 37 parameters parameter NOUN american_scientific_journal-2747 46 38 . . PUNCT american_scientific_journal-2747 47 1 𝑺𝑺𝑺𝑺 𝑺𝑺𝑺𝑺 PROPN american_scientific_journal-2747 47 2 first first ADV american_scientific_journal-2747 47 3 chooses choose VERB american_scientific_journal-2747 47 4 two two NUM american_scientific_journal-2747 47 5 large large ADJ american_scientific_journal-2747 47 6 primes prime NOUN american_scientific_journal-2747 47 7 𝒑𝒑 𝒑𝒑 NOUN american_scientific_journal-2747 48 1 and and CCONJ american_scientific_journal-2747 48 2 𝒒𝒒 𝒒𝒒 NOUN american_scientific_journal-2747 48 3 of of ADP american_scientific_journal-2747 48 4 almost almost ADV american_scientific_journal-2747 48 5 the the DET american_scientific_journal-2747 48 6 same same ADJ american_scientific_journal-2747 48 7 size size NOUN american_scientific_journal-2747 49 1 such such ADJ american_scientific_journal-2747 49 2 that that SCONJ american_scientific_journal-2747 49 3 𝒑𝒑 𝒑𝒑 PROPN american_scientific_journal-2747 49 4 = = SYM american_scientific_journal-2747 49 5 πŸπŸπ’‘π’‘β€² πŸπŸπ’‘π’‘β€² PROPN american_scientific_journal-2747 50 1 + + CCONJ american_scientific_journal-2747 50 2 𝟏𝟏 𝟏𝟏 NUM american_scientific_journal-2747 50 3 and and CCONJ american_scientific_journal-2747 50 4 𝒒𝒒 𝒒𝒒 NOUN american_scientific_journal-2747 51 1 = = PUNCT american_scientific_journal-2747 51 2 πŸπŸπ’’π’’β€² πŸπŸπ’’π’’β€² PROPN american_scientific_journal-2747 52 1 + + CCONJ american_scientific_journal-2747 52 2 𝟏𝟏 𝟏𝟏 NUM american_scientific_journal-2747 52 3 , , PUNCT american_scientific_journal-2747 52 4 where where SCONJ american_scientific_journal-2747 52 5 𝐩𝐩′ 𝐩𝐩′ PRON american_scientific_journal-2747 52 6 and and CCONJ american_scientific_journal-2747 52 7 𝒒𝒒′ 𝒒𝒒′ NUM american_scientific_journal-2747 52 8 are be AUX american_scientific_journal-2747 52 9 also also ADV american_scientific_journal-2747 52 10 primes prime NOUN american_scientific_journal-2747 52 11 . . PUNCT american_scientific_journal-2747 53 1 then then ADV american_scientific_journal-2747 53 2 , , PUNCT american_scientific_journal-2747 53 3 he he PRON american_scientific_journal-2747 53 4 computes compute VERB american_scientific_journal-2747 53 5 𝑡𝑡 𝑡𝑡 PROPN american_scientific_journal-2747 53 6 = = SYM american_scientific_journal-2747 53 7 𝒑𝒑.𝒒𝒒. 𝒑𝒑.𝒒𝒒. X american_scientific_journal-2747 53 8 afterwards afterwards ADV american_scientific_journal-2747 53 9 , , PUNCT american_scientific_journal-2747 53 10 he he PRON american_scientific_journal-2747 53 11 chooses choose VERB american_scientific_journal-2747 53 12 an an DET american_scientific_journal-2747 53 13 integer integer NOUN american_scientific_journal-2747 53 14 π’ˆπ’ˆ π’ˆπ’ˆ PROPN american_scientific_journal-2747 53 15 which which PRON american_scientific_journal-2747 53 16 is be AUX american_scientific_journal-2747 53 17 a a DET american_scientific_journal-2747 53 18 base base NOUN american_scientific_journal-2747 53 19 element element NOUN american_scientific_journal-2747 53 20 of of ADP american_scientific_journal-2747 53 21 order order NOUN american_scientific_journal-2747 53 22 𝒑𝒑’.𝒒𝒒 𝒑𝒑’.𝒒𝒒 ADJ american_scientific_journal-2747 53 23 ’ ' PUNCT american_scientific_journal-2747 53 24 . . PUNCT american_scientific_journal-2747 54 1 the the DET american_scientific_journal-2747 54 2 system system NOUN american_scientific_journal-2747 54 3 authority authority NOUN american_scientific_journal-2747 54 4 keeps keep VERB american_scientific_journal-2747 54 5 𝒑𝒑,𝒒𝒒,𝒑𝒑 𝒑𝒑,𝒒𝒒,𝒑𝒑 PROPN american_scientific_journal-2747 54 6 ’ ' PUNCT american_scientific_journal-2747 54 7 and and CCONJ american_scientific_journal-2747 54 8 𝒒𝒒 𝒒𝒒 NOUN american_scientific_journal-2747 54 9 ’ ' PUNCT american_scientific_journal-2747 54 10 secret secret NOUN american_scientific_journal-2747 54 11 and and CCONJ american_scientific_journal-2747 54 12 publishes publishe NOUN american_scientific_journal-2747 54 13 π’ˆπ’ˆ,𝒏𝒏 π’ˆπ’ˆ,𝒏𝒏 VERB american_scientific_journal-2747 54 14 , , PUNCT american_scientific_journal-2747 54 15 the the DET american_scientific_journal-2747 54 16 group group NOUN american_scientific_journal-2747 54 17 β„€π’π’βˆ— β„€π’π’βˆ— X american_scientific_journal-2747 54 18 , , PUNCT american_scientific_journal-2747 54 19 and and CCONJ american_scientific_journal-2747 54 20 four four NUM american_scientific_journal-2747 54 21 collision collision NOUN american_scientific_journal-2747 54 22 free free ADJ american_scientific_journal-2747 54 23 oneway oneway ADJ american_scientific_journal-2747 54 24 hash hash NOUN american_scientific_journal-2747 54 25 functions function NOUN american_scientific_journal-2747 54 26 as as SCONJ american_scientific_journal-2747 54 27 follows follow VERB american_scientific_journal-2747 54 28 : : PUNCT american_scientific_journal-2747 54 29 american american ADJ american_scientific_journal-2747 54 30 scientific scientific ADJ american_scientific_journal-2747 54 31 research research PROPN american_scientific_journal-2747 54 32 journal journal NOUN american_scientific_journal-2747 54 33 for for ADP american_scientific_journal-2747 54 34 engineering engineering NOUN american_scientific_journal-2747 54 35 , , PUNCT american_scientific_journal-2747 54 36 technology technology NOUN american_scientific_journal-2747 54 37 , , PUNCT american_scientific_journal-2747 54 38 and and CCONJ american_scientific_journal-2747 54 39 sciences science NOUN american_scientific_journal-2747 54 40 ( ( PUNCT american_scientific_journal-2747 54 41 asrjets asrjet NOUN american_scientific_journal-2747 54 42 ) ) PUNCT american_scientific_journal-2747 54 43 ( ( PUNCT american_scientific_journal-2747 54 44 2017 2017 NUM american_scientific_journal-2747 54 45 ) ) PUNCT american_scientific_journal-2747 54 46 volume volume NOUN american_scientific_journal-2747 54 47 28 28 NUM american_scientific_journal-2747 54 48 , , PUNCT american_scientific_journal-2747 54 49 no no DET american_scientific_journal-2747 54 50 1 1 NUM american_scientific_journal-2747 54 51 , , PUNCT american_scientific_journal-2747 54 52 pp pp ADV american_scientific_journal-2747 54 53 257 257 NUM american_scientific_journal-2747 54 54 - - SYM american_scientific_journal-2747 54 55 265 265 NUM american_scientific_journal-2747 54 56 259 259 NUM american_scientific_journal-2747 54 57 𝑭𝑭,𝑯𝑯 𝑭𝑭,𝑯𝑯 NOUN american_scientific_journal-2747 54 58 : : PUNCT american_scientific_journal-2747 54 59 { { PUNCT american_scientific_journal-2747 54 60 𝟎𝟎,𝟏𝟏}βˆ— 𝟎𝟎,𝟏𝟏}βˆ— NUM american_scientific_journal-2747 54 61 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 62 ⎯ ⎯ PROPN american_scientific_journal-2747 54 63 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 64 { { PUNCT american_scientific_journal-2747 54 65 𝟎𝟎,𝟏𝟏}π’Œπ’Œ 𝟎𝟎,𝟏𝟏}π’Œπ’Œ PROPN american_scientific_journal-2747 54 66 π‘­π‘­πŸπŸ π‘­π‘­πŸπŸ PROPN american_scientific_journal-2747 54 67 : : PUNCT american_scientific_journal-2747 54 68 { { PUNCT american_scientific_journal-2747 54 69 𝟎𝟎,𝟏𝟏}βˆ— 𝟎𝟎,𝟏𝟏}βˆ— NUM american_scientific_journal-2747 54 70 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 71 ⎯ ⎯ PROPN american_scientific_journal-2747 54 72 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 73 { { PUNCT american_scientific_journal-2747 54 74 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ PROPN american_scientific_journal-2747 54 75 π‘­π‘­πŸπŸ π‘­π‘­πŸπŸ PROPN american_scientific_journal-2747 54 76 : : PUNCT american_scientific_journal-2747 54 77 { { PUNCT american_scientific_journal-2747 54 78 𝟎𝟎,𝟏𝟏}βˆ— 𝟎𝟎,𝟏𝟏}βˆ— NUM american_scientific_journal-2747 54 79 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 80 ⎯ ⎯ PROPN american_scientific_journal-2747 54 81 οΏ½ οΏ½ PROPN american_scientific_journal-2747 54 82 { { PUNCT american_scientific_journal-2747 54 83 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ NOUN american_scientific_journal-2747 54 84 where where SCONJ american_scientific_journal-2747 54 85 𝒍𝒍𝑡𝑡 𝒍𝒍𝑡𝑡 NOUN american_scientific_journal-2747 54 86 is be AUX american_scientific_journal-2747 54 87 of of ADP american_scientific_journal-2747 54 88 the the DET american_scientific_journal-2747 54 89 length length NOUN american_scientific_journal-2747 54 90 of of ADP american_scientific_journal-2747 54 91 𝑡𝑡 𝑡𝑡 PROPN american_scientific_journal-2747 54 92 in in ADP american_scientific_journal-2747 54 93 binary binary NOUN american_scientific_journal-2747 54 94 , , PUNCT american_scientific_journal-2747 54 95 and and CCONJ american_scientific_journal-2747 54 96 𝒍𝒍𝑡𝑡 𝒍𝒍𝑡𝑡 NOUN american_scientific_journal-2747 54 97 = = SYM american_scientific_journal-2747 54 98 π’π’πŸπŸ π’π’πŸπŸ PROPN american_scientific_journal-2747 54 99 + + CCONJ american_scientific_journal-2747 54 100 π’π’πŸπŸ. π’π’πŸπŸ. VERB american_scientific_journal-2747 54 101 the the DET american_scientific_journal-2747 54 102 scheme scheme NOUN american_scientific_journal-2747 54 103 can can AUX american_scientific_journal-2747 54 104 deal deal VERB american_scientific_journal-2747 54 105 with with ADP american_scientific_journal-2747 54 106 𝑴𝑴 𝑴𝑴 PROPN american_scientific_journal-2747 54 107 ∈ ∈ PROPN american_scientific_journal-2747 54 108 { { PUNCT american_scientific_journal-2747 54 109 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ. 𝟎𝟎,𝟏𝟏}π’π’πŸπŸ. PROPN american_scientific_journal-2747 54 110 in in ADP american_scientific_journal-2747 54 111 this this DET american_scientific_journal-2747 54 112 scheme scheme NOUN american_scientific_journal-2747 54 113 , , PUNCT american_scientific_journal-2747 54 114 π’Œπ’Œ π’Œπ’Œ PROPN american_scientific_journal-2747 54 115 = = SYM american_scientific_journal-2747 54 116 ⌈π₯π₯π₯π₯π₯π₯(𝑷𝑷)βŒ‰,and ⌈π₯π₯π₯π₯π₯π₯(𝑷𝑷)βŒ‰,and NUM american_scientific_journal-2747 54 117 𝑷𝑷 𝑷𝑷 NOUN american_scientific_journal-2747 54 118 = = SYM american_scientific_journal-2747 54 119 𝐦𝐦𝐦𝐦𝐦𝐦(𝒑𝒑′,𝒒𝒒′ 𝐦𝐦𝐦𝐦𝐦𝐦(𝒑𝒑′,𝒒𝒒′ NUM american_scientific_journal-2747 54 120 ) ) PUNCT american_scientific_journal-2747 54 121 . . PUNCT american_scientific_journal-2747 55 1 when when SCONJ american_scientific_journal-2747 55 2 the the DET american_scientific_journal-2747 55 3 user user NOUN american_scientific_journal-2747 55 4 π‘Όπ‘Όπ’Šπ’Š π‘Όπ‘Όπ’Šπ’Š PROPN american_scientific_journal-2747 55 5 wants want VERB american_scientific_journal-2747 55 6 to to PART american_scientific_journal-2747 55 7 join join VERB american_scientific_journal-2747 55 8 the the DET american_scientific_journal-2747 55 9 system system NOUN american_scientific_journal-2747 55 10 , , PUNCT american_scientific_journal-2747 55 11 he he PRON american_scientific_journal-2747 55 12 chooses choose VERB american_scientific_journal-2747 55 13 his his PRON american_scientific_journal-2747 55 14 private private ADJ american_scientific_journal-2747 55 15 key key ADJ american_scientific_journal-2747 55 16 π’™π’™π’Šπ’Š π’™π’™π’Šπ’Š NOUN american_scientific_journal-2747 55 17 at at ADP american_scientific_journal-2747 55 18 random random ADJ american_scientific_journal-2747 55 19 and and CCONJ american_scientific_journal-2747 55 20 computes compute VERB american_scientific_journal-2747 55 21 π’‘π’‘π’Šπ’Š π’‘π’‘π’Šπ’Š NOUN american_scientific_journal-2747 55 22 = = NOUN american_scientific_journal-2747 55 23 π’ˆπ’ˆπ’™π’™π’Šπ’Š π’ˆπ’ˆπ’™π’™π’Šπ’Š NOUN american_scientific_journal-2747 55 24 π’Žπ’Žπ’Žπ’Žπ’Žπ’Žπ’π’. π’Žπ’Žπ’Žπ’Žπ’Žπ’Žπ’π’. NOUN american_scientific_journal-2747 55 25 then then ADV american_scientific_journal-2747 55 26 , , PUNCT american_scientific_journal-2747 55 27 he he PRON american_scientific_journal-2747 55 28 submits submit VERB american_scientific_journal-2747 55 29 ( ( PUNCT american_scientific_journal-2747 55 30 π’‘π’‘π’Šπ’Š π’‘π’‘π’Šπ’Š NOUN american_scientific_journal-2747 55 31 , , PUNCT american_scientific_journal-2747 55 32 π‘°π‘°π‘°π‘°π’Šπ’Š π‘°π‘°π‘°π‘°π’Šπ’Š PROPN american_scientific_journal-2747 55 33 ) ) PUNCT american_scientific_journal-2747 55 34 to to ADP american_scientific_journal-2747 55 35 the the DET american_scientific_journal-2747 55 36 𝑺𝑺𝑺𝑺. 𝑺𝑺𝑺𝑺. NOUN american_scientific_journal-2747 55 37 after after ADP american_scientific_journal-2747 55 38 receiving receive VERB american_scientific_journal-2747 55 39 ( ( PUNCT american_scientific_journal-2747 55 40 π’‘π’‘π’Šπ’Š π’‘π’‘π’Šπ’Š NOUN american_scientific_journal-2747 55 41 , , PUNCT american_scientific_journal-2747 55 42 π‘°π‘°π‘°π‘°π’Šπ’Š π‘°π‘°π‘°π‘°π’Šπ’Š PROPN american_scientific_journal-2747 55 43 ) ) PUNCT american_scientific_journal-2747 55 44 , , PUNCT american_scientific_journal-2747 55 45 the the DET american_scientific_journal-2747 55 46 system system NOUN american_scientific_journal-2747 55 47 authority authority NOUN american_scientific_journal-2747 55 48 computes compute VERB american_scientific_journal-2747 55 49 π’šπ’šπ’Šπ’Š π’šπ’šπ’Šπ’Š X american_scientific_journal-2747 55 50 = = SYM american_scientific_journal-2747 55 51 ( ( PUNCT american_scientific_journal-2747 55 52 π’‘π’‘π’Šπ’Š π’‘π’‘π’Šπ’Š PROPN american_scientific_journal-2747 55 53 βˆ’ βˆ’ PROPN american_scientific_journal-2747 55 54 π‘°π‘°π‘°π‘°π’Šπ’Š)𝑭𝑭(π‘°π‘°π‘°π‘°π’Šπ’Š)βˆ’πŸπŸπ’Žπ’Žπ’Žπ’Žπ’Žπ’Ž π‘°π‘°π‘°π‘°π’Šπ’Š)𝑭𝑭(π‘°π‘°π‘°π‘°π’Šπ’Š)βˆ’πŸπŸπ’Žπ’Žπ’Žπ’Žπ’Žπ’Ž VERB american_scientific_journal-2747 55 55 𝒏𝒏 𝒏𝒏 NOUN american_scientific_journal-2747 55 56 , , PUNCT american_scientific_journal-2747 55 57 and and CCONJ american_scientific_journal-2747 55 58 publishes publish VERB american_scientific_journal-2747 55 59 π’šπ’šπ’Šπ’Š. π’šπ’šπ’Šπ’Š. NOUN american_scientific_journal-2747 56 1 the the DET american_scientific_journal-2747 56 2 user user NOUN american_scientific_journal-2747 56 3 π‘Όπ‘Όπ’Šπ’Š π‘Όπ‘Όπ’Šπ’Š PROPN american_scientific_journal-2747 56 4 can can AUX american_scientific_journal-2747 56 5 easily easily ADV american_scientific_journal-2747 56 6 check check VERB american_scientific_journal-2747 56 7 the the DET american_scientific_journal-2747 56 8 validity validity NOUN american_scientific_journal-2747 56 9 of of ADP american_scientific_journal-2747 56 10 π’šπ’šπ’Šπ’Š. π’šπ’šπ’Šπ’Š. NOUN american_scientific_journal-2747 56 11 2.2 2.2 NUM american_scientific_journal-2747 56 12 . . PUNCT american_scientific_journal-2747 57 1 signature signature NOUN american_scientific_journal-2747 57 2 generation generation NOUN american_scientific_journal-2747 57 3 phase phase NOUN american_scientific_journal-2747 57 4 when when SCONJ american_scientific_journal-2747 57 5 π‘Όπ‘Όπ’Šπ’Š π‘Όπ‘Όπ’Šπ’Š PROPN american_scientific_journal-2747 57 6 decides decide VERB american_scientific_journal-2747 57 7 to to PART american_scientific_journal-2747 57 8 sign sign VERB american_scientific_journal-2747 57 9 a a DET american_scientific_journal-2747 57 10 message message NOUN american_scientific_journal-2747 57 11 𝑴𝑴 𝑴𝑴 PROPN american_scientific_journal-2747 57 12 with with ADP american_scientific_journal-2747 57 13 the the DET american_scientific_journal-2747 57 14 length length NOUN american_scientific_journal-2747 57 15 π’Œπ’Œ π’Œπ’Œ NOUN american_scientific_journal-2747 57 16 to to ADP american_scientific_journal-2747 57 17 the the DET american_scientific_journal-2747 57 18 verifier verifier NOUN american_scientific_journal-2747 57 19 𝑼𝑼𝒋𝒋 𝑼𝑼𝒋𝒋 PROPN american_scientific_journal-2747 57 20 , , PUNCT american_scientific_journal-2747 57 21 he he PRON american_scientific_journal-2747 57 22 chooses choose VERB american_scientific_journal-2747 57 23 a a DET american_scientific_journal-2747 57 24 number number NOUN american_scientific_journal-2747 57 25 π’Œπ’Œπ’Šπ’Š π’Œπ’Œπ’Šπ’Š NOUN american_scientific_journal-2747 57 26 at at ADP american_scientific_journal-2747 57 27 random random ADJ american_scientific_journal-2747 57 28 and and CCONJ american_scientific_journal-2747 57 29 computes compute VERB american_scientific_journal-2747 57 30 the the DET american_scientific_journal-2747 57 31 following following ADJ american_scientific_journal-2747 57 32 variables variable NOUN american_scientific_journal-2747 57 33 : : PUNCT american_scientific_journal-2747 57 34 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 57 35 = = SYM american_scientific_journal-2747 57 36 π’ˆπ’ˆπ’Œπ’Œπ’Šπ’Š π’ˆπ’ˆπ’Œπ’Œπ’Šπ’Š NOUN american_scientific_journal-2747 57 37 π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž VERB american_scientific_journal-2747 57 38 𝒏𝒏 𝒏𝒏 X american_scientific_journal-2747 57 39 π‘Ήπ‘Ήπ’Šπ’Š π‘Ήπ‘Ήπ’Šπ’Š PROPN american_scientific_journal-2747 57 40 = = PUNCT american_scientific_journal-2747 58 1 ( ( PUNCT american_scientific_journal-2747 58 2 π’šπ’šπ’‹π’‹π‘­π‘­ π’šπ’šπ’‹π’‹π‘­π‘­ PROPN american_scientific_journal-2747 58 3 οΏ½ οΏ½ PROPN american_scientific_journal-2747 58 4 𝑰𝑰𝑰𝑰𝒋𝒋 𝑰𝑰𝑰𝑰𝒋𝒋 PROPN american_scientific_journal-2747 58 5 οΏ½ οΏ½ AUX american_scientific_journal-2747 58 6 + + CCONJ american_scientific_journal-2747 58 7 𝑰𝑰𝑰𝑰𝒋𝒋)π’Œπ’Œπ’Šπ’Š 𝑰𝑰𝑰𝑰𝒋𝒋)π’Œπ’Œπ’Šπ’Š VERB american_scientific_journal-2747 58 8 π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž VERB american_scientific_journal-2747 58 9 𝒏𝒏 𝒏𝒏 NOUN american_scientific_journal-2747 58 10 π’‡π’‡π’Šπ’Š π’‡π’‡π’Šπ’Š VERB american_scientific_journal-2747 58 11 = = SYM american_scientific_journal-2747 58 12 π‘­π‘­πŸπŸ(𝑴𝑴 π‘­π‘­πŸπŸ(𝑴𝑴 NOUN american_scientific_journal-2747 58 13 ) ) PUNCT american_scientific_journal-2747 58 14 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 58 15 π‘­π‘­πŸπŸ π‘­π‘­πŸπŸ PROPN american_scientific_journal-2747 58 16 οΏ½ οΏ½ PROPN american_scientific_journal-2747 58 17 π‘­π‘­πŸπŸ(𝑴𝑴) π‘­π‘­πŸπŸ(𝑴𝑴) NOUN american_scientific_journal-2747 58 18 οΏ½ οΏ½ NOUN american_scientific_journal-2747 58 19 ⨁𝑴𝑴 ⨁𝑴𝑴 NOUN american_scientific_journal-2747 58 20 π‘»π‘»π’Šπ’Š π‘»π‘»π’Šπ’Š NOUN american_scientific_journal-2747 58 21 = = PUNCT american_scientific_journal-2747 59 1 π‘Ήπ‘Ήπ’Šπ’Š π‘Ήπ‘Ήπ’Šπ’Š PROPN american_scientific_journal-2747 59 2 βŠ• βŠ• PROPN american_scientific_journal-2747 59 3 π’‡π’‡π’Šπ’Š π’‡π’‡π’Šπ’Š PROPN american_scientific_journal-2747 59 4 π’•π’•π’Šπ’Š π’•π’•π’Šπ’Š VERB american_scientific_journal-2747 59 5 = = SYM american_scientific_journal-2747 59 6 𝑯𝑯(𝑴𝑴 𝑯𝑯(𝑴𝑴 PROPN american_scientific_journal-2747 59 7 , , PUNCT american_scientific_journal-2747 59 8 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 59 9 ) ) PUNCT american_scientific_journal-2747 59 10 π’”π’”π’Šπ’Š π’”π’”π’Šπ’Š PROPN american_scientific_journal-2747 59 11 = = SYM american_scientific_journal-2747 59 12 π’Œπ’Œπ’Šπ’Š π’Œπ’Œπ’Šπ’Š PROPN american_scientific_journal-2747 59 13 βˆ’ βˆ’ PROPN american_scientific_journal-2747 59 14 π’™π’™π’Šπ’Š. π’™π’™π’Šπ’Š. NOUN american_scientific_journal-2747 60 1 π’•π’•π’Šπ’Š.π’‡π’‡π’Šπ’Š π’•π’•π’Šπ’Š.π’‡π’‡π’Šπ’Š PROPN american_scientific_journal-2747 60 2 where where SCONJ american_scientific_journal-2747 60 3 β€œ " PUNCT american_scientific_journal-2747 60 4 ⨁ ⨁ PROPN american_scientific_journal-2747 60 5 ” " PUNCT american_scientific_journal-2747 60 6 denotes denote VERB american_scientific_journal-2747 60 7 the the DET american_scientific_journal-2747 60 8 exclusive exclusive ADJ american_scientific_journal-2747 60 9 - - PUNCT american_scientific_journal-2747 60 10 or or CCONJ american_scientific_journal-2747 60 11 operator operator NOUN american_scientific_journal-2747 60 12 , , PUNCT american_scientific_journal-2747 60 13 and and CCONJ american_scientific_journal-2747 60 14 β€œ " PUNCT american_scientific_journal-2747 60 15 βˆ₯ βˆ₯ NUM american_scientific_journal-2747 60 16 ” " PUNCT american_scientific_journal-2747 60 17 denotes denote VERB american_scientific_journal-2747 60 18 the the DET american_scientific_journal-2747 60 19 concatenation concatenation NOUN american_scientific_journal-2747 60 20 operator operator NOUN american_scientific_journal-2747 60 21 . . PUNCT american_scientific_journal-2747 61 1 at at ADP american_scientific_journal-2747 61 2 last last ADJ american_scientific_journal-2747 61 3 , , PUNCT american_scientific_journal-2747 61 4 π‘Όπ‘Όπ’Šπ’Š π‘Όπ‘Όπ’Šπ’Š PROPN american_scientific_journal-2747 61 5 sends send VERB american_scientific_journal-2747 61 6 ( ( PUNCT american_scientific_journal-2747 61 7 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 61 8 , , PUNCT american_scientific_journal-2747 61 9 π’”π’”π’Šπ’Š,π‘»π‘»π’Šπ’Š π’”π’”π’Šπ’Š,π‘»π‘»π’Šπ’Š PROPN american_scientific_journal-2747 61 10 ) ) PUNCT american_scientific_journal-2747 61 11 to to ADP american_scientific_journal-2747 61 12 𝑼𝑼𝒋𝒋 𝑼𝑼𝒋𝒋 PROPN american_scientific_journal-2747 61 13 as as ADP american_scientific_journal-2747 61 14 the the DET american_scientific_journal-2747 61 15 signature signature NOUN american_scientific_journal-2747 61 16 of of ADP american_scientific_journal-2747 61 17 𝑴𝑴. 𝑴𝑴. ADP american_scientific_journal-2747 61 18 2.3 2.3 NUM american_scientific_journal-2747 61 19 . . PUNCT american_scientific_journal-2747 62 1 message message NOUN american_scientific_journal-2747 62 2 recovery recovery NOUN american_scientific_journal-2747 62 3 phase phase NOUN american_scientific_journal-2747 62 4 after after ADP american_scientific_journal-2747 62 5 receiving receive VERB american_scientific_journal-2747 62 6 ( ( PUNCT american_scientific_journal-2747 62 7 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 62 8 , , PUNCT american_scientific_journal-2747 62 9 π’”π’”π’Šπ’Š,π‘»π‘»π’Šπ’Š π’”π’”π’Šπ’Š,π‘»π‘»π’Šπ’Š PROPN american_scientific_journal-2747 62 10 ) ) PUNCT american_scientific_journal-2747 63 1 , , PUNCT american_scientific_journal-2747 63 2 the the DET american_scientific_journal-2747 63 3 verifier verifier NOUN american_scientific_journal-2747 63 4 𝑼𝑼𝒋𝒋 𝑼𝑼𝒋𝒋 PROPN american_scientific_journal-2747 63 5 computes compute VERB american_scientific_journal-2747 63 6 π‘Ήπ‘Ήπ’Šπ’Š π‘Ήπ‘Ήπ’Šπ’Š PROPN american_scientific_journal-2747 63 7 = = SYM american_scientific_journal-2747 63 8 π’†π’†π’Šπ’Šπ’™π’™π’‹π’‹ π’†π’†π’Šπ’Šπ’™π’™π’‹π’‹ PROPN american_scientific_journal-2747 63 9 π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž PROPN american_scientific_journal-2747 63 10 𝒏𝒏 𝒏𝒏 PROPN american_scientific_journal-2747 63 11 , , PUNCT american_scientific_journal-2747 63 12 and and CCONJ american_scientific_journal-2747 63 13 calculates calculate VERB american_scientific_journal-2747 63 14 π’‡π’‡π’Šπ’Š π’‡π’‡π’Šπ’Š ADJ american_scientific_journal-2747 63 15 = = PUNCT american_scientific_journal-2747 63 16 π‘Ήπ‘Ήπ’Šπ’Šβ¨π‘»π‘»π’Šπ’Š. π‘Ήπ‘Ήπ’Šπ’Šβ¨π‘»π‘»π’Šπ’Š. PROPN american_scientific_journal-2747 63 17 then then ADV american_scientific_journal-2747 63 18 , , PUNCT american_scientific_journal-2747 63 19 he he PRON american_scientific_journal-2747 63 20 can can AUX american_scientific_journal-2747 63 21 achieve achieve VERB american_scientific_journal-2747 63 22 the the DET american_scientific_journal-2747 63 23 message message NOUN american_scientific_journal-2747 63 24 𝑴𝑴 𝑴𝑴 PROPN american_scientific_journal-2747 63 25 by by ADP american_scientific_journal-2747 63 26 the the DET american_scientific_journal-2747 63 27 following follow VERB american_scientific_journal-2747 63 28 equation equation NOUN american_scientific_journal-2747 63 29 𝑴𝑴 𝑴𝑴 PROPN american_scientific_journal-2747 63 30 = = SYM american_scientific_journal-2747 63 31 π‘­π‘­πŸπŸ([π’‡π’‡π’Šπ’Š]π’π’πŸπŸ)⨁[π’‡π’‡π’Šπ’Š]π’π’πŸπŸ π‘­π‘­πŸπŸ([π’‡π’‡π’Šπ’Š]π’π’πŸπŸ)⨁[π’‡π’‡π’Šπ’Š]π’π’πŸπŸ PROPN american_scientific_journal-2747 63 32 american american PROPN american_scientific_journal-2747 63 33 scientific scientific ADJ american_scientific_journal-2747 63 34 research research PROPN american_scientific_journal-2747 63 35 journal journal NOUN american_scientific_journal-2747 63 36 for for ADP american_scientific_journal-2747 63 37 engineering engineering NOUN american_scientific_journal-2747 63 38 , , PUNCT american_scientific_journal-2747 63 39 technology technology NOUN american_scientific_journal-2747 63 40 , , PUNCT american_scientific_journal-2747 63 41 and and CCONJ american_scientific_journal-2747 63 42 sciences science NOUN american_scientific_journal-2747 63 43 ( ( PUNCT american_scientific_journal-2747 63 44 asrjets asrjet NOUN american_scientific_journal-2747 63 45 ) ) PUNCT american_scientific_journal-2747 63 46 ( ( PUNCT american_scientific_journal-2747 63 47 2017 2017 NUM american_scientific_journal-2747 63 48 ) ) PUNCT american_scientific_journal-2747 63 49 volume volume NOUN american_scientific_journal-2747 63 50 28 28 NUM american_scientific_journal-2747 63 51 , , PUNCT american_scientific_journal-2747 63 52 no no DET american_scientific_journal-2747 63 53 1 1 NUM american_scientific_journal-2747 63 54 , , PUNCT american_scientific_journal-2747 63 55 pp pp ADV american_scientific_journal-2747 63 56 257 257 NUM american_scientific_journal-2747 63 57 - - SYM american_scientific_journal-2747 63 58 265 265 NUM american_scientific_journal-2747 63 59 260 260 NUM american_scientific_journal-2747 63 60 where where SCONJ american_scientific_journal-2747 63 61 [ [ X american_scientific_journal-2747 63 62 π’‡π’‡π’Šπ’Š]π’π’πŸπŸ π’‡π’‡π’Šπ’Š]π’π’πŸπŸ X american_scientific_journal-2747 63 63 is be AUX american_scientific_journal-2747 63 64 the the DET american_scientific_journal-2747 63 65 left left ADJ american_scientific_journal-2747 63 66 π’π’πŸπŸ π’π’πŸπŸ PROPN american_scientific_journal-2747 63 67 bits bit NOUN american_scientific_journal-2747 63 68 of of ADP american_scientific_journal-2747 63 69 π’‡π’‡π’Šπ’Š π’‡π’‡π’Šπ’Š ADJ american_scientific_journal-2747 63 70 , , PUNCT american_scientific_journal-2747 63 71 and and CCONJ american_scientific_journal-2747 63 72 [ [ X american_scientific_journal-2747 63 73 π’‡π’‡π’Šπ’Š]π’π’πŸπŸ π’‡π’‡π’Šπ’Š]π’π’πŸπŸ X american_scientific_journal-2747 63 74 is be AUX american_scientific_journal-2747 63 75 the the DET american_scientific_journal-2747 63 76 right right ADJ american_scientific_journal-2747 63 77 π’π’πŸπŸ π’π’πŸπŸ PROPN american_scientific_journal-2747 63 78 bits bit NOUN american_scientific_journal-2747 63 79 of of ADP american_scientific_journal-2747 63 80 π’‡π’‡π’Šπ’Š. π’‡π’‡π’Šπ’Š. NOUN american_scientific_journal-2747 63 81 in in ADP american_scientific_journal-2747 63 82 order order NOUN american_scientific_journal-2747 63 83 to to PART american_scientific_journal-2747 63 84 check check VERB american_scientific_journal-2747 63 85 the the DET american_scientific_journal-2747 63 86 validity validity NOUN american_scientific_journal-2747 63 87 of of ADP american_scientific_journal-2747 63 88 the the DET american_scientific_journal-2747 63 89 signature signature NOUN american_scientific_journal-2747 63 90 , , PUNCT american_scientific_journal-2747 63 91 𝑼𝑼𝒋𝒋 𝑼𝑼𝒋𝒋 PROPN american_scientific_journal-2747 63 92 first first ADV american_scientific_journal-2747 63 93 computes compute NOUN american_scientific_journal-2747 63 94 π’•π’•π’Šπ’Š π’•π’•π’Šπ’Š VERB american_scientific_journal-2747 63 95 = = SYM american_scientific_journal-2747 63 96 𝑯𝑯(𝑴𝑴 𝑯𝑯(𝑴𝑴 PROPN american_scientific_journal-2747 63 97 , , PUNCT american_scientific_journal-2747 63 98 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 63 99 ) ) PUNCT american_scientific_journal-2747 63 100 and and CCONJ american_scientific_journal-2747 63 101 then then ADV american_scientific_journal-2747 63 102 , , PUNCT american_scientific_journal-2747 63 103 he he PRON american_scientific_journal-2747 63 104 checks check VERB american_scientific_journal-2747 63 105 whether whether SCONJ american_scientific_journal-2747 63 106 the the DET american_scientific_journal-2747 63 107 following follow VERB american_scientific_journal-2747 63 108 equation equation NOUN american_scientific_journal-2747 63 109 holds hold VERB american_scientific_journal-2747 63 110 or or CCONJ american_scientific_journal-2747 63 111 not not PART american_scientific_journal-2747 63 112 . . PUNCT american_scientific_journal-2747 64 1 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 64 2 = = SYM american_scientific_journal-2747 64 3 π’ˆπ’ˆπ’”π’”π’Šπ’Š(π’šπ’šπ’Šπ’Šπ‘­π‘­(π‘°π‘°π‘°π‘°π’Šπ’Š π’ˆπ’ˆπ’”π’”π’Šπ’Š(π’šπ’šπ’Šπ’Šπ‘­π‘­(π‘°π‘°π‘°π‘°π’Šπ’Š NOUN american_scientific_journal-2747 64 4 ) ) PUNCT american_scientific_journal-2747 65 1 + + CCONJ american_scientific_journal-2747 65 2 π‘°π‘°π‘°π‘°π’Šπ’Š)π’•π’•π’Šπ’Šπ’‡π’‡π’Šπ’Š π‘°π‘°π‘°π‘°π’Šπ’Š)π’•π’•π’Šπ’Šπ’‡π’‡π’Šπ’Š ADJ american_scientific_journal-2747 65 3 π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž π’Žπ’Žπ’Žπ’Žπ’Žπ’Ž ADJ american_scientific_journal-2747 65 4 𝒏𝒏 𝒏𝒏 NOUN american_scientific_journal-2747 65 5 if if SCONJ american_scientific_journal-2747 65 6 the the DET american_scientific_journal-2747 65 7 above above ADJ american_scientific_journal-2747 65 8 equation equation NOUN american_scientific_journal-2747 65 9 holds hold VERB american_scientific_journal-2747 65 10 , , PUNCT american_scientific_journal-2747 65 11 he he PRON american_scientific_journal-2747 65 12 accepts accept VERB american_scientific_journal-2747 65 13 the the DET american_scientific_journal-2747 65 14 signature signature NOUN american_scientific_journal-2747 65 15 as as ADP american_scientific_journal-2747 65 16 a a DET american_scientific_journal-2747 65 17 valid valid ADJ american_scientific_journal-2747 65 18 signature signature NOUN american_scientific_journal-2747 65 19 for for ADP american_scientific_journal-2747 65 20 𝑴𝑴. 𝑴𝑴. X american_scientific_journal-2747 65 21 otherwise otherwise ADV american_scientific_journal-2747 65 22 , , PUNCT american_scientific_journal-2747 65 23 he he PRON american_scientific_journal-2747 65 24 rejects reject VERB american_scientific_journal-2747 65 25 the the DET american_scientific_journal-2747 65 26 signature signature NOUN american_scientific_journal-2747 65 27 . . PUNCT american_scientific_journal-2747 66 1 2.4 2.4 NUM american_scientific_journal-2747 66 2 . . PUNCT american_scientific_journal-2747 67 1 signature signature NOUN american_scientific_journal-2747 67 2 conversation conversation NOUN american_scientific_journal-2747 67 3 phase phase NOUN american_scientific_journal-2747 67 4 𝑼𝑼𝒋𝒋 𝑼𝑼𝒋𝒋 PROPN american_scientific_journal-2747 67 5 can can AUX american_scientific_journal-2747 67 6 publish publish VERB american_scientific_journal-2747 67 7 ( ( PUNCT american_scientific_journal-2747 67 8 𝑴𝑴 𝑴𝑴 PROPN american_scientific_journal-2747 67 9 , , PUNCT american_scientific_journal-2747 67 10 π’•π’•π’Šπ’Š π’•π’•π’Šπ’Š PROPN american_scientific_journal-2747 67 11 , , PUNCT american_scientific_journal-2747 67 12 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š PROPN american_scientific_journal-2747 67 13 ) ) PUNCT american_scientific_journal-2747 67 14 , , PUNCT american_scientific_journal-2747 67 15 and and CCONJ american_scientific_journal-2747 67 16 anyone anyone PRON american_scientific_journal-2747 67 17 can can AUX american_scientific_journal-2747 67 18 confirm confirm VERB american_scientific_journal-2747 67 19 the the DET american_scientific_journal-2747 67 20 validity validity NOUN american_scientific_journal-2747 67 21 of of ADP american_scientific_journal-2747 67 22 the the DET american_scientific_journal-2747 67 23 signature signature NOUN american_scientific_journal-2747 67 24 by by ADP american_scientific_journal-2747 67 25 the the DET american_scientific_journal-2747 67 26 following follow VERB american_scientific_journal-2747 67 27 equation equation NOUN american_scientific_journal-2747 67 28 : : PUNCT american_scientific_journal-2747 67 29 π’•π’•π’Šπ’Š π’•π’•π’Šπ’Š VERB american_scientific_journal-2747 67 30 = = SYM american_scientific_journal-2747 67 31 𝑯𝑯(𝑴𝑴 𝑯𝑯(𝑴𝑴 PROPN american_scientific_journal-2747 67 32 , , PUNCT american_scientific_journal-2747 67 33 π’†π’†π’Šπ’Š π’†π’†π’Šπ’Š NOUN american_scientific_journal-2747 67 34 ) ) PUNCT american_scientific_journal-2747 67 35 phase phase NOUN american_scientific_journal-2747 67 36 𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆 NOUN american_scientific_journal-2747 67 37 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 67 38 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— ADJ american_scientific_journal-2747 67 39 system system NOUN american_scientific_journal-2747 67 40 initialization initialization NOUN american_scientific_journal-2747 67 41 phase phase NOUN american_scientific_journal-2747 67 42 computes compute VERB american_scientific_journal-2747 67 43 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-2747 67 44 = = SYM american_scientific_journal-2747 67 45 ( ( PUNCT american_scientific_journal-2747 67 46 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 PROPN american_scientific_journal-2747 67 47 βˆ’ βˆ’ PUNCT american_scientific_journal-2747 67 48 𝐼𝐼𝐼𝐼𝑖𝑖)𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖)βˆ’1π‘šπ‘šπ‘šπ‘šπ‘šπ‘š 𝐼𝐼𝐼𝐼𝑖𝑖)𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖)βˆ’1π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 67 49 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 67 50 , , PUNCT american_scientific_journal-2747 67 51 and and CCONJ american_scientific_journal-2747 67 52 publicize publicize VERB american_scientific_journal-2747 67 53 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-2747 67 54 . . PUNCT american_scientific_journal-2747 68 1 chooses choose VERB american_scientific_journal-2747 68 2 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 68 3 randomly randomly ADV american_scientific_journal-2747 68 4 and and CCONJ american_scientific_journal-2747 68 5 computes compute VERB american_scientific_journal-2747 68 6 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 VERB american_scientific_journal-2747 68 7 = = SYM american_scientific_journal-2747 68 8 𝑔𝑔π‘₯π‘₯𝑖𝑖 𝑔𝑔π‘₯π‘₯𝑖𝑖 ADJ american_scientific_journal-2747 68 9 π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. NOUN american_scientific_journal-2747 68 10 submits submit NOUN american_scientific_journal-2747 68 11 ( ( PUNCT american_scientific_journal-2747 68 12 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 X american_scientific_journal-2747 68 13 , , PUNCT american_scientific_journal-2747 68 14 𝐼𝐼𝐼𝐼𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖 PROPN american_scientific_journal-2747 68 15 ) ) PUNCT american_scientific_journal-2747 68 16 to to ADP american_scientific_journal-2747 68 17 the the DET american_scientific_journal-2747 68 18 𝑆𝑆𝑆𝑆. 𝑆𝑆𝑆𝑆. PROPN american_scientific_journal-2747 68 19 signature signature NOUN american_scientific_journal-2747 68 20 generation generation NOUN american_scientific_journal-2747 68 21 phase phase NOUN american_scientific_journal-2747 68 22 computes compute VERB american_scientific_journal-2747 68 23 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 68 24 = = PRON american_scientific_journal-2747 68 25 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– NOUN american_scientific_journal-2747 68 26 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 68 27 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 68 28 , , PUNCT american_scientific_journal-2747 68 29 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 ADV american_scientific_journal-2747 68 30 = = PUNCT american_scientific_journal-2747 68 31 ( ( PUNCT american_scientific_journal-2747 68 32 𝑦𝑦𝑗𝑗𝐹𝐹 𝑦𝑦𝑗𝑗𝐹𝐹 PROPN american_scientific_journal-2747 68 33 οΏ½ οΏ½ PROPN american_scientific_journal-2747 68 34 𝐼𝐼𝐷𝐷𝑗𝑗 𝐼𝐼𝐷𝐷𝑗𝑗 PROPN american_scientific_journal-2747 68 35 οΏ½ οΏ½ PROPN american_scientific_journal-2747 68 36 + + CCONJ american_scientific_journal-2747 68 37 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘–π‘šπ‘šπ‘šπ‘šπ‘šπ‘š 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘–π‘šπ‘šπ‘šπ‘šπ‘šπ‘š PROPN american_scientific_journal-2747 68 38 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 68 39 , , PUNCT american_scientific_journal-2747 68 40 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 68 41 = = X american_scientific_journal-2747 68 42 𝐹𝐹1(𝑀𝑀 𝐹𝐹1(𝑀𝑀 PROPN american_scientific_journal-2747 68 43 ) ) PUNCT american_scientific_journal-2747 68 44 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 68 45 𝐹𝐹2 𝐹𝐹2 PROPN american_scientific_journal-2747 68 46 οΏ½ οΏ½ PROPN american_scientific_journal-2747 68 47 𝐹𝐹1(𝑀𝑀) 𝐹𝐹1(𝑀𝑀) NOUN american_scientific_journal-2747 68 48 οΏ½ οΏ½ PROPN american_scientific_journal-2747 68 49 ⨁𝑀𝑀 ⨁𝑀𝑀 PROPN american_scientific_journal-2747 68 50 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 68 51 = = PUNCT american_scientific_journal-2747 69 1 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PROPN american_scientific_journal-2747 69 2 βŠ• βŠ• VERB american_scientific_journal-2747 69 3 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 69 4 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 69 5 = = SYM american_scientific_journal-2747 69 6 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 69 7 , , PUNCT american_scientific_journal-2747 69 8 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 69 9 ) ) PUNCT american_scientific_journal-2747 69 10 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 69 11 = = PUNCT american_scientific_journal-2747 69 12 π‘˜π‘˜π‘–π‘– π‘˜π‘˜π‘–π‘– ADJ american_scientific_journal-2747 69 13 βˆ’ βˆ’ PROPN american_scientific_journal-2747 69 14 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 69 15 . . PUNCT american_scientific_journal-2747 70 1 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 70 2 . . PUNCT american_scientific_journal-2747 71 1 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 71 2 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– NOUN american_scientific_journal-2747 71 3 sends send VERB american_scientific_journal-2747 71 4 ( ( PUNCT american_scientific_journal-2747 71 5 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 71 6 , , PUNCT american_scientific_journal-2747 71 7 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 71 8 , , PUNCT american_scientific_journal-2747 71 9 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 71 10 ) ) PUNCT american_scientific_journal-2747 71 11 to to ADP american_scientific_journal-2747 71 12 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 71 13 message message NOUN american_scientific_journal-2747 71 14 recovery recovery NOUN american_scientific_journal-2747 71 15 phase phase NOUN american_scientific_journal-2747 71 16 calculates calculate VERB american_scientific_journal-2747 71 17 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PUNCT american_scientific_journal-2747 71 18 = = PUNCT american_scientific_journal-2747 71 19 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 NOUN american_scientific_journal-2747 71 20 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 71 21 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 71 22 , , PUNCT american_scientific_journal-2747 71 23 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 71 24 = = NOUN american_scientific_journal-2747 71 25 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 ADJ american_scientific_journal-2747 71 26 , , PUNCT american_scientific_journal-2747 71 27 and and CCONJ american_scientific_journal-2747 71 28 obtains obtain VERB american_scientific_journal-2747 71 29 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 71 30 = = SYM american_scientific_journal-2747 71 31 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 PROPN american_scientific_journal-2747 71 32 . . PUNCT american_scientific_journal-2747 72 1 computes compute VERB american_scientific_journal-2747 72 2 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 72 3 = = SYM american_scientific_journal-2747 72 4 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 72 5 , , PUNCT american_scientific_journal-2747 72 6 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 72 7 ) ) PUNCT american_scientific_journal-2747 72 8 . . PUNCT american_scientific_journal-2747 73 1 then then ADV american_scientific_journal-2747 73 2 , , PUNCT american_scientific_journal-2747 73 3 checks check VERB american_scientific_journal-2747 73 4 whether whether SCONJ american_scientific_journal-2747 73 5 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 73 6 = = SYM american_scientific_journal-2747 73 7 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 73 8 ) ) PUNCT american_scientific_journal-2747 74 1 + + CCONJ american_scientific_journal-2747 74 2 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 74 3 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 74 4 𝑛𝑛 𝑛𝑛 PRON american_scientific_journal-2747 74 5 figure figure VERB american_scientific_journal-2747 74 6 1 1 NUM american_scientific_journal-2747 74 7 : : PUNCT american_scientific_journal-2747 74 8 scheme scheme NOUN american_scientific_journal-2747 74 9 of of ADP american_scientific_journal-2747 74 10 wu wu PROPN american_scientific_journal-2747 74 11 and and CCONJ american_scientific_journal-2747 74 12 xu xu PROPN american_scientific_journal-2747 74 13 american american PROPN american_scientific_journal-2747 74 14 scientific scientific PROPN american_scientific_journal-2747 74 15 research research PROPN american_scientific_journal-2747 74 16 journal journal NOUN american_scientific_journal-2747 74 17 for for ADP american_scientific_journal-2747 74 18 engineering engineering NOUN american_scientific_journal-2747 74 19 , , PUNCT american_scientific_journal-2747 74 20 technology technology NOUN american_scientific_journal-2747 74 21 , , PUNCT american_scientific_journal-2747 74 22 and and CCONJ american_scientific_journal-2747 74 23 sciences science NOUN american_scientific_journal-2747 74 24 ( ( PUNCT american_scientific_journal-2747 74 25 asrjets asrjet NOUN american_scientific_journal-2747 74 26 ) ) PUNCT american_scientific_journal-2747 74 27 ( ( PUNCT american_scientific_journal-2747 74 28 2017 2017 NUM american_scientific_journal-2747 74 29 ) ) PUNCT american_scientific_journal-2747 74 30 volume volume NOUN american_scientific_journal-2747 74 31 28 28 NUM american_scientific_journal-2747 74 32 , , PUNCT american_scientific_journal-2747 74 33 no no DET american_scientific_journal-2747 74 34 1 1 NUM american_scientific_journal-2747 74 35 , , PUNCT american_scientific_journal-2747 74 36 pp pp ADV american_scientific_journal-2747 74 37 257 257 NUM american_scientific_journal-2747 74 38 - - SYM american_scientific_journal-2747 74 39 265 265 NUM american_scientific_journal-2747 74 40 261 261 NUM american_scientific_journal-2747 74 41 3 3 NUM american_scientific_journal-2747 74 42 . . PUNCT american_scientific_journal-2747 74 43 insider insider NOUN american_scientific_journal-2747 74 44 forgery forgery NOUN american_scientific_journal-2747 74 45 attack attack NOUN american_scientific_journal-2747 74 46 to to PART american_scientific_journal-2747 74 47 scheme scheme VERB american_scientific_journal-2747 74 48 of of ADP american_scientific_journal-2747 74 49 wu wu PROPN american_scientific_journal-2747 74 50 and and CCONJ american_scientific_journal-2747 74 51 xu xu VERB american_scientific_journal-2747 74 52 in in ADP american_scientific_journal-2747 74 53 this this DET american_scientific_journal-2747 74 54 section section NOUN american_scientific_journal-2747 74 55 , , PUNCT american_scientific_journal-2747 74 56 an an DET american_scientific_journal-2747 74 57 insider insider NOUN american_scientific_journal-2747 74 58 forgery forgery NOUN american_scientific_journal-2747 74 59 attack attack NOUN american_scientific_journal-2747 74 60 to to ADP american_scientific_journal-2747 74 61 the the DET american_scientific_journal-2747 74 62 aforementioned aforementioned ADJ american_scientific_journal-2747 74 63 scheme scheme NOUN american_scientific_journal-2747 74 64 will will AUX american_scientific_journal-2747 74 65 be be AUX american_scientific_journal-2747 74 66 presented present VERB american_scientific_journal-2747 74 67 . . PUNCT american_scientific_journal-2747 75 1 in in ADP american_scientific_journal-2747 75 2 the the DET american_scientific_journal-2747 75 3 insider insider NOUN american_scientific_journal-2747 75 4 forgery forgery NOUN american_scientific_journal-2747 75 5 attack attack NOUN american_scientific_journal-2747 75 6 , , PUNCT american_scientific_journal-2747 75 7 the the DET american_scientific_journal-2747 75 8 specified specify VERB american_scientific_journal-2747 75 9 receiver receiver NOUN american_scientific_journal-2747 75 10 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 75 11 forges forge VERB american_scientific_journal-2747 75 12 the the DET american_scientific_journal-2747 75 13 received receive VERB american_scientific_journal-2747 75 14 signature signature NOUN american_scientific_journal-2747 75 15 of of ADP american_scientific_journal-2747 75 16 a a DET american_scientific_journal-2747 75 17 given give VERB american_scientific_journal-2747 75 18 message message NOUN american_scientific_journal-2747 75 19 for for ADP american_scientific_journal-2747 75 20 other other ADJ american_scientific_journal-2747 75 21 system system NOUN american_scientific_journal-2747 75 22 users user NOUN american_scientific_journal-2747 75 23 . . PUNCT american_scientific_journal-2747 76 1 the the DET american_scientific_journal-2747 76 2 other other ADJ american_scientific_journal-2747 76 3 user user NOUN american_scientific_journal-2747 76 4 is be AUX american_scientific_journal-2747 76 5 denoted denote VERB american_scientific_journal-2747 76 6 by by ADP american_scientific_journal-2747 76 7 π‘ˆπ‘ˆπ‘‚π‘‚. π‘ˆπ‘ˆπ‘‚π‘‚. NOUN american_scientific_journal-2747 76 8 if if SCONJ american_scientific_journal-2747 76 9 π‘ˆπ‘ˆπ‘‚π‘‚is π‘ˆπ‘ˆπ‘‚π‘‚i NOUN american_scientific_journal-2747 76 10 willing willing ADJ american_scientific_journal-2747 76 11 to to PART american_scientific_journal-2747 76 12 provide provide VERB american_scientific_journal-2747 76 13 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 76 14 with with ADP american_scientific_journal-2747 76 15 his his PRON american_scientific_journal-2747 76 16 secret secret ADJ american_scientific_journal-2747 76 17 key key NOUN american_scientific_journal-2747 76 18 π‘₯π‘₯π‘œπ‘œ π‘₯π‘₯π‘œπ‘œ NOUN american_scientific_journal-2747 76 19 , , PUNCT american_scientific_journal-2747 76 20 then then ADV american_scientific_journal-2747 76 21 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 76 22 is be AUX american_scientific_journal-2747 76 23 able able ADJ american_scientific_journal-2747 76 24 to to PART american_scientific_journal-2747 76 25 forge forge VERB american_scientific_journal-2747 76 26 a a DET american_scientific_journal-2747 76 27 valid valid ADJ american_scientific_journal-2747 76 28 signature signature NOUN american_scientific_journal-2747 76 29 for for ADP american_scientific_journal-2747 76 30 him he PRON american_scientific_journal-2747 76 31 . . PUNCT american_scientific_journal-2747 77 1 this this DET american_scientific_journal-2747 77 2 cooperation cooperation NOUN american_scientific_journal-2747 77 3 between between ADP american_scientific_journal-2747 77 4 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ PROPN american_scientific_journal-2747 77 5 and and CCONJ american_scientific_journal-2747 77 6 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 77 7 makes make VERB american_scientific_journal-2747 77 8 sense sense NOUN american_scientific_journal-2747 77 9 in in ADP american_scientific_journal-2747 77 10 many many ADJ american_scientific_journal-2747 77 11 cases case NOUN american_scientific_journal-2747 77 12 of of ADP american_scientific_journal-2747 77 13 applications application NOUN american_scientific_journal-2747 77 14 of of ADP american_scientific_journal-2747 77 15 digital digital ADJ american_scientific_journal-2747 77 16 signature signature NOUN american_scientific_journal-2747 77 17 scheme scheme NOUN american_scientific_journal-2747 77 18 with with ADP american_scientific_journal-2747 77 19 message message NOUN american_scientific_journal-2747 77 20 recovery recovery NOUN american_scientific_journal-2747 77 21 , , PUNCT american_scientific_journal-2747 77 22 e.g. e.g. ADV american_scientific_journal-2747 77 23 in in ADP american_scientific_journal-2747 77 24 electronic electronic ADJ american_scientific_journal-2747 77 25 election election NOUN american_scientific_journal-2747 77 26 or or CCONJ american_scientific_journal-2747 77 27 in in ADP american_scientific_journal-2747 77 28 electronic electronic ADJ american_scientific_journal-2747 77 29 commerce commerce NOUN american_scientific_journal-2747 77 30 . . PUNCT american_scientific_journal-2747 78 1 as as ADP american_scientific_journal-2747 78 2 an an DET american_scientific_journal-2747 78 3 instance instance NOUN american_scientific_journal-2747 78 4 , , PUNCT american_scientific_journal-2747 78 5 consider consider VERB american_scientific_journal-2747 78 6 that that SCONJ american_scientific_journal-2747 78 7 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 78 8 and and CCONJ american_scientific_journal-2747 78 9 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 78 10 are be AUX american_scientific_journal-2747 78 11 two two NUM american_scientific_journal-2747 78 12 friends friend NOUN american_scientific_journal-2747 78 13 who who PRON american_scientific_journal-2747 78 14 want want VERB american_scientific_journal-2747 78 15 to to PART american_scientific_journal-2747 78 16 purchase purchase VERB american_scientific_journal-2747 78 17 e e NOUN american_scientific_journal-2747 78 18 - - NOUN american_scientific_journal-2747 78 19 tickets ticket NOUN american_scientific_journal-2747 78 20 for for ADP american_scientific_journal-2747 78 21 some some DET american_scientific_journal-2747 78 22 mp3 mp3 NOUN american_scientific_journal-2747 78 23 files file NOUN american_scientific_journal-2747 78 24 . . PUNCT american_scientific_journal-2747 79 1 they they PRON american_scientific_journal-2747 79 2 decide decide VERB american_scientific_journal-2747 79 3 to to PART american_scientific_journal-2747 79 4 buy buy VERB american_scientific_journal-2747 79 5 just just ADV american_scientific_journal-2747 79 6 one one NUM american_scientific_journal-2747 79 7 e e NOUN american_scientific_journal-2747 79 8 - - NOUN american_scientific_journal-2747 79 9 ticket ticket NOUN american_scientific_journal-2747 79 10 and and CCONJ american_scientific_journal-2747 79 11 forge forge VERB american_scientific_journal-2747 79 12 another another DET american_scientific_journal-2747 79 13 e e NOUN american_scientific_journal-2747 79 14 - - NOUN american_scientific_journal-2747 79 15 ticket ticket NOUN american_scientific_journal-2747 79 16 cooperatively cooperatively ADV american_scientific_journal-2747 79 17 . . PUNCT american_scientific_journal-2747 80 1 thus thus ADV american_scientific_journal-2747 80 2 , , PUNCT american_scientific_journal-2747 80 3 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 80 4 buys buy VERB american_scientific_journal-2747 80 5 the the DET american_scientific_journal-2747 80 6 ticket ticket NOUN american_scientific_journal-2747 80 7 ( ( PUNCT american_scientific_journal-2747 80 8 which which PRON american_scientific_journal-2747 80 9 is be AUX american_scientific_journal-2747 80 10 π‘ˆπ‘ˆπ‘–π‘–β€²π‘ π‘  π‘ˆπ‘ˆπ‘–π‘–β€²π‘ π‘  PROPN american_scientific_journal-2747 80 11 signature signature NOUN american_scientific_journal-2747 80 12 with with ADP american_scientific_journal-2747 80 13 message message NOUN american_scientific_journal-2747 80 14 recovery recovery NOUN american_scientific_journal-2747 80 15 ) ) PUNCT american_scientific_journal-2747 80 16 and and CCONJ american_scientific_journal-2747 80 17 offers offer VERB american_scientific_journal-2747 80 18 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ PROPN american_scientific_journal-2747 80 19 a a DET american_scientific_journal-2747 80 20 forged forge VERB american_scientific_journal-2747 80 21 e e NOUN american_scientific_journal-2747 80 22 - - NOUN american_scientific_journal-2747 80 23 ticket ticket NOUN american_scientific_journal-2747 80 24 . . PUNCT american_scientific_journal-2747 81 1 if if SCONJ american_scientific_journal-2747 81 2 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 81 3 trusts trust VERB american_scientific_journal-2747 81 4 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 81 5 , , PUNCT american_scientific_journal-2747 81 6 he he PRON american_scientific_journal-2747 81 7 might might AUX american_scientific_journal-2747 81 8 reveal reveal VERB american_scientific_journal-2747 81 9 his his PRON american_scientific_journal-2747 81 10 secret secret ADJ american_scientific_journal-2747 81 11 key key NOUN american_scientific_journal-2747 81 12 to to ADP american_scientific_journal-2747 81 13 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 81 14 in in ADP american_scientific_journal-2747 81 15 order order NOUN american_scientific_journal-2747 81 16 to to PART american_scientific_journal-2747 81 17 obtain obtain VERB american_scientific_journal-2747 81 18 a a DET american_scientific_journal-2747 81 19 forged forge VERB american_scientific_journal-2747 81 20 e e NOUN american_scientific_journal-2747 81 21 - - NOUN american_scientific_journal-2747 81 22 ticket ticket NOUN american_scientific_journal-2747 81 23 . . PUNCT american_scientific_journal-2747 82 1 follows follow VERB american_scientific_journal-2747 82 2 demonstrate demonstrate VERB american_scientific_journal-2747 82 3 how how SCONJ american_scientific_journal-2747 82 4 this this DET american_scientific_journal-2747 82 5 forgery forgery NOUN american_scientific_journal-2747 82 6 attack attack NOUN american_scientific_journal-2747 82 7 operates operate VERB american_scientific_journal-2747 82 8 . . PUNCT american_scientific_journal-2747 83 1 assume assume VERB american_scientific_journal-2747 83 2 that that SCONJ american_scientific_journal-2747 83 3 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 83 4 has have AUX american_scientific_journal-2747 83 5 recovered recover VERB american_scientific_journal-2747 83 6 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 83 7 from from ADP american_scientific_journal-2747 83 8 the the DET american_scientific_journal-2747 83 9 signature signature NOUN american_scientific_journal-2747 83 10 ( ( PUNCT american_scientific_journal-2747 83 11 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 83 12 , , PUNCT american_scientific_journal-2747 83 13 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 83 14 , , PUNCT american_scientific_journal-2747 83 15 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 83 16 ) ) PUNCT american_scientific_journal-2747 83 17 signed sign VERB american_scientific_journal-2747 83 18 by by ADP american_scientific_journal-2747 83 19 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 83 20 . . PUNCT american_scientific_journal-2747 84 1 he he PRON american_scientific_journal-2747 84 2 wants want VERB american_scientific_journal-2747 84 3 to to PART american_scientific_journal-2747 84 4 forge forge VERB american_scientific_journal-2747 84 5 a a DET american_scientific_journal-2747 84 6 signature signature NOUN american_scientific_journal-2747 84 7 ( ( PUNCT american_scientific_journal-2747 84 8 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 84 9 , , PUNCT american_scientific_journal-2747 84 10 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 84 11 , , PUNCT american_scientific_journal-2747 84 12 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 84 13 ) ) PUNCT american_scientific_journal-2747 84 14 of of ADP american_scientific_journal-2747 84 15 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 84 16 for for ADP american_scientific_journal-2747 84 17 π‘ˆπ‘ˆπ‘‚π‘‚. π‘ˆπ‘ˆπ‘‚π‘‚. NOUN american_scientific_journal-2747 84 18 the the DET american_scientific_journal-2747 84 19 claim claim NOUN american_scientific_journal-2747 84 20 is be AUX american_scientific_journal-2747 84 21 that that SCONJ american_scientific_journal-2747 84 22 ( ( PUNCT american_scientific_journal-2747 84 23 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 84 24 , , PUNCT american_scientific_journal-2747 84 25 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 84 26 , , PUNCT american_scientific_journal-2747 84 27 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 84 28 ) ) PUNCT american_scientific_journal-2747 84 29 is be AUX american_scientific_journal-2747 84 30 a a DET american_scientific_journal-2747 84 31 valid valid ADJ american_scientific_journal-2747 84 32 signature signature NOUN american_scientific_journal-2747 84 33 of of ADP american_scientific_journal-2747 84 34 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 84 35 signed sign VERB american_scientific_journal-2747 84 36 by by ADP american_scientific_journal-2747 84 37 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 84 38 for for ADP american_scientific_journal-2747 84 39 π‘ˆπ‘ˆπ‘‚π‘‚. π‘ˆπ‘ˆπ‘‚π‘‚. NOUN american_scientific_journal-2747 84 40 first first ADV american_scientific_journal-2747 84 41 , , PUNCT american_scientific_journal-2747 84 42 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 84 43 reveals reveal VERB american_scientific_journal-2747 84 44 his his PRON american_scientific_journal-2747 84 45 own own ADJ american_scientific_journal-2747 84 46 private private ADJ american_scientific_journal-2747 84 47 key key NOUN american_scientific_journal-2747 84 48 π‘₯π‘₯π‘œπ‘œ π‘₯π‘₯π‘œπ‘œ NOUN american_scientific_journal-2747 84 49 to to ADP american_scientific_journal-2747 84 50 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 84 51 . . PUNCT american_scientific_journal-2747 85 1 thereafter thereafter ADV american_scientific_journal-2747 85 2 , , PUNCT american_scientific_journal-2747 85 3 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 85 4 performs perform VERB american_scientific_journal-2747 85 5 the the DET american_scientific_journal-2747 85 6 following follow VERB american_scientific_journal-2747 85 7 steps step NOUN american_scientific_journal-2747 85 8 to to PART american_scientific_journal-2747 85 9 forge forge VERB american_scientific_journal-2747 85 10 a a DET american_scientific_journal-2747 85 11 valid valid ADJ american_scientific_journal-2747 85 12 signature signature NOUN american_scientific_journal-2747 85 13 : : PUNCT american_scientific_journal-2747 85 14 1 1 X american_scientific_journal-2747 85 15 ) ) PUNCT american_scientific_journal-2747 85 16 compute compute NOUN american_scientific_journal-2747 85 17 𝑅𝑅′𝑖𝑖 𝑅𝑅′𝑖𝑖 PROPN american_scientific_journal-2747 85 18 = = PUNCT american_scientific_journal-2747 85 19 𝑒𝑒𝑖𝑖π‘₯π‘₯0 𝑒𝑒𝑖𝑖π‘₯π‘₯0 NOUN american_scientific_journal-2747 85 20 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 85 21 𝑛𝑛. 𝑛𝑛. NOUN american_scientific_journal-2747 85 22 2 2 X american_scientific_journal-2747 85 23 ) ) PUNCT american_scientific_journal-2747 85 24 compute compute NOUN american_scientific_journal-2747 85 25 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 85 26 = = SYM american_scientific_journal-2747 85 27 𝑅𝑅′𝑖𝑖 𝑅𝑅′𝑖𝑖 PROPN american_scientific_journal-2747 85 28 βŠ• βŠ• PROPN american_scientific_journal-2747 85 29 𝑓𝑓𝑖𝑖. 𝑓𝑓𝑖𝑖. ADJ american_scientific_journal-2747 85 30 ( ( PUNCT american_scientific_journal-2747 85 31 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 85 32 has have AUX american_scientific_journal-2747 85 33 obtained obtain VERB american_scientific_journal-2747 85 34 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 85 35 in in ADP american_scientific_journal-2747 85 36 the the DET american_scientific_journal-2747 85 37 message message NOUN american_scientific_journal-2747 85 38 recovery recovery NOUN american_scientific_journal-2747 85 39 phase phase NOUN american_scientific_journal-2747 85 40 . . PUNCT american_scientific_journal-2747 85 41 ) ) PUNCT american_scientific_journal-2747 86 1 3 3 X american_scientific_journal-2747 86 2 ) ) PUNCT american_scientific_journal-2747 86 3 send send VERB american_scientific_journal-2747 86 4 the the DET american_scientific_journal-2747 86 5 forged forge VERB american_scientific_journal-2747 86 6 signature signature NOUN american_scientific_journal-2747 86 7 ( ( PUNCT american_scientific_journal-2747 86 8 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 86 9 , , PUNCT american_scientific_journal-2747 86 10 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 86 11 , , PUNCT american_scientific_journal-2747 86 12 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 86 13 ) ) PUNCT american_scientific_journal-2747 86 14 to to PART american_scientific_journal-2747 86 15 π‘ˆπ‘ˆπ‘‚π‘‚. π‘ˆπ‘ˆπ‘‚π‘‚. VERB american_scientific_journal-2747 86 16 the the DET american_scientific_journal-2747 86 17 signature signature NOUN american_scientific_journal-2747 86 18 ( ( PUNCT american_scientific_journal-2747 86 19 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 86 20 , , PUNCT american_scientific_journal-2747 86 21 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 86 22 , , PUNCT american_scientific_journal-2747 86 23 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 86 24 ) ) PUNCT american_scientific_journal-2747 86 25 can can AUX american_scientific_journal-2747 86 26 be be AUX american_scientific_journal-2747 86 27 verified verify VERB american_scientific_journal-2747 86 28 easily easily ADV american_scientific_journal-2747 86 29 since since SCONJ american_scientific_journal-2747 86 30 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 86 31 = = SYM american_scientific_journal-2747 86 32 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 PROPN american_scientific_journal-2747 86 33 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 86 34 = = SYM american_scientific_journal-2747 86 35 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 86 36 , , PUNCT american_scientific_journal-2747 86 37 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 86 38 ) ) PUNCT american_scientific_journal-2747 86 39 , , PUNCT american_scientific_journal-2747 86 40 and and CCONJ american_scientific_journal-2747 86 41 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 86 42 = = SYM american_scientific_journal-2747 86 43 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 86 44 ) ) PUNCT american_scientific_journal-2747 87 1 + + CCONJ american_scientific_journal-2747 87 2 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 87 3 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 87 4 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 87 5 , , PUNCT american_scientific_journal-2747 87 6 therefore therefore ADV american_scientific_journal-2747 87 7 ; ; PUNCT american_scientific_journal-2747 87 8 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 87 9 can can AUX american_scientific_journal-2747 87 10 claim claim VERB american_scientific_journal-2747 87 11 that that SCONJ american_scientific_journal-2747 87 12 ( ( PUNCT american_scientific_journal-2747 87 13 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 87 14 , , PUNCT american_scientific_journal-2747 87 15 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 87 16 , , PUNCT american_scientific_journal-2747 87 17 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 87 18 ) ) PUNCT american_scientific_journal-2747 87 19 is be AUX american_scientific_journal-2747 87 20 the the DET american_scientific_journal-2747 87 21 signature signature NOUN american_scientific_journal-2747 87 22 of of ADP american_scientific_journal-2747 87 23 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 87 24 signed sign VERB american_scientific_journal-2747 87 25 by by ADP american_scientific_journal-2747 87 26 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 87 27 for for ADP american_scientific_journal-2747 87 28 him he PRON american_scientific_journal-2747 87 29 . . PUNCT american_scientific_journal-2747 88 1 in in ADP american_scientific_journal-2747 88 2 case case NOUN american_scientific_journal-2747 88 3 of of ADP american_scientific_journal-2747 88 4 any any DET american_scientific_journal-2747 88 5 disputes dispute NOUN american_scientific_journal-2747 88 6 over over ADP american_scientific_journal-2747 88 7 the the DET american_scientific_journal-2747 88 8 validity validity NOUN american_scientific_journal-2747 88 9 of of ADP american_scientific_journal-2747 88 10 the the DET american_scientific_journal-2747 88 11 signature signature NOUN american_scientific_journal-2747 88 12 , , PUNCT american_scientific_journal-2747 88 13 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 88 14 publishes publish VERB american_scientific_journal-2747 88 15 ( ( PUNCT american_scientific_journal-2747 88 16 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 88 17 , , PUNCT american_scientific_journal-2747 88 18 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 88 19 , , PUNCT american_scientific_journal-2747 88 20 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 88 21 ) ) PUNCT american_scientific_journal-2747 88 22 , , PUNCT american_scientific_journal-2747 88 23 to to PART american_scientific_journal-2747 88 24 satisfy satisfy VERB american_scientific_journal-2747 88 25 whomever whomever ADJ american_scientific_journal-2747 88 26 questions question NOUN american_scientific_journal-2747 88 27 the the DET american_scientific_journal-2747 88 28 validity validity NOUN american_scientific_journal-2747 88 29 of of ADP american_scientific_journal-2747 88 30 ( ( PUNCT american_scientific_journal-2747 88 31 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 88 32 , , PUNCT american_scientific_journal-2747 88 33 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 88 34 , , PUNCT american_scientific_journal-2747 88 35 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 88 36 ) ) PUNCT american_scientific_journal-2747 88 37 . . PUNCT american_scientific_journal-2747 89 1 the the DET american_scientific_journal-2747 89 2 reason reason NOUN american_scientific_journal-2747 89 3 of of ADP american_scientific_journal-2747 89 4 vulnerability vulnerability NOUN american_scientific_journal-2747 89 5 of of ADP american_scientific_journal-2747 89 6 wu wu PROPN american_scientific_journal-2747 89 7 and and CCONJ american_scientific_journal-2747 89 8 xu xu PROPN american_scientific_journal-2747 89 9 ’s ’s PART american_scientific_journal-2747 89 10 scheme scheme NOUN american_scientific_journal-2747 89 11 to to ADP american_scientific_journal-2747 89 12 this this DET american_scientific_journal-2747 89 13 attack attack NOUN american_scientific_journal-2747 89 14 is be AUX american_scientific_journal-2747 89 15 that that SCONJ american_scientific_journal-2747 89 16 the the DET american_scientific_journal-2747 89 17 verification verification NOUN american_scientific_journal-2747 89 18 equations equation NOUN american_scientific_journal-2747 89 19 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 89 20 = = PUNCT american_scientific_journal-2747 89 21 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 89 22 , , PUNCT american_scientific_journal-2747 89 23 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 89 24 ) ) PUNCT american_scientific_journal-2747 89 25 , , PUNCT american_scientific_journal-2747 89 26 and and CCONJ american_scientific_journal-2747 89 27 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 89 28 = = SYM american_scientific_journal-2747 89 29 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 89 30 ) ) PUNCT american_scientific_journal-2747 90 1 + + CCONJ american_scientific_journal-2747 91 1 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 91 2 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 91 3 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 91 4 can can AUX american_scientific_journal-2747 91 5 not not PART american_scientific_journal-2747 91 6 detect detect VERB american_scientific_journal-2747 91 7 the the DET american_scientific_journal-2747 91 8 change change NOUN american_scientific_journal-2747 91 9 in in ADP american_scientific_journal-2747 91 10 the the DET american_scientific_journal-2747 91 11 amount amount NOUN american_scientific_journal-2747 91 12 of of ADP american_scientific_journal-2747 91 13 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 91 14 which which PRON american_scientific_journal-2747 91 15 is be AUX american_scientific_journal-2747 91 16 replaced replace VERB american_scientific_journal-2747 91 17 by by ADP american_scientific_journal-2747 91 18 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 91 19 in in ADP american_scientific_journal-2747 91 20 the the DET american_scientific_journal-2747 91 21 forged forged ADJ american_scientific_journal-2747 91 22 signature signature NOUN american_scientific_journal-2747 91 23 . . PUNCT american_scientific_journal-2747 92 1 american american ADJ american_scientific_journal-2747 92 2 scientific scientific ADJ american_scientific_journal-2747 92 3 research research PROPN american_scientific_journal-2747 92 4 journal journal NOUN american_scientific_journal-2747 92 5 for for ADP american_scientific_journal-2747 92 6 engineering engineering NOUN american_scientific_journal-2747 92 7 , , PUNCT american_scientific_journal-2747 92 8 technology technology NOUN american_scientific_journal-2747 92 9 , , PUNCT american_scientific_journal-2747 92 10 and and CCONJ american_scientific_journal-2747 92 11 sciences science NOUN american_scientific_journal-2747 92 12 ( ( PUNCT american_scientific_journal-2747 92 13 asrjets asrjet NOUN american_scientific_journal-2747 92 14 ) ) PUNCT american_scientific_journal-2747 92 15 ( ( PUNCT american_scientific_journal-2747 92 16 2017 2017 NUM american_scientific_journal-2747 92 17 ) ) PUNCT american_scientific_journal-2747 92 18 volume volume NOUN american_scientific_journal-2747 92 19 28 28 NUM american_scientific_journal-2747 92 20 , , PUNCT american_scientific_journal-2747 92 21 no no DET american_scientific_journal-2747 92 22 1 1 NUM american_scientific_journal-2747 92 23 , , PUNCT american_scientific_journal-2747 92 24 pp pp ADV american_scientific_journal-2747 92 25 257 257 NUM american_scientific_journal-2747 92 26 - - SYM american_scientific_journal-2747 92 27 265 265 NUM american_scientific_journal-2747 92 28 262 262 NUM american_scientific_journal-2747 92 29 the the DET american_scientific_journal-2747 92 30 process process NOUN american_scientific_journal-2747 92 31 of of ADP american_scientific_journal-2747 92 32 the the DET american_scientific_journal-2747 92 33 attack attack NOUN american_scientific_journal-2747 92 34 is be AUX american_scientific_journal-2747 92 35 illustrated illustrate VERB american_scientific_journal-2747 92 36 in in ADP american_scientific_journal-2747 92 37 figure figure NOUN american_scientific_journal-2747 92 38 2 2 NUM american_scientific_journal-2747 92 39 . . NOUN american_scientific_journal-2747 92 40 phase phase NOUN american_scientific_journal-2747 92 41 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 92 42 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 92 43 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 92 44 signature signature NOUN american_scientific_journal-2747 92 45 generation generation NOUN american_scientific_journal-2747 92 46 phase phase NOUN american_scientific_journal-2747 92 47 computes compute VERB american_scientific_journal-2747 92 48 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 92 49 = = PRON american_scientific_journal-2747 92 50 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– VERB american_scientific_journal-2747 92 51 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 92 52 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 92 53 , , PUNCT american_scientific_journal-2747 92 54 and and CCONJ american_scientific_journal-2747 92 55 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 ADV american_scientific_journal-2747 92 56 = = PUNCT american_scientific_journal-2747 92 57 ( ( PUNCT american_scientific_journal-2747 92 58 𝑦𝑦𝑗𝑗𝐹𝐹 𝑦𝑦𝑗𝑗𝐹𝐹 PROPN american_scientific_journal-2747 92 59 οΏ½ οΏ½ PROPN american_scientific_journal-2747 92 60 𝐼𝐼𝐷𝐷𝑗𝑗 𝐼𝐼𝐷𝐷𝑗𝑗 PROPN american_scientific_journal-2747 92 61 οΏ½ οΏ½ PROPN american_scientific_journal-2747 92 62 + + CCONJ american_scientific_journal-2747 92 63 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘– 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘– VERB american_scientific_journal-2747 92 64 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 92 65 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 92 66 , , PUNCT american_scientific_journal-2747 92 67 and and CCONJ american_scientific_journal-2747 92 68 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 92 69 = = SYM american_scientific_journal-2747 92 70 𝐹𝐹1(𝑀𝑀 𝐹𝐹1(𝑀𝑀 PROPN american_scientific_journal-2747 92 71 ) ) PUNCT american_scientific_journal-2747 93 1 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 93 2 𝐹𝐹2 𝐹𝐹2 PROPN american_scientific_journal-2747 93 3 οΏ½ οΏ½ PROPN american_scientific_journal-2747 93 4 𝐹𝐹1(𝑀𝑀) 𝐹𝐹1(𝑀𝑀) NOUN american_scientific_journal-2747 93 5 οΏ½ οΏ½ NOUN american_scientific_journal-2747 93 6 ⨁𝑀𝑀 ⨁𝑀𝑀 PROPN american_scientific_journal-2747 93 7 , , PUNCT american_scientific_journal-2747 93 8 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 93 9 = = PUNCT american_scientific_journal-2747 94 1 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PROPN american_scientific_journal-2747 94 2 βŠ• βŠ• PROPN american_scientific_journal-2747 94 3 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 94 4 , , PUNCT american_scientific_journal-2747 94 5 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 94 6 = = PUNCT american_scientific_journal-2747 94 7 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 94 8 , , PUNCT american_scientific_journal-2747 94 9 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 94 10 ) ) PUNCT american_scientific_journal-2747 94 11 , , PUNCT american_scientific_journal-2747 94 12 and and CCONJ american_scientific_journal-2747 94 13 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 94 14 = = PUNCT american_scientific_journal-2747 94 15 π‘˜π‘˜π‘–π‘– π‘˜π‘˜π‘–π‘– ADJ american_scientific_journal-2747 94 16 βˆ’ βˆ’ PROPN american_scientific_journal-2747 94 17 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 94 18 . . PUNCT american_scientific_journal-2747 95 1 𝑑𝑑𝑖𝑖. 𝑑𝑑𝑖𝑖. ADV american_scientific_journal-2747 96 1 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 96 2 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 96 3 ( ( PUNCT american_scientific_journal-2747 96 4 𝑒𝑒𝑖𝑖,𝑠𝑠𝑖𝑖,𝑇𝑇𝑖𝑖) 𝑒𝑒𝑖𝑖,𝑠𝑠𝑖𝑖,𝑇𝑇𝑖𝑖) PROPN american_scientific_journal-2747 96 5 οΏ½ οΏ½ NOUN american_scientific_journal-2747 96 6 ⎯⎯⎯⎯ ⎯⎯⎯⎯ ADJ american_scientific_journal-2747 96 7 οΏ½ οΏ½ ADJ american_scientific_journal-2747 96 8 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 96 9 message message NOUN american_scientific_journal-2747 96 10 recovery recovery NOUN american_scientific_journal-2747 96 11 phase phase NOUN american_scientific_journal-2747 96 12 calculates calculate VERB american_scientific_journal-2747 96 13 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PUNCT american_scientific_journal-2747 96 14 = = PUNCT american_scientific_journal-2747 96 15 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 NOUN american_scientific_journal-2747 96 16 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 96 17 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 96 18 , , PUNCT american_scientific_journal-2747 96 19 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 96 20 = = NOUN american_scientific_journal-2747 96 21 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 ADJ american_scientific_journal-2747 96 22 , , PUNCT american_scientific_journal-2747 96 23 and and CCONJ american_scientific_journal-2747 96 24 obtains obtain VERB american_scientific_journal-2747 96 25 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 96 26 = = SYM american_scientific_journal-2747 96 27 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 PROPN american_scientific_journal-2747 96 28 . . PUNCT american_scientific_journal-2747 97 1 computes compute VERB american_scientific_journal-2747 97 2 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 97 3 = = SYM american_scientific_journal-2747 97 4 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 97 5 , , PUNCT american_scientific_journal-2747 97 6 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 97 7 ) ) PUNCT american_scientific_journal-2747 97 8 . . PUNCT american_scientific_journal-2747 98 1 then then ADV american_scientific_journal-2747 98 2 , , PUNCT american_scientific_journal-2747 98 3 checks check VERB american_scientific_journal-2747 98 4 whether whether SCONJ american_scientific_journal-2747 98 5 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 98 6 = = SYM american_scientific_journal-2747 98 7 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 98 8 ) ) PUNCT american_scientific_journal-2747 99 1 + + CCONJ american_scientific_journal-2747 99 2 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 99 3 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 99 4 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 99 5 insider insider NOUN american_scientific_journal-2747 99 6 forgery forgery NOUN american_scientific_journal-2747 99 7 attack attack NOUN american_scientific_journal-2747 99 8 computes compute VERB american_scientific_journal-2747 99 9 𝑅𝑅′𝑖𝑖 𝑅𝑅′𝑖𝑖 NOUN american_scientific_journal-2747 99 10 = = SYM american_scientific_journal-2747 99 11 𝑒𝑒𝑖𝑖π‘₯π‘₯0 𝑒𝑒𝑖𝑖π‘₯π‘₯0 NOUN american_scientific_journal-2747 99 12 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 99 13 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 99 14 , , PUNCT american_scientific_journal-2747 99 15 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 99 16 = = SYM american_scientific_journal-2747 99 17 𝑅𝑅′𝑖𝑖 𝑅𝑅′𝑖𝑖 PROPN american_scientific_journal-2747 99 18 βŠ• βŠ• PROPN american_scientific_journal-2747 99 19 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 PROPN american_scientific_journal-2747 99 20 forges forge VERB american_scientific_journal-2747 99 21 the the DET american_scientific_journal-2747 99 22 signature signature NOUN american_scientific_journal-2747 99 23 and and CCONJ american_scientific_journal-2747 99 24 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 99 25 ( ( PUNCT american_scientific_journal-2747 99 26 𝑒𝑒𝑖𝑖,𝑠𝑠𝑖𝑖,𝑇𝑇′𝑖𝑖) 𝑒𝑒𝑖𝑖,𝑠𝑠𝑖𝑖,𝑇𝑇′𝑖𝑖) X american_scientific_journal-2747 99 27 οΏ½ οΏ½ ADP american_scientific_journal-2747 99 28 ⎯⎯⎯⎯⎯ ⎯⎯⎯⎯⎯ NOUN american_scientific_journal-2747 99 29 οΏ½ οΏ½ PROPN american_scientific_journal-2747 99 30 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 99 31 chooses choose VERB american_scientific_journal-2747 99 32 π‘₯π‘₯𝑂𝑂 π‘₯π‘₯𝑂𝑂 NOUN american_scientific_journal-2747 99 33 as as ADP american_scientific_journal-2747 99 34 his his PRON american_scientific_journal-2747 99 35 secret secret ADJ american_scientific_journal-2747 99 36 key key NOUN american_scientific_journal-2747 99 37 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 99 38 π‘₯π‘₯𝑂𝑂 π‘₯π‘₯𝑂𝑂 NOUN american_scientific_journal-2747 99 39 οΏ½ οΏ½ NOUN american_scientific_journal-2747 99 40 ⎯⎯⎯⎯ ⎯⎯⎯⎯ NOUN american_scientific_journal-2747 99 41 οΏ½ οΏ½ NOUN american_scientific_journal-2747 99 42 π‘ˆπ‘ˆπ‘‚π‘‚ π‘ˆπ‘ˆπ‘‚π‘‚ NOUN american_scientific_journal-2747 99 43 claims claim VERB american_scientific_journal-2747 99 44 that that SCONJ american_scientific_journal-2747 99 45 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 99 46 signed sign VERB american_scientific_journal-2747 99 47 ( ( PUNCT american_scientific_journal-2747 99 48 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 99 49 , , PUNCT american_scientific_journal-2747 99 50 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 99 51 , , PUNCT american_scientific_journal-2747 99 52 𝑇𝑇′𝑖𝑖 𝑇𝑇′𝑖𝑖 PROPN american_scientific_journal-2747 99 53 ) ) PUNCT american_scientific_journal-2747 99 54 for for ADP american_scientific_journal-2747 99 55 him he PRON american_scientific_journal-2747 99 56 . . PUNCT american_scientific_journal-2747 100 1 figure figure VERB american_scientific_journal-2747 100 2 2 2 NUM american_scientific_journal-2747 100 3 : : PUNCT american_scientific_journal-2747 100 4 insider insider NOUN american_scientific_journal-2747 100 5 forgery forgery NOUN american_scientific_journal-2747 100 6 attack attack NOUN american_scientific_journal-2747 100 7 to to ADP american_scientific_journal-2747 100 8 the the DET american_scientific_journal-2747 100 9 scheme scheme NOUN american_scientific_journal-2747 100 10 of of ADP american_scientific_journal-2747 100 11 wu wu PROPN american_scientific_journal-2747 100 12 and and CCONJ american_scientific_journal-2747 100 13 xu xu PROPN american_scientific_journal-2747 100 14 4 4 X american_scientific_journal-2747 100 15 . . X american_scientific_journal-2747 100 16 modification modification NOUN american_scientific_journal-2747 100 17 of of ADP american_scientific_journal-2747 100 18 wu wu PROPN american_scientific_journal-2747 100 19 and and CCONJ american_scientific_journal-2747 100 20 xu xu PROPN american_scientific_journal-2747 100 21 ’s ’s PART american_scientific_journal-2747 100 22 self self NOUN american_scientific_journal-2747 100 23 - - PUNCT american_scientific_journal-2747 100 24 certified certify VERB american_scientific_journal-2747 100 25 digital digital ADJ american_scientific_journal-2747 100 26 signature signature NOUN american_scientific_journal-2747 100 27 scheme scheme NOUN american_scientific_journal-2747 100 28 with with ADP american_scientific_journal-2747 100 29 message message NOUN american_scientific_journal-2747 100 30 recovery recovery NOUN american_scientific_journal-2747 100 31 this this DET american_scientific_journal-2747 100 32 section section NOUN american_scientific_journal-2747 100 33 represents represent VERB american_scientific_journal-2747 100 34 a a DET american_scientific_journal-2747 100 35 slight slight ADJ american_scientific_journal-2747 100 36 modification modification NOUN american_scientific_journal-2747 100 37 to to PART american_scientific_journal-2747 100 38 overcome overcome VERB american_scientific_journal-2747 100 39 the the DET american_scientific_journal-2747 100 40 security security NOUN american_scientific_journal-2747 100 41 flaw flaw NOUN american_scientific_journal-2747 100 42 in in ADP american_scientific_journal-2747 100 43 the the DET american_scientific_journal-2747 100 44 scheme scheme NOUN american_scientific_journal-2747 100 45 of of ADP american_scientific_journal-2747 100 46 wu wu PROPN american_scientific_journal-2747 100 47 and and CCONJ american_scientific_journal-2747 100 48 xu xu PROPN american_scientific_journal-2747 100 49 . . PUNCT american_scientific_journal-2747 101 1 given give VERB american_scientific_journal-2747 101 2 the the DET american_scientific_journal-2747 101 3 fact fact NOUN american_scientific_journal-2747 101 4 that that SCONJ american_scientific_journal-2747 101 5 the the DET american_scientific_journal-2747 101 6 reason reason NOUN american_scientific_journal-2747 101 7 of of ADP american_scientific_journal-2747 101 8 insecurity insecurity NOUN american_scientific_journal-2747 101 9 of of ADP american_scientific_journal-2747 101 10 wu wu PROPN american_scientific_journal-2747 101 11 and and CCONJ american_scientific_journal-2747 101 12 xu xu PROPN american_scientific_journal-2747 101 13 ’s ’s PART american_scientific_journal-2747 101 14 scheme scheme NOUN american_scientific_journal-2747 101 15 against against ADP american_scientific_journal-2747 101 16 insider insider NOUN american_scientific_journal-2747 101 17 forgery forgery NOUN american_scientific_journal-2747 101 18 attack attack NOUN american_scientific_journal-2747 101 19 is be AUX american_scientific_journal-2747 101 20 that that SCONJ american_scientific_journal-2747 101 21 the the DET american_scientific_journal-2747 101 22 verification verification NOUN american_scientific_journal-2747 101 23 equation equation NOUN american_scientific_journal-2747 101 24 can can AUX american_scientific_journal-2747 101 25 not not PART american_scientific_journal-2747 101 26 find find VERB american_scientific_journal-2747 101 27 the the DET american_scientific_journal-2747 101 28 change change NOUN american_scientific_journal-2747 101 29 in in ADP american_scientific_journal-2747 101 30 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 101 31 , , PUNCT american_scientific_journal-2747 101 32 it it PRON american_scientific_journal-2747 101 33 is be AUX american_scientific_journal-2747 101 34 sufficed suffice VERB american_scientific_journal-2747 101 35 to to PART american_scientific_journal-2747 101 36 make make VERB american_scientific_journal-2747 101 37 a a DET american_scientific_journal-2747 101 38 slight slight ADJ american_scientific_journal-2747 101 39 change change NOUN american_scientific_journal-2747 101 40 in in ADP american_scientific_journal-2747 101 41 the the DET american_scientific_journal-2747 101 42 equation equation NOUN american_scientific_journal-2747 101 43 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 101 44 = = PUNCT american_scientific_journal-2747 101 45 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 101 46 , , PUNCT american_scientific_journal-2747 101 47 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 101 48 ) ) PUNCT american_scientific_journal-2747 101 49 . . PUNCT american_scientific_journal-2747 102 1 with with ADP american_scientific_journal-2747 102 2 changing change VERB american_scientific_journal-2747 102 3 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 102 4 = = SYM american_scientific_journal-2747 102 5 𝐻𝐻(𝑀𝑀 𝐻𝐻(𝑀𝑀 ADV american_scientific_journal-2747 102 6 , , PUNCT american_scientific_journal-2747 102 7 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 102 8 ) ) PUNCT american_scientific_journal-2747 102 9 to to ADP american_scientific_journal-2747 102 10 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 102 11 = = SYM american_scientific_journal-2747 102 12 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 102 13 , , PUNCT american_scientific_journal-2747 102 14 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 102 15 ) ) PUNCT american_scientific_journal-2747 102 16 where where SCONJ american_scientific_journal-2747 102 17 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 102 18 = = SYM american_scientific_journal-2747 102 19 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 102 20 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 102 21 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 102 22 , , PUNCT american_scientific_journal-2747 102 23 the the DET american_scientific_journal-2747 102 24 insider insider NOUN american_scientific_journal-2747 102 25 forgery forgery NOUN american_scientific_journal-2747 102 26 attack attack NOUN american_scientific_journal-2747 102 27 is be AUX american_scientific_journal-2747 102 28 not not PART american_scientific_journal-2747 102 29 successful successful ADJ american_scientific_journal-2747 102 30 against against ADP american_scientific_journal-2747 102 31 the the DET american_scientific_journal-2747 102 32 modified modify VERB american_scientific_journal-2747 102 33 scheme scheme NOUN american_scientific_journal-2747 102 34 because because SCONJ american_scientific_journal-2747 102 35 any any DET american_scientific_journal-2747 102 36 changes change NOUN american_scientific_journal-2747 102 37 in in ADP american_scientific_journal-2747 102 38 term term NOUN american_scientific_journal-2747 102 39 of of ADP american_scientific_journal-2747 102 40 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 102 41 would would AUX american_scientific_journal-2747 102 42 cause cause VERB american_scientific_journal-2747 102 43 changes change NOUN american_scientific_journal-2747 102 44 in in ADP american_scientific_journal-2747 102 45 the the DET american_scientific_journal-2747 102 46 amount amount NOUN american_scientific_journal-2747 102 47 of of ADP american_scientific_journal-2747 102 48 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 102 49 and and CCONJ american_scientific_journal-2747 102 50 𝑑𝑑𝑖𝑖. 𝑑𝑑𝑖𝑖. ADV american_scientific_journal-2747 102 51 the the DET american_scientific_journal-2747 102 52 modified modify VERB american_scientific_journal-2747 102 53 scheme scheme NOUN american_scientific_journal-2747 102 54 has have VERB american_scientific_journal-2747 102 55 also also ADV american_scientific_journal-2747 102 56 four four NUM american_scientific_journal-2747 102 57 phases phase NOUN american_scientific_journal-2747 102 58 : : PUNCT american_scientific_journal-2747 102 59 system system NOUN american_scientific_journal-2747 102 60 initialization initialization NOUN american_scientific_journal-2747 102 61 phase phase NOUN american_scientific_journal-2747 102 62 , , PUNCT american_scientific_journal-2747 102 63 signature signature NOUN american_scientific_journal-2747 102 64 generation generation NOUN american_scientific_journal-2747 102 65 phase phase NOUN american_scientific_journal-2747 102 66 , , PUNCT american_scientific_journal-2747 102 67 message message NOUN american_scientific_journal-2747 102 68 recovery recovery NOUN american_scientific_journal-2747 102 69 phase phase NOUN american_scientific_journal-2747 102 70 , , PUNCT american_scientific_journal-2747 102 71 and and CCONJ american_scientific_journal-2747 102 72 dispute dispute NOUN american_scientific_journal-2747 102 73 arbitration arbitration NOUN american_scientific_journal-2747 102 74 phase phase NOUN american_scientific_journal-2747 102 75 . . PUNCT american_scientific_journal-2747 103 1 the the DET american_scientific_journal-2747 103 2 modified modify VERB american_scientific_journal-2747 103 3 scheme scheme NOUN american_scientific_journal-2747 103 4 is be AUX american_scientific_journal-2747 103 5 represented represent VERB american_scientific_journal-2747 103 6 in in ADP american_scientific_journal-2747 103 7 figure figure NOUN american_scientific_journal-2747 103 8 3 3 NUM american_scientific_journal-2747 103 9 . . PROPN american_scientific_journal-2747 103 10 4.1 4.1 NUM american_scientific_journal-2747 103 11 . . PUNCT american_scientific_journal-2747 103 12 system system NOUN american_scientific_journal-2747 103 13 initialization initialization NOUN american_scientific_journal-2747 103 14 phase phase NOUN american_scientific_journal-2747 103 15 this this DET american_scientific_journal-2747 103 16 phase phase NOUN american_scientific_journal-2747 103 17 is be AUX american_scientific_journal-2747 103 18 exactly exactly ADV american_scientific_journal-2747 103 19 the the DET american_scientific_journal-2747 103 20 same same ADJ american_scientific_journal-2747 103 21 as as ADP american_scientific_journal-2747 103 22 system system NOUN american_scientific_journal-2747 103 23 initialization initialization NOUN american_scientific_journal-2747 103 24 phase phase NOUN american_scientific_journal-2747 103 25 in in ADP american_scientific_journal-2747 103 26 wu wu PROPN american_scientific_journal-2747 103 27 and and CCONJ american_scientific_journal-2747 103 28 xu xu PROPN american_scientific_journal-2747 103 29 ’s ’s PART american_scientific_journal-2747 103 30 scheme scheme NOUN american_scientific_journal-2747 103 31 . . PUNCT american_scientific_journal-2747 104 1 american american ADJ american_scientific_journal-2747 104 2 scientific scientific ADJ american_scientific_journal-2747 104 3 research research PROPN american_scientific_journal-2747 104 4 journal journal NOUN american_scientific_journal-2747 104 5 for for ADP american_scientific_journal-2747 104 6 engineering engineering NOUN american_scientific_journal-2747 104 7 , , PUNCT american_scientific_journal-2747 104 8 technology technology NOUN american_scientific_journal-2747 104 9 , , PUNCT american_scientific_journal-2747 104 10 and and CCONJ american_scientific_journal-2747 104 11 sciences science NOUN american_scientific_journal-2747 104 12 ( ( PUNCT american_scientific_journal-2747 104 13 asrjets asrjet NOUN american_scientific_journal-2747 104 14 ) ) PUNCT american_scientific_journal-2747 104 15 ( ( PUNCT american_scientific_journal-2747 104 16 2017 2017 NUM american_scientific_journal-2747 104 17 ) ) PUNCT american_scientific_journal-2747 104 18 volume volume NOUN american_scientific_journal-2747 104 19 28 28 NUM american_scientific_journal-2747 104 20 , , PUNCT american_scientific_journal-2747 104 21 no no DET american_scientific_journal-2747 104 22 1 1 NUM american_scientific_journal-2747 104 23 , , PUNCT american_scientific_journal-2747 104 24 pp pp ADV american_scientific_journal-2747 104 25 257 257 NUM american_scientific_journal-2747 104 26 - - SYM american_scientific_journal-2747 104 27 265 265 NUM american_scientific_journal-2747 104 28 263 263 NUM american_scientific_journal-2747 104 29 4.2 4.2 NUM american_scientific_journal-2747 104 30 . . PUNCT american_scientific_journal-2747 105 1 signature signature NOUN american_scientific_journal-2747 105 2 generation generation NOUN american_scientific_journal-2747 105 3 phase phase NOUN american_scientific_journal-2747 105 4 when when SCONJ american_scientific_journal-2747 105 5 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 105 6 wants want VERB american_scientific_journal-2747 105 7 to to PART american_scientific_journal-2747 105 8 sign sign VERB american_scientific_journal-2747 105 9 a a DET american_scientific_journal-2747 105 10 message message NOUN american_scientific_journal-2747 105 11 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 105 12 with with ADP american_scientific_journal-2747 105 13 the the DET american_scientific_journal-2747 105 14 length length NOUN american_scientific_journal-2747 105 15 π‘˜π‘˜ π‘˜π‘˜ NOUN american_scientific_journal-2747 105 16 to to ADP american_scientific_journal-2747 105 17 the the DET american_scientific_journal-2747 105 18 verifier verifier NOUN american_scientific_journal-2747 105 19 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 105 20 , , PUNCT american_scientific_journal-2747 105 21 he he PRON american_scientific_journal-2747 105 22 chooses choose VERB american_scientific_journal-2747 105 23 a a DET american_scientific_journal-2747 105 24 number number NOUN american_scientific_journal-2747 105 25 π‘˜π‘˜π‘–π‘– π‘˜π‘˜π‘–π‘– ADV american_scientific_journal-2747 105 26 randomly randomly ADV american_scientific_journal-2747 105 27 and and CCONJ american_scientific_journal-2747 105 28 calculates calculate VERB american_scientific_journal-2747 105 29 the the DET american_scientific_journal-2747 105 30 following following ADJ american_scientific_journal-2747 105 31 variables variable NOUN american_scientific_journal-2747 105 32 : : PUNCT american_scientific_journal-2747 105 33 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 105 34 = = PRON american_scientific_journal-2747 105 35 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– VERB american_scientific_journal-2747 105 36 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 105 37 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 105 38 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PRON american_scientific_journal-2747 105 39 = = PUNCT american_scientific_journal-2747 105 40 ( ( PUNCT american_scientific_journal-2747 105 41 𝑦𝑦𝑗𝑗𝐹𝐹 𝑦𝑦𝑗𝑗𝐹𝐹 PROPN american_scientific_journal-2747 105 42 οΏ½ οΏ½ PROPN american_scientific_journal-2747 105 43 𝐼𝐼𝐷𝐷𝑗𝑗 𝐼𝐼𝐷𝐷𝑗𝑗 PROPN american_scientific_journal-2747 105 44 οΏ½ οΏ½ PROPN american_scientific_journal-2747 105 45 + + CCONJ american_scientific_journal-2747 105 46 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘– 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘– VERB american_scientific_journal-2747 105 47 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 105 48 𝑛𝑛 𝑛𝑛 VERB american_scientific_journal-2747 105 49 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 105 50 = = SYM american_scientific_journal-2747 105 51 𝐹𝐹1(𝑀𝑀 𝐹𝐹1(𝑀𝑀 PROPN american_scientific_journal-2747 105 52 ) ) PUNCT american_scientific_journal-2747 105 53 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 105 54 𝐹𝐹2 𝐹𝐹2 PROPN american_scientific_journal-2747 105 55 οΏ½ οΏ½ PROPN american_scientific_journal-2747 105 56 𝐹𝐹1(𝑀𝑀) 𝐹𝐹1(𝑀𝑀) NOUN american_scientific_journal-2747 105 57 οΏ½ οΏ½ PROPN american_scientific_journal-2747 105 58 ⨁𝑀𝑀 ⨁𝑀𝑀 PROPN american_scientific_journal-2747 105 59 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 105 60 = = PUNCT american_scientific_journal-2747 106 1 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PROPN american_scientific_journal-2747 106 2 βŠ• βŠ• VERB american_scientific_journal-2747 106 3 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 106 4 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 107 1 = = SYM american_scientific_journal-2747 107 2 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 107 3 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 107 4 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 107 5 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 107 6 = = PUNCT american_scientific_journal-2747 107 7 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 107 8 , , PUNCT american_scientific_journal-2747 107 9 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 107 10 ) ) PUNCT american_scientific_journal-2747 107 11 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 107 12 = = PUNCT american_scientific_journal-2747 107 13 π‘˜π‘˜π‘–π‘– π‘˜π‘˜π‘–π‘– ADJ american_scientific_journal-2747 107 14 βˆ’ βˆ’ PROPN american_scientific_journal-2747 107 15 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 107 16 . . PUNCT american_scientific_journal-2747 108 1 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 108 2 . . PUNCT american_scientific_journal-2747 109 1 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 109 2 where where SCONJ american_scientific_journal-2747 109 3 β€œ " PUNCT american_scientific_journal-2747 109 4 ⨁ ⨁ PROPN american_scientific_journal-2747 109 5 ” " PUNCT american_scientific_journal-2747 109 6 denotes denote VERB american_scientific_journal-2747 109 7 the the DET american_scientific_journal-2747 109 8 exclusive exclusive ADJ american_scientific_journal-2747 109 9 - - PUNCT american_scientific_journal-2747 109 10 or or CCONJ american_scientific_journal-2747 109 11 operator operator NOUN american_scientific_journal-2747 109 12 , , PUNCT american_scientific_journal-2747 109 13 and and CCONJ american_scientific_journal-2747 109 14 β€œ " PUNCT american_scientific_journal-2747 109 15 βˆ₯ βˆ₯ NUM american_scientific_journal-2747 109 16 ” " PUNCT american_scientific_journal-2747 109 17 denotes denote VERB american_scientific_journal-2747 109 18 the the DET american_scientific_journal-2747 109 19 concatenation concatenation NOUN american_scientific_journal-2747 109 20 operator operator NOUN american_scientific_journal-2747 109 21 . . PUNCT american_scientific_journal-2747 110 1 then then ADV american_scientific_journal-2747 110 2 , , PUNCT american_scientific_journal-2747 110 3 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 110 4 sends send VERB american_scientific_journal-2747 110 5 ( ( PUNCT american_scientific_journal-2747 110 6 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 110 7 , , PUNCT american_scientific_journal-2747 110 8 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 110 9 , , PUNCT american_scientific_journal-2747 110 10 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 110 11 ) ) PUNCT american_scientific_journal-2747 110 12 to to ADP american_scientific_journal-2747 110 13 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 110 14 as as ADP american_scientific_journal-2747 110 15 the the DET american_scientific_journal-2747 110 16 signature signature NOUN american_scientific_journal-2747 110 17 of of ADP american_scientific_journal-2747 110 18 𝑀𝑀. 𝑀𝑀. PROPN american_scientific_journal-2747 110 19 4.3 4.3 NUM american_scientific_journal-2747 110 20 . . PUNCT american_scientific_journal-2747 111 1 message message NOUN american_scientific_journal-2747 111 2 recovery recovery NOUN american_scientific_journal-2747 111 3 phase phase NOUN american_scientific_journal-2747 111 4 upon upon SCONJ american_scientific_journal-2747 111 5 receiving receive VERB american_scientific_journal-2747 111 6 ( ( PUNCT american_scientific_journal-2747 111 7 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 111 8 , , PUNCT american_scientific_journal-2747 111 9 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 111 10 , , PUNCT american_scientific_journal-2747 111 11 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 111 12 ) ) PUNCT american_scientific_journal-2747 111 13 , , PUNCT american_scientific_journal-2747 111 14 the the DET american_scientific_journal-2747 111 15 verifier verifier NOUN american_scientific_journal-2747 111 16 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 111 17 computes compute VERB american_scientific_journal-2747 111 18 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 ADV american_scientific_journal-2747 111 19 = = PUNCT american_scientific_journal-2747 111 20 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 NOUN american_scientific_journal-2747 111 21 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 111 22 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 111 23 , , PUNCT american_scientific_journal-2747 111 24 and and CCONJ american_scientific_journal-2747 111 25 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 111 26 = = NOUN american_scientific_journal-2747 111 27 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 111 28 . . PUNCT american_scientific_journal-2747 112 1 then then ADV american_scientific_journal-2747 112 2 , , PUNCT american_scientific_journal-2747 112 3 he he PRON american_scientific_journal-2747 112 4 can can AUX american_scientific_journal-2747 112 5 achieve achieve VERB american_scientific_journal-2747 112 6 the the DET american_scientific_journal-2747 112 7 message message NOUN american_scientific_journal-2747 112 8 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 112 9 = = SYM american_scientific_journal-2747 112 10 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 PROPN american_scientific_journal-2747 112 11 , , PUNCT american_scientific_journal-2747 112 12 where where SCONJ american_scientific_journal-2747 112 13 [ [ X american_scientific_journal-2747 112 14 𝑓𝑓𝑖𝑖]𝑙𝑙1 𝑓𝑓𝑖𝑖]𝑙𝑙1 X american_scientific_journal-2747 112 15 is be AUX american_scientific_journal-2747 112 16 the the DET american_scientific_journal-2747 112 17 left left ADJ american_scientific_journal-2747 112 18 𝑙𝑙1 𝑙𝑙1 NOUN american_scientific_journal-2747 112 19 bits bit NOUN american_scientific_journal-2747 112 20 of of ADP american_scientific_journal-2747 112 21 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 112 22 , , PUNCT american_scientific_journal-2747 112 23 and and CCONJ american_scientific_journal-2747 112 24 [ [ X american_scientific_journal-2747 112 25 𝑓𝑓𝑖𝑖]𝑙𝑙2 𝑓𝑓𝑖𝑖]𝑙𝑙2 NOUN american_scientific_journal-2747 112 26 is be AUX american_scientific_journal-2747 112 27 the the DET american_scientific_journal-2747 112 28 right right ADJ american_scientific_journal-2747 112 29 𝑙𝑙2 𝑙𝑙2 NOUN american_scientific_journal-2747 112 30 bits bit NOUN american_scientific_journal-2747 112 31 of of ADP american_scientific_journal-2747 112 32 𝑓𝑓𝑖𝑖. 𝑓𝑓𝑖𝑖. NOUN american_scientific_journal-2747 112 33 in in ADP american_scientific_journal-2747 112 34 order order NOUN american_scientific_journal-2747 112 35 to to PART american_scientific_journal-2747 112 36 check check VERB american_scientific_journal-2747 112 37 the the DET american_scientific_journal-2747 112 38 validity validity NOUN american_scientific_journal-2747 112 39 of of ADP american_scientific_journal-2747 112 40 the the DET american_scientific_journal-2747 112 41 signature signature NOUN american_scientific_journal-2747 112 42 , , PUNCT american_scientific_journal-2747 112 43 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 112 44 first first ADV american_scientific_journal-2747 112 45 computes compute VERB american_scientific_journal-2747 112 46 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 112 47 = = SYM american_scientific_journal-2747 112 48 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 112 49 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 112 50 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 112 51 , , PUNCT american_scientific_journal-2747 112 52 and and CCONJ american_scientific_journal-2747 112 53 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 112 54 = = PUNCT american_scientific_journal-2747 112 55 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 112 56 , , PUNCT american_scientific_journal-2747 112 57 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 112 58 ) ) PUNCT american_scientific_journal-2747 112 59 . . PUNCT american_scientific_journal-2747 113 1 then then ADV american_scientific_journal-2747 113 2 , , PUNCT american_scientific_journal-2747 113 3 he he PRON american_scientific_journal-2747 113 4 checks check VERB american_scientific_journal-2747 113 5 whether whether SCONJ american_scientific_journal-2747 113 6 the the DET american_scientific_journal-2747 113 7 following follow VERB american_scientific_journal-2747 113 8 equation equation NOUN american_scientific_journal-2747 113 9 holds hold VERB american_scientific_journal-2747 113 10 or or CCONJ american_scientific_journal-2747 113 11 not not PART american_scientific_journal-2747 113 12 . . PUNCT american_scientific_journal-2747 114 1 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 114 2 = = SYM american_scientific_journal-2747 114 3 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 114 4 ) ) PUNCT american_scientific_journal-2747 115 1 + + CCONJ american_scientific_journal-2747 116 1 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 116 2 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 116 3 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 116 4 if if SCONJ american_scientific_journal-2747 116 5 the the DET american_scientific_journal-2747 116 6 above above ADJ american_scientific_journal-2747 116 7 equation equation NOUN american_scientific_journal-2747 116 8 holds hold VERB american_scientific_journal-2747 116 9 , , PUNCT american_scientific_journal-2747 116 10 he he PRON american_scientific_journal-2747 116 11 accepts accept VERB american_scientific_journal-2747 116 12 the the DET american_scientific_journal-2747 116 13 signature signature NOUN american_scientific_journal-2747 116 14 as as ADP american_scientific_journal-2747 116 15 a a DET american_scientific_journal-2747 116 16 valid valid ADJ american_scientific_journal-2747 116 17 signature signature NOUN american_scientific_journal-2747 116 18 for for ADP american_scientific_journal-2747 116 19 𝑀𝑀. 𝑀𝑀. NOUN american_scientific_journal-2747 116 20 otherwise otherwise ADV american_scientific_journal-2747 116 21 , , PUNCT american_scientific_journal-2747 116 22 he he PRON american_scientific_journal-2747 116 23 rejects reject VERB american_scientific_journal-2747 116 24 the the DET american_scientific_journal-2747 116 25 signature signature NOUN american_scientific_journal-2747 116 26 . . PUNCT american_scientific_journal-2747 117 1 if if SCONJ american_scientific_journal-2747 117 2 the the DET american_scientific_journal-2747 117 3 signature signature NOUN american_scientific_journal-2747 117 4 is be AUX american_scientific_journal-2747 117 5 valid valid ADJ american_scientific_journal-2747 117 6 and and CCONJ american_scientific_journal-2747 117 7 signed sign VERB american_scientific_journal-2747 117 8 by by ADP american_scientific_journal-2747 117 9 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 117 10 , , PUNCT american_scientific_journal-2747 117 11 then then ADV american_scientific_journal-2747 117 12 the the DET american_scientific_journal-2747 117 13 above above ADJ american_scientific_journal-2747 117 14 equation equation NOUN american_scientific_journal-2747 117 15 must must AUX american_scientific_journal-2747 117 16 hold hold VERB american_scientific_journal-2747 117 17 because because SCONJ american_scientific_journal-2747 117 18 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 117 19 ) ) PUNCT american_scientific_journal-2747 118 1 + + CCONJ american_scientific_journal-2747 118 2 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 118 3 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 118 4 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 118 5 = = PUNCT american_scientific_journal-2747 118 6 𝑔𝑔𝑠𝑠𝑖𝑖(𝑔𝑔π‘₯π‘₯𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑔𝑔π‘₯π‘₯𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 118 7 = = SYM american_scientific_journal-2747 118 8 𝑔𝑔𝑠𝑠𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖 ADJ american_scientific_journal-2747 118 9 .π‘”π‘”π‘˜π‘˜π‘–π‘–βˆ’π‘ π‘ π‘–π‘– .π‘”π‘”π‘˜π‘˜π‘–π‘–βˆ’π‘ π‘ π‘–π‘– NOUN american_scientific_journal-2747 118 10 = = PUNCT american_scientific_journal-2747 118 11 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– NOUN american_scientific_journal-2747 118 12 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 118 13 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 118 14 , , PUNCT american_scientific_journal-2747 118 15 and and CCONJ american_scientific_journal-2747 118 16 as as SCONJ american_scientific_journal-2747 118 17 mentioned mention VERB american_scientific_journal-2747 118 18 in in ADP american_scientific_journal-2747 118 19 signature signature NOUN american_scientific_journal-2747 118 20 generation generation NOUN american_scientific_journal-2747 118 21 phase phase NOUN american_scientific_journal-2747 118 22 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– NOUN american_scientific_journal-2747 118 23 = = NOUN american_scientific_journal-2747 118 24 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 118 25 π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. VERB american_scientific_journal-2747 118 26 4.4 4.4 NUM american_scientific_journal-2747 118 27 . . PUNCT american_scientific_journal-2747 119 1 dispute dispute NOUN american_scientific_journal-2747 119 2 arbitration arbitration NOUN american_scientific_journal-2747 119 3 phase phase NOUN american_scientific_journal-2747 119 4 in in ADP american_scientific_journal-2747 119 5 case case NOUN american_scientific_journal-2747 119 6 of of ADP american_scientific_journal-2747 119 7 any any DET american_scientific_journal-2747 119 8 dispute dispute NOUN american_scientific_journal-2747 119 9 over over ADP american_scientific_journal-2747 119 10 the the DET american_scientific_journal-2747 119 11 validity validity NOUN american_scientific_journal-2747 119 12 of of ADP american_scientific_journal-2747 119 13 the the DET american_scientific_journal-2747 119 14 signature signature NOUN american_scientific_journal-2747 119 15 , , PUNCT american_scientific_journal-2747 119 16 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 119 17 can can AUX american_scientific_journal-2747 119 18 publish publish VERB american_scientific_journal-2747 119 19 ( ( PUNCT american_scientific_journal-2747 119 20 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 119 21 , , PUNCT american_scientific_journal-2747 119 22 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 119 23 , , PUNCT american_scientific_journal-2747 119 24 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 119 25 ) ) PUNCT american_scientific_journal-2747 119 26 , , PUNCT american_scientific_journal-2747 119 27 and and CCONJ american_scientific_journal-2747 119 28 anyone anyone PRON american_scientific_journal-2747 119 29 can can AUX american_scientific_journal-2747 119 30 confirm confirm VERB american_scientific_journal-2747 119 31 the the DET american_scientific_journal-2747 119 32 american american PROPN american_scientific_journal-2747 119 33 scientific scientific ADJ american_scientific_journal-2747 119 34 research research PROPN american_scientific_journal-2747 119 35 journal journal NOUN american_scientific_journal-2747 119 36 for for ADP american_scientific_journal-2747 119 37 engineering engineering NOUN american_scientific_journal-2747 119 38 , , PUNCT american_scientific_journal-2747 119 39 technology technology NOUN american_scientific_journal-2747 119 40 , , PUNCT american_scientific_journal-2747 119 41 and and CCONJ american_scientific_journal-2747 119 42 sciences science NOUN american_scientific_journal-2747 119 43 ( ( PUNCT american_scientific_journal-2747 119 44 asrjets asrjet NOUN american_scientific_journal-2747 119 45 ) ) PUNCT american_scientific_journal-2747 119 46 ( ( PUNCT american_scientific_journal-2747 119 47 2017 2017 NUM american_scientific_journal-2747 119 48 ) ) PUNCT american_scientific_journal-2747 119 49 volume volume NOUN american_scientific_journal-2747 119 50 28 28 NUM american_scientific_journal-2747 119 51 , , PUNCT american_scientific_journal-2747 119 52 no no DET american_scientific_journal-2747 119 53 1 1 NUM american_scientific_journal-2747 119 54 , , PUNCT american_scientific_journal-2747 119 55 pp pp ADV american_scientific_journal-2747 119 56 257 257 NUM american_scientific_journal-2747 119 57 - - SYM american_scientific_journal-2747 119 58 265 265 NUM american_scientific_journal-2747 119 59 264 264 NUM american_scientific_journal-2747 119 60 validity validity NOUN american_scientific_journal-2747 119 61 of of ADP american_scientific_journal-2747 119 62 the the DET american_scientific_journal-2747 119 63 signature signature NOUN american_scientific_journal-2747 119 64 by by ADP american_scientific_journal-2747 119 65 the the DET american_scientific_journal-2747 119 66 following follow VERB american_scientific_journal-2747 119 67 equation equation NOUN american_scientific_journal-2747 119 68 : : PUNCT american_scientific_journal-2747 119 69 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 119 70 = = PUNCT american_scientific_journal-2747 119 71 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 119 72 , , PUNCT american_scientific_journal-2747 119 73 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 119 74 ) ) PUNCT american_scientific_journal-2747 119 75 phase phase NOUN american_scientific_journal-2747 119 76 𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆 NOUN american_scientific_journal-2747 119 77 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– PROPN american_scientific_journal-2747 119 78 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— ADJ american_scientific_journal-2747 119 79 system system NOUN american_scientific_journal-2747 119 80 initialization initialization NOUN american_scientific_journal-2747 119 81 phase phase NOUN american_scientific_journal-2747 119 82 computes compute VERB american_scientific_journal-2747 119 83 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-2747 119 84 = = SYM american_scientific_journal-2747 119 85 ( ( PUNCT american_scientific_journal-2747 119 86 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 PROPN american_scientific_journal-2747 119 87 βˆ’ βˆ’ PUNCT american_scientific_journal-2747 119 88 𝐼𝐼𝐼𝐼𝑖𝑖)𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖)βˆ’1π‘šπ‘šπ‘šπ‘šπ‘šπ‘š 𝐼𝐼𝐼𝐼𝑖𝑖)𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖)βˆ’1π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 119 89 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 119 90 , , PUNCT american_scientific_journal-2747 119 91 and and CCONJ american_scientific_journal-2747 119 92 publicize publicize VERB american_scientific_journal-2747 119 93 𝑦𝑦𝑖𝑖 𝑦𝑦𝑖𝑖 NOUN american_scientific_journal-2747 119 94 . . PUNCT american_scientific_journal-2747 120 1 chooses choose VERB american_scientific_journal-2747 120 2 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 120 3 randomly randomly ADV american_scientific_journal-2747 120 4 and and CCONJ american_scientific_journal-2747 120 5 computes compute VERB american_scientific_journal-2747 120 6 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 VERB american_scientific_journal-2747 120 7 = = SYM american_scientific_journal-2747 120 8 𝑔𝑔π‘₯π‘₯𝑖𝑖 𝑔𝑔π‘₯π‘₯𝑖𝑖 ADJ american_scientific_journal-2747 120 9 π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘›π‘›. NOUN american_scientific_journal-2747 120 10 submits submit NOUN american_scientific_journal-2747 120 11 ( ( PUNCT american_scientific_journal-2747 120 12 𝑝𝑝𝑖𝑖 𝑝𝑝𝑖𝑖 X american_scientific_journal-2747 120 13 , , PUNCT american_scientific_journal-2747 120 14 𝐼𝐼𝐼𝐼𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖 PROPN american_scientific_journal-2747 120 15 ) ) PUNCT american_scientific_journal-2747 120 16 to to ADP american_scientific_journal-2747 120 17 the the DET american_scientific_journal-2747 120 18 𝑆𝑆𝑆𝑆. 𝑆𝑆𝑆𝑆. PROPN american_scientific_journal-2747 120 19 signature signature NOUN american_scientific_journal-2747 120 20 generation generation NOUN american_scientific_journal-2747 120 21 phase phase NOUN american_scientific_journal-2747 120 22 computes compute VERB american_scientific_journal-2747 120 23 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 120 24 = = PRON american_scientific_journal-2747 120 25 π‘”π‘”π‘˜π‘˜π‘–π‘– π‘”π‘”π‘˜π‘˜π‘–π‘– NOUN american_scientific_journal-2747 120 26 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 120 27 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 120 28 , , PUNCT american_scientific_journal-2747 120 29 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 ADV american_scientific_journal-2747 120 30 = = PUNCT american_scientific_journal-2747 120 31 ( ( PUNCT american_scientific_journal-2747 120 32 𝑦𝑦𝑗𝑗𝐹𝐹 𝑦𝑦𝑗𝑗𝐹𝐹 PROPN american_scientific_journal-2747 120 33 οΏ½ οΏ½ PROPN american_scientific_journal-2747 120 34 𝐼𝐼𝐷𝐷𝑗𝑗 𝐼𝐼𝐷𝐷𝑗𝑗 PROPN american_scientific_journal-2747 120 35 οΏ½ οΏ½ PROPN american_scientific_journal-2747 120 36 + + CCONJ american_scientific_journal-2747 120 37 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘–π‘šπ‘šπ‘šπ‘šπ‘šπ‘š 𝐼𝐼𝐼𝐼𝑗𝑗)π‘˜π‘˜π‘–π‘–π‘šπ‘šπ‘šπ‘šπ‘šπ‘š PROPN american_scientific_journal-2747 120 38 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 120 39 , , PUNCT american_scientific_journal-2747 120 40 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 120 41 = = X american_scientific_journal-2747 120 42 𝐹𝐹1(𝑀𝑀 𝐹𝐹1(𝑀𝑀 PROPN american_scientific_journal-2747 120 43 ) ) PUNCT american_scientific_journal-2747 120 44 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 120 45 𝐹𝐹2 𝐹𝐹2 PROPN american_scientific_journal-2747 120 46 οΏ½ οΏ½ PROPN american_scientific_journal-2747 120 47 𝐹𝐹1(𝑀𝑀) 𝐹𝐹1(𝑀𝑀) NOUN american_scientific_journal-2747 120 48 οΏ½ οΏ½ NOUN american_scientific_journal-2747 120 49 ⨁𝑀𝑀 ⨁𝑀𝑀 PROPN american_scientific_journal-2747 120 50 , , PUNCT american_scientific_journal-2747 120 51 and and CCONJ american_scientific_journal-2747 120 52 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 120 53 = = PUNCT american_scientific_journal-2747 121 1 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PROPN american_scientific_journal-2747 121 2 βŠ• βŠ• VERB american_scientific_journal-2747 121 3 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 121 4 then then ADV american_scientific_journal-2747 121 5 , , PUNCT american_scientific_journal-2747 121 6 computes compute VERB american_scientific_journal-2747 121 7 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 121 8 = = SYM american_scientific_journal-2747 121 9 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 121 10 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 121 11 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 121 12 , , PUNCT american_scientific_journal-2747 121 13 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 121 14 = = PUNCT american_scientific_journal-2747 121 15 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 121 16 , , PUNCT american_scientific_journal-2747 121 17 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 121 18 ) ) PUNCT american_scientific_journal-2747 121 19 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 121 20 = = PUNCT american_scientific_journal-2747 122 1 π‘˜π‘˜π‘–π‘– π‘˜π‘˜π‘–π‘– ADJ american_scientific_journal-2747 122 2 βˆ’ βˆ’ PROPN american_scientific_journal-2747 122 3 π‘₯π‘₯𝑖𝑖 π‘₯π‘₯𝑖𝑖 NOUN american_scientific_journal-2747 122 4 . . PUNCT american_scientific_journal-2747 123 1 𝑑𝑑𝑖𝑖. 𝑑𝑑𝑖𝑖. ADV american_scientific_journal-2747 124 1 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 124 2 π‘ˆπ‘ˆπ‘–π‘– π‘ˆπ‘ˆπ‘–π‘– NOUN american_scientific_journal-2747 124 3 sends send VERB american_scientific_journal-2747 124 4 ( ( PUNCT american_scientific_journal-2747 124 5 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 124 6 , , PUNCT american_scientific_journal-2747 124 7 𝑠𝑠𝑖𝑖 𝑠𝑠𝑖𝑖 NOUN american_scientific_journal-2747 124 8 , , PUNCT american_scientific_journal-2747 124 9 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 124 10 ) ) PUNCT american_scientific_journal-2747 124 11 to to ADP american_scientific_journal-2747 124 12 π‘ˆπ‘ˆπ‘—π‘— π‘ˆπ‘ˆπ‘—π‘— PROPN american_scientific_journal-2747 124 13 message message NOUN american_scientific_journal-2747 124 14 recovery recovery NOUN american_scientific_journal-2747 124 15 phase phase NOUN american_scientific_journal-2747 124 16 calculates calculate VERB american_scientific_journal-2747 124 17 𝑅𝑅𝑖𝑖 𝑅𝑅𝑖𝑖 PUNCT american_scientific_journal-2747 124 18 = = PUNCT american_scientific_journal-2747 124 19 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 𝑒𝑒𝑖𝑖π‘₯π‘₯𝑗𝑗 NOUN american_scientific_journal-2747 124 20 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 124 21 𝑛𝑛 𝑛𝑛 NOUN american_scientific_journal-2747 124 22 , , PUNCT american_scientific_journal-2747 124 23 𝑓𝑓𝑖𝑖 𝑓𝑓𝑖𝑖 ADJ american_scientific_journal-2747 124 24 = = NOUN american_scientific_journal-2747 124 25 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 𝑅𝑅𝑖𝑖⨁𝑇𝑇𝑖𝑖 ADJ american_scientific_journal-2747 124 26 , , PUNCT american_scientific_journal-2747 124 27 and and CCONJ american_scientific_journal-2747 124 28 obtains obtain VERB american_scientific_journal-2747 124 29 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 124 30 = = SYM american_scientific_journal-2747 124 31 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 𝐹𝐹2([𝑓𝑓𝑖𝑖]𝑙𝑙1)⨁[𝑓𝑓𝑖𝑖]𝑙𝑙2 PROPN american_scientific_journal-2747 124 32 . . PUNCT american_scientific_journal-2747 125 1 computes compute VERB american_scientific_journal-2747 125 2 π‘€π‘€βˆ— π‘€π‘€βˆ— NOUN american_scientific_journal-2747 126 1 = = SYM american_scientific_journal-2747 126 2 𝑀𝑀 𝑀𝑀 PROPN american_scientific_journal-2747 126 3 βˆ₯ βˆ₯ PUNCT american_scientific_journal-2747 126 4 𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖 PROPN american_scientific_journal-2747 126 5 , , PUNCT american_scientific_journal-2747 126 6 𝑑𝑑𝑖𝑖 𝑑𝑑𝑖𝑖 ADV american_scientific_journal-2747 126 7 = = PUNCT american_scientific_journal-2747 126 8 𝐻𝐻(π‘€π‘€βˆ— 𝐻𝐻(π‘€π‘€βˆ— NOUN american_scientific_journal-2747 126 9 , , PUNCT american_scientific_journal-2747 126 10 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 126 11 ) ) PUNCT american_scientific_journal-2747 126 12 . . PUNCT american_scientific_journal-2747 127 1 then then ADV american_scientific_journal-2747 127 2 , , PUNCT american_scientific_journal-2747 127 3 checks check VERB american_scientific_journal-2747 127 4 whether whether SCONJ american_scientific_journal-2747 127 5 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 NOUN american_scientific_journal-2747 127 6 = = SYM american_scientific_journal-2747 127 7 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 𝑔𝑔𝑠𝑠𝑖𝑖(𝑦𝑦𝑖𝑖𝐹𝐹(𝐼𝐼𝐷𝐷𝑖𝑖 NOUN american_scientific_journal-2747 127 8 ) ) PUNCT american_scientific_journal-2747 128 1 + + CCONJ american_scientific_journal-2747 128 2 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑖𝑖𝑓𝑓𝑖𝑖 NOUN american_scientific_journal-2747 128 3 π‘šπ‘šπ‘šπ‘šπ‘šπ‘š π‘šπ‘šπ‘šπ‘šπ‘šπ‘š ADJ american_scientific_journal-2747 128 4 𝑛𝑛 𝑛𝑛 PRON american_scientific_journal-2747 128 5 figure figure VERB american_scientific_journal-2747 128 6 3 3 NUM american_scientific_journal-2747 128 7 : : PUNCT american_scientific_journal-2747 128 8 modification modification NOUN american_scientific_journal-2747 128 9 of of ADP american_scientific_journal-2747 128 10 an an DET american_scientific_journal-2747 128 11 improved improved ADJ american_scientific_journal-2747 128 12 self self NOUN american_scientific_journal-2747 128 13 - - PUNCT american_scientific_journal-2747 128 14 certified certify VERB american_scientific_journal-2747 128 15 digital digital ADJ american_scientific_journal-2747 128 16 signature signature NOUN american_scientific_journal-2747 128 17 scheme scheme NOUN american_scientific_journal-2747 128 18 with with ADP american_scientific_journal-2747 128 19 message message NOUN american_scientific_journal-2747 128 20 recovery recovery NOUN american_scientific_journal-2747 128 21 5 5 NUM american_scientific_journal-2747 128 22 . . PUNCT american_scientific_journal-2747 128 23 conclusion conclusion NOUN american_scientific_journal-2747 128 24 in in ADP american_scientific_journal-2747 128 25 the the DET american_scientific_journal-2747 128 26 present present ADJ american_scientific_journal-2747 128 27 paper paper NOUN american_scientific_journal-2747 128 28 an an DET american_scientific_journal-2747 128 29 improved improved ADJ american_scientific_journal-2747 128 30 self self NOUN american_scientific_journal-2747 128 31 - - PUNCT american_scientific_journal-2747 128 32 certified certify VERB american_scientific_journal-2747 128 33 digital digital ADJ american_scientific_journal-2747 128 34 signature signature NOUN american_scientific_journal-2747 128 35 scheme scheme NOUN american_scientific_journal-2747 128 36 with with ADP american_scientific_journal-2747 128 37 message message NOUN american_scientific_journal-2747 128 38 recovery recovery NOUN american_scientific_journal-2747 128 39 is be AUX american_scientific_journal-2747 128 40 reviewed review VERB american_scientific_journal-2747 128 41 . . PUNCT american_scientific_journal-2747 129 1 a a DET american_scientific_journal-2747 129 2 security security NOUN american_scientific_journal-2747 129 3 analysis analysis NOUN american_scientific_journal-2747 129 4 for for ADP american_scientific_journal-2747 129 5 the the DET american_scientific_journal-2747 129 6 scheme scheme NOUN american_scientific_journal-2747 129 7 is be AUX american_scientific_journal-2747 129 8 presented present VERB american_scientific_journal-2747 129 9 by by ADP american_scientific_journal-2747 129 10 proposing propose VERB american_scientific_journal-2747 129 11 an an DET american_scientific_journal-2747 129 12 insider insider NOUN american_scientific_journal-2747 129 13 forgery forgery NOUN american_scientific_journal-2747 129 14 attack attack NOUN american_scientific_journal-2747 129 15 against against ADP american_scientific_journal-2747 129 16 this this DET american_scientific_journal-2747 129 17 scheme scheme NOUN american_scientific_journal-2747 129 18 , , PUNCT american_scientific_journal-2747 129 19 and and CCONJ american_scientific_journal-2747 129 20 it it PRON american_scientific_journal-2747 129 21 is be AUX american_scientific_journal-2747 129 22 demonstrated demonstrate VERB american_scientific_journal-2747 129 23 that that SCONJ american_scientific_journal-2747 129 24 this this DET american_scientific_journal-2747 129 25 scheme scheme NOUN american_scientific_journal-2747 129 26 can can AUX american_scientific_journal-2747 129 27 not not PART american_scientific_journal-2747 129 28 withstand withstand VERB american_scientific_journal-2747 129 29 the the DET american_scientific_journal-2747 129 30 attack attack NOUN american_scientific_journal-2747 129 31 . . PUNCT american_scientific_journal-2747 130 1 it it PRON american_scientific_journal-2747 130 2 is be AUX american_scientific_journal-2747 130 3 also also ADV american_scientific_journal-2747 130 4 argued argue VERB american_scientific_journal-2747 130 5 that that SCONJ american_scientific_journal-2747 130 6 in in ADP american_scientific_journal-2747 130 7 modern modern ADJ american_scientific_journal-2747 130 8 electronic electronic ADJ american_scientific_journal-2747 130 9 environments environment NOUN american_scientific_journal-2747 130 10 , , PUNCT american_scientific_journal-2747 130 11 the the DET american_scientific_journal-2747 130 12 aforementioned aforementioned ADJ american_scientific_journal-2747 130 13 attack attack NOUN american_scientific_journal-2747 130 14 can can AUX american_scientific_journal-2747 130 15 cause cause VERB american_scientific_journal-2747 130 16 negative negative ADJ american_scientific_journal-2747 130 17 consequences consequence NOUN american_scientific_journal-2747 130 18 , , PUNCT american_scientific_journal-2747 130 19 particularly particularly ADV american_scientific_journal-2747 130 20 in in ADP american_scientific_journal-2747 130 21 electronic electronic ADJ american_scientific_journal-2747 130 22 commerce commerce NOUN american_scientific_journal-2747 130 23 and and CCONJ american_scientific_journal-2747 130 24 electronic electronic ADJ american_scientific_journal-2747 130 25 voting voting NOUN american_scientific_journal-2747 130 26 systems system NOUN american_scientific_journal-2747 130 27 . . PUNCT american_scientific_journal-2747 131 1 a a DET american_scientific_journal-2747 131 2 slight slight ADJ american_scientific_journal-2747 131 3 improvement improvement NOUN american_scientific_journal-2747 131 4 for for ADP american_scientific_journal-2747 131 5 the the DET american_scientific_journal-2747 131 6 scheme scheme NOUN american_scientific_journal-2747 131 7 is be AUX american_scientific_journal-2747 131 8 suggested suggest VERB american_scientific_journal-2747 131 9 in in ADP american_scientific_journal-2747 131 10 order order NOUN american_scientific_journal-2747 131 11 to to PART american_scientific_journal-2747 131 12 remove remove VERB american_scientific_journal-2747 131 13 the the DET american_scientific_journal-2747 131 14 weakness weakness NOUN american_scientific_journal-2747 131 15 . . PUNCT american_scientific_journal-2747 132 1 the the DET american_scientific_journal-2747 132 2 propose propose ADJ american_scientific_journal-2747 132 3 modification modification NOUN american_scientific_journal-2747 132 4 is be AUX american_scientific_journal-2747 132 5 secure secure ADJ american_scientific_journal-2747 132 6 against against ADP american_scientific_journal-2747 132 7 insider insider NOUN american_scientific_journal-2747 132 8 forgery forgery NOUN american_scientific_journal-2747 132 9 attack attack NOUN american_scientific_journal-2747 132 10 . . PUNCT american_scientific_journal-2747 133 1 acknowledgement acknowledgement NOUN american_scientific_journal-2747 133 2 the the DET american_scientific_journal-2747 133 3 author author NOUN american_scientific_journal-2747 133 4 would would AUX american_scientific_journal-2747 133 5 like like VERB american_scientific_journal-2747 133 6 to to PART american_scientific_journal-2747 133 7 thank thank VERB american_scientific_journal-2747 133 8 the the DET american_scientific_journal-2747 133 9 anonymous anonymous ADJ american_scientific_journal-2747 133 10 reviewers reviewer NOUN american_scientific_journal-2747 133 11 for for ADP american_scientific_journal-2747 133 12 their their PRON american_scientific_journal-2747 133 13 comments comment NOUN american_scientific_journal-2747 133 14 . . PUNCT american_scientific_journal-2747 134 1 american american ADJ american_scientific_journal-2747 134 2 scientific scientific ADJ american_scientific_journal-2747 134 3 research research PROPN american_scientific_journal-2747 134 4 journal journal NOUN american_scientific_journal-2747 134 5 for for ADP american_scientific_journal-2747 134 6 engineering engineering NOUN american_scientific_journal-2747 134 7 , , PUNCT american_scientific_journal-2747 134 8 technology technology NOUN american_scientific_journal-2747 134 9 , , PUNCT american_scientific_journal-2747 134 10 and and CCONJ american_scientific_journal-2747 134 11 sciences science NOUN american_scientific_journal-2747 134 12 ( ( PUNCT american_scientific_journal-2747 134 13 asrjets asrjet NOUN american_scientific_journal-2747 134 14 ) ) PUNCT american_scientific_journal-2747 134 15 ( ( PUNCT american_scientific_journal-2747 134 16 2017 2017 NUM american_scientific_journal-2747 134 17 ) ) PUNCT american_scientific_journal-2747 134 18 volume volume NOUN american_scientific_journal-2747 134 19 28 28 NUM american_scientific_journal-2747 134 20 , , PUNCT american_scientific_journal-2747 134 21 no no DET american_scientific_journal-2747 134 22 1 1 NUM american_scientific_journal-2747 134 23 , , PUNCT american_scientific_journal-2747 134 24 pp pp ADV american_scientific_journal-2747 134 25 257 257 NUM american_scientific_journal-2747 134 26 - - SYM american_scientific_journal-2747 134 27 265 265 NUM american_scientific_journal-2747 134 28 265 265 NUM american_scientific_journal-2747 134 29 references reference NOUN american_scientific_journal-2747 134 30 [ [ X american_scientific_journal-2747 134 31 1 1 NUM american_scientific_journal-2747 134 32 ] ] PUNCT american_scientific_journal-2747 134 33 m. m. NOUN american_scientific_journal-2747 134 34 girault girault NOUN american_scientific_journal-2747 134 35 , , PUNCT american_scientific_journal-2747 134 36 β€œ " PUNCT american_scientific_journal-2747 134 37 self self NOUN american_scientific_journal-2747 134 38 - - PUNCT american_scientific_journal-2747 134 39 certified certify VERB american_scientific_journal-2747 134 40 public public ADJ american_scientific_journal-2747 134 41 - - PUNCT american_scientific_journal-2747 134 42 keys key NOUN american_scientific_journal-2747 134 43 ” " PUNCT american_scientific_journal-2747 134 44 , , PUNCT american_scientific_journal-2747 134 45 advances advance NOUN american_scientific_journal-2747 134 46 in in ADP american_scientific_journal-2747 134 47 cryptology cryptology NOUN american_scientific_journal-2747 134 48 β€” β€” PUNCT american_scientific_journal-2747 134 49 eurocrypt’91 eurocrypt’91 PROPN american_scientific_journal-2747 134 50 , , PUNCT american_scientific_journal-2747 134 51 berlin berlin NOUN american_scientific_journal-2747 134 52 : : PUNCT american_scientific_journal-2747 134 53 springer springer NOUN american_scientific_journal-2747 134 54 , , PUNCT american_scientific_journal-2747 134 55 1991 1991 NUM american_scientific_journal-2747 134 56 , , PUNCT american_scientific_journal-2747 134 57 pp pp ADP american_scientific_journal-2747 134 58 . . PUNCT american_scientific_journal-2747 135 1 491 491 NUM american_scientific_journal-2747 135 2 - - SYM american_scientific_journal-2747 135 3 497 497 NUM american_scientific_journal-2747 135 4 . . PUNCT american_scientific_journal-2747 135 5 
 
 SPACE american_scientific_journal-2747 136 1 [ [ X american_scientific_journal-2747 136 2 2 2 X american_scientific_journal-2747 136 3 ] ] PUNCT american_scientific_journal-2747 136 4 k. k. PROPN american_scientific_journal-2747 136 5 neyberg neyberg PROPN american_scientific_journal-2747 136 6 and and CCONJ american_scientific_journal-2747 136 7 r. r. PROPN american_scientific_journal-2747 136 8 ruppel ruppel NOUN american_scientific_journal-2747 136 9 , , PUNCT american_scientific_journal-2747 136 10 β€œ " PUNCT american_scientific_journal-2747 136 11 message message NOUN american_scientific_journal-2747 136 12 recovery recovery NOUN american_scientific_journal-2747 136 13 for for ADP american_scientific_journal-2747 136 14 signature signature NOUN american_scientific_journal-2747 136 15 schemes scheme NOUN american_scientific_journal-2747 136 16 based base VERB american_scientific_journal-2747 136 17 on on ADP american_scientific_journal-2747 136 18 the the DET american_scientific_journal-2747 136 19 discrete discrete ADJ american_scientific_journal-2747 136 20 logarithm logarithm NOUN american_scientific_journal-2747 136 21 problem problem NOUN american_scientific_journal-2747 136 22 ” " PUNCT american_scientific_journal-2747 136 23 , , PUNCT american_scientific_journal-2747 136 24 advances advance NOUN american_scientific_journal-2747 136 25 in in ADP american_scientific_journal-2747 136 26 cryptologyerocryt’94 cryptologyerocryt’94 NOUN american_scientific_journal-2747 136 27 , , PUNCT american_scientific_journal-2747 136 28 lncs lncs VERB american_scientific_journal-2747 136 29 950 950 NUM american_scientific_journal-2747 136 30 , , PUNCT american_scientific_journal-2747 136 31 berlin berlin PROPN american_scientific_journal-2747 136 32 : : PUNCT american_scientific_journal-2747 136 33 springer springer NOUN american_scientific_journal-2747 136 34 , , PUNCT american_scientific_journal-2747 136 35 1994 1994 NUM american_scientific_journal-2747 136 36 , , PUNCT american_scientific_journal-2747 136 37 pp pp ADJ american_scientific_journal-2747 136 38 . . PUNCT american_scientific_journal-2747 137 1 175 175 NUM american_scientific_journal-2747 137 2 - - SYM american_scientific_journal-2747 137 3 190 190 NUM american_scientific_journal-2747 137 4 . . PUNCT american_scientific_journal-2747 137 5 
 
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PUNCT american_scientific_journal-2747 164 1 http://ieeexplore.ieee.org/document/311896 http://ieeexplore.ieee.org/document/311896 PROPN american_scientific_journal-2747 164 2 http://www.sciencedirect.com/science/article/pii/s0096300302000103 http://www.sciencedirect.com/science/article/pii/s0096300302000103 PROPN american_scientific_journal-2747 165 1 http://www.sciencedirect.com/science/article/pii/s0096300303012220 http://www.sciencedirect.com/science/article/pii/s0096300303012220 ADP american_scientific_journal-2747 165 2 http://onlinelibrary.wiley.com/wol1/doi/10.1002/dac.2673/full http://onlinelibrary.wiley.com/wol1/doi/10.1002/dac.2673/full NOUN american_scientific_journal-2747 165 3 abstract abstract ADJ american_scientific_journal-2747 165 4 2.1 2.1 NUM american_scientific_journal-2747 165 5 . . PUNCT american_scientific_journal-2747 165 6 system system NOUN american_scientific_journal-2747 165 7 initialization initialization NOUN american_scientific_journal-2747 165 8 phase phase NOUN american_scientific_journal-2747 165 9 where where SCONJ american_scientific_journal-2747 165 10 , , PUNCT american_scientific_journal-2747 165 11 𝒍-𝑡. 𝒍-𝑡. 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PUNCT american_scientific_journal-2747 165 25 the the DET american_scientific_journal-2747 165 26 scheme scheme NOUN american_scientific_journal-2747 165 27 can can AUX american_scientific_journal-2747 165 28 deal deal VERB american_scientific_journal-2747 165 29 with with ADP american_scientific_journal-2747 165 30 π‘΄βˆˆ,{𝟎,𝟏}-,𝒍-𝟐 π‘΄βˆˆ,{𝟎,𝟏}-,𝒍-𝟐 PROPN american_scientific_journal-2747 165 31 ... ... PUNCT american_scientific_journal-2747 165 32 in in ADP american_scientific_journal-2747 165 33 this this DET american_scientific_journal-2747 165 34 scheme scheme NOUN american_scientific_journal-2747 165 35 , , PUNCT american_scientific_journal-2747 165 36 π’Œ=,,π₯𝐨𝐠-(𝑷) π’Œ=,,π₯𝐨𝐠-(𝑷) NUM american_scientific_journal-2747 165 37 .. .. PUNCT american_scientific_journal-2747 165 38 ,and ,and PUNCT american_scientific_journal-2747 165 39 𝑷=,𝐦𝐒𝐧-(,𝒑-β€². 𝑷=,𝐦𝐒𝐧-(,𝒑-β€². PROPN american_scientific_journal-2747 165 40 , , PUNCT american_scientific_journal-2747 165 41 , , PUNCT american_scientific_journal-2747 165 42 𝒒-β€². 𝒒-β€². NUM american_scientific_journal-2747 165 43 ) ) PUNCT american_scientific_journal-2747 165 44 .. .. PUNCT american_scientific_journal-2747 166 1 2.2 2.2 NUM american_scientific_journal-2747 166 2 . . PUNCT american_scientific_journal-2747 166 3 signature signature NOUN american_scientific_journal-2747 166 4 generation generation NOUN american_scientific_journal-2747 166 5 phase phase NOUN american_scientific_journal-2747 166 6 at at ADP american_scientific_journal-2747 166 7 last last ADJ american_scientific_journal-2747 166 8 , , PUNCT american_scientific_journal-2747 166 9 , , PUNCT american_scientific_journal-2747 166 10 𝑼-π’Š. 𝑼-π’Š. PUNCT american_scientific_journal-2747 166 11 sends send VERB american_scientific_journal-2747 166 12 ( ( PUNCT american_scientific_journal-2747 166 13 , , PUNCT american_scientific_journal-2747 166 14 𝒆-π’Š. 𝒆-π’Š. PROPN american_scientific_journal-2747 166 15 , , PUNCT american_scientific_journal-2747 166 16 , , PUNCT american_scientific_journal-2747 166 17 𝒔-π’Š. 𝒔-π’Š. PROPN american_scientific_journal-2747 166 18 , , PUNCT american_scientific_journal-2747 166 19 , , PUNCT american_scientific_journal-2747 166 20 𝑻-π’Š. 𝑻-π’Š. NUM american_scientific_journal-2747 166 21 ) ) PUNCT american_scientific_journal-2747 166 22 to to ADP american_scientific_journal-2747 166 23 , , PUNCT american_scientific_journal-2747 166 24 𝑼-𝒋. 𝑼-𝒋. PROPN american_scientific_journal-2747 166 25 as as ADP american_scientific_journal-2747 166 26 the the DET american_scientific_journal-2747 166 27 signature signature NOUN american_scientific_journal-2747 166 28 of of ADP american_scientific_journal-2747 166 29 𝑴. 𝑴. PROPN american_scientific_journal-2747 166 30 2.3 2.3 NUM american_scientific_journal-2747 166 31 . . PUNCT american_scientific_journal-2747 167 1 message message NOUN american_scientific_journal-2747 167 2 recovery recovery NOUN american_scientific_journal-2747 167 3 phase phase NOUN american_scientific_journal-2747 167 4 after after ADP american_scientific_journal-2747 167 5 receiving receive VERB american_scientific_journal-2747 167 6 , , PUNCT american_scientific_journal-2747 167 7 , , PUNCT american_scientific_journal-2747 167 8 𝒆-π’Š. 𝒆-π’Š. PROPN american_scientific_journal-2747 167 9 , , PUNCT american_scientific_journal-2747 167 10 , , PUNCT american_scientific_journal-2747 167 11 𝒔-π’Š. 𝒔-π’Š. PROPN american_scientific_journal-2747 167 12 , , PUNCT american_scientific_journal-2747 167 13 , , PUNCT american_scientific_journal-2747 167 14 𝑻-π’Š 𝑻-π’Š PROPN american_scientific_journal-2747 167 15 .. .. PUNCT american_scientific_journal-2747 167 16 , , PUNCT american_scientific_journal-2747 167 17 the the DET american_scientific_journal-2747 167 18 verifier verifier NOUN american_scientific_journal-2747 167 19 , , PUNCT american_scientific_journal-2747 167 20 𝑼-𝒋. 𝑼-𝒋. NUM american_scientific_journal-2747 167 21 computes compute NOUN american_scientific_journal-2747 167 22 , , PUNCT american_scientific_journal-2747 167 23 𝑹-π’Š.=,,𝒆-π’Š.-,𝒙-𝒋 𝑹-π’Š.=,,𝒆-π’Š.-,𝒙-𝒋 PROPN american_scientific_journal-2747 167 24 .. .. PUNCT american_scientific_journal-2747 167 25 π’Žπ’π’… π’Žπ’π’… NOUN american_scientific_journal-2747 167 26 𝒏 𝒏 NOUN american_scientific_journal-2747 167 27 , , PUNCT american_scientific_journal-2747 167 28 and and CCONJ american_scientific_journal-2747 167 29 calculates calculate NOUN american_scientific_journal-2747 167 30 , , PUNCT american_scientific_journal-2747 167 31 𝒇-π’Š.=,𝑹-π’Š.⨁,𝑻-π’Š 𝒇-π’Š.=,𝑹-π’Š.⨁,𝑻-π’Š INTJ american_scientific_journal-2747 167 32 .. .. PUNCT american_scientific_journal-2747 168 1 then then ADV american_scientific_journal-2747 168 2 , , PUNCT american_scientific_journal-2747 168 3 he he PRON american_scientific_journal-2747 168 4 can can AUX american_scientific_journal-2747 168 5 achieve achieve VERB american_scientific_journal-2747 168 6 the the DET american_scientific_journal-2747 168 7 message message NOUN american_scientific_journal-2747 168 8 𝑴 𝑴 NOUN american_scientific_journal-2747 168 9 by by ADP american_scientific_journal-2747 168 10 the the DET american_scientific_journal-2747 168 11 following follow VERB american_scientific_journal-2747 168 12 equation equation NOUN american_scientific_journal-2747 168 13 2.4 2.4 NUM american_scientific_journal-2747 168 14 . . PUNCT american_scientific_journal-2747 169 1 signature signature NOUN american_scientific_journal-2747 169 2 conversation conversation NOUN american_scientific_journal-2747 169 3 phase phase NOUN american_scientific_journal-2747 169 4 4.1 4.1 NUM american_scientific_journal-2747 169 5 . . PUNCT american_scientific_journal-2747 170 1 system system NOUN american_scientific_journal-2747 170 2 initialization initialization NOUN american_scientific_journal-2747 170 3 phase phase NOUN american_scientific_journal-2747 170 4 this this DET american_scientific_journal-2747 170 5 phase phase NOUN american_scientific_journal-2747 170 6 is be AUX american_scientific_journal-2747 170 7 exactly exactly ADV american_scientific_journal-2747 170 8 the the DET american_scientific_journal-2747 170 9 same same ADJ american_scientific_journal-2747 170 10 as as ADP american_scientific_journal-2747 170 11 system system NOUN american_scientific_journal-2747 170 12 initialization initialization NOUN american_scientific_journal-2747 170 13 phase phase NOUN american_scientific_journal-2747 170 14 in in ADP american_scientific_journal-2747 170 15 wu wu PROPN american_scientific_journal-2747 170 16 and and CCONJ american_scientific_journal-2747 170 17 xu xu PROPN american_scientific_journal-2747 170 18 ’s ’s PART american_scientific_journal-2747 170 19 scheme scheme NOUN american_scientific_journal-2747 170 20 . . PUNCT american_scientific_journal-2747 171 1 4.2 4.2 NUM american_scientific_journal-2747 171 2 . . PUNCT american_scientific_journal-2747 171 3 signature signature NOUN american_scientific_journal-2747 171 4 generation generation NOUN american_scientific_journal-2747 171 5 phase phase NOUN american_scientific_journal-2747 171 6 4.3 4.3 NUM american_scientific_journal-2747 171 7 . . PUNCT american_scientific_journal-2747 171 8 message message NOUN american_scientific_journal-2747 171 9 recovery recovery NOUN american_scientific_journal-2747 171 10 phase phase NOUN american_scientific_journal-2747 171 11 4.4 4.4 NUM american_scientific_journal-2747 171 12 . . PUNCT american_scientific_journal-2747 172 1 dispute dispute NOUN american_scientific_journal-2747 172 2 arbitration arbitration NOUN american_scientific_journal-2747 172 3 phase phase NOUN american_scientific_journal-2747 172 4 acknowledgement acknowledgement NOUN american_scientific_journal-2747 172 5 references reference VERB