TX_1~ABS:AT/TX_2:ABS~AT


UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1 87

1. INTRODUCTION

Computing technology is seeing significant progress and 
significant interest, especially when the computation outsourcing 
has been outsourced to a third party as the cloud is the most 
frequently used form [1]. That is why many companies no longer 
trust to store their sensitive data in the cloud, which uses traditional 
unsecured encryption systems [2]. From this, the need to use 
homomorphic encryption for banking data is coming, which 
is a new approach that can help banks to increase data security 
and management [3]. There are two types of  homomorphic 
cryptosystems: Partially homomorphic systems and fully 
homomorphic systems [4]. Partially homomorphic schemes 

support one of  the additions or multiplication operations, these 
systems are divided into two parts according to the process that 
supports like the RSA, where it only supports the multiplication 
process and does not support the addition process, for example, 
if  we have two numbers M1, M2 and they are encrypted by the 
RSA, then its value becomes C1, C2 and on obtaining the product 
of  multiplying the two encrypted values C1 * C2 = C3 and then 
we decrypt the encrypted output C3, we will get a result similar to 
M1 * M2 = M3, but if  we add the two values C1 + C2 = C4 and 
when decrypting the result C4 we do not get a result similar to M1 
+ M2 = M4. On the contrary, when the two values are encrypted 
using Paillier, we find that only the result of  C1+C2=C5 is similar 
to M1+M2=M3 and C1*C2=C6 do not equal to M1+M2=M4. 
Therefore, we say that the two algorithms (RSA and Paillier) are 
not a fully homomorphic systems [5], [6]. The first FHE was 
given in 2009 by Craig Gentry [7]. Researchers first researched 
a (FHE) system in the late last century, specifically at the end of  
the seventies, and soon after, in 1987, RSA was published, the 
RSA algorithm became a leading approach by many researchers 
because at that time there was no idea of  the public key cipher 

A Proposed Fully Homomorphic for Securing 
Cloud Banking Data at Rest
Zana Thalage Omar1,2*, Fadhil Salman abed1,2
1University of Human Development, College of Science and Technology, Department of Computer Science, 
Sulaymaniyah, Kurdistan Region of Iraq, Iraq, 2University of Sulaimani, College of Science, Computer Department, 
Sulaymaniyah, Kurdistan Region of Iraq, Iraq

A B S T R A C T
Fully homomorphic encryption (FHE) reaped the importance and amazement of most researchers and followers in data 
encryption issues, as programs are allowed to perform arithmetic operations on encrypted data without decrypting it and 
obtain results similar to the effects of arithmetic operations on unencrypted data. The first (FHE) model was introduced 
by Craig Gentry in 2009, and it was just theoretical research, but later significant progress was made on it, this research 
offers FHE system based on directly of factoring big prime numbers which consider open problem now, The proposed 
scheme offers a fully homomorphic system for data encryption and stores it in encrypted form on the cloud based on a 
new algorithm that has been tried on a local cloud and compared with two previous encryption systems (RSA and Paillier) 
and shows us that this algorithm reduces the time of encryption and decryption by 5 times compared to other systems.

Index Terms: Cloud Computing Security, Encryption, Decryption, Cloud Storage, Homomorphic Encryption

Corresponding author’s e-mail: Zana Thalage Omar, University of Human Development, College of Science and Technology, Department 
of Computer Science, Sulaymaniyah, Kurdistan Region of Iraq, Iraq, University of Sulaimani, College of Science, Computer Department, 
Sulaymaniyah, Kurdistan Region of Iraq, Iraq. E-mail: zana.th.omar@gmail.com

Received: 13-03-2020 Accepted: 10-05-2020 Published: 12-05-2020

Access this article online

DOI: 10.21928/uhdjst.v4n1y2020.pp87-95 E-ISSN: 2521-4217

P-ISSN: 2521-4209

Copyright © 2020 Omar and abed. This is an open access article 
distributed under the Creative Commons Attribution Non-Commercial 
No Derivatives License 4.0 (CC BY-NC-ND 4.0)

O R I G I N A L  RE SE A RC H  A RT I C L E UHD JOURNAL OF SCIENCE AND TECHNOLOGY

mailto:zana.th.omar@gmail.com


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88 UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1

that was presented during the RSA scheme for the first time [5]. 
Because this kind of  encryption allows the key to decrypt the 
encrypted data, and thus one can read and know all the data, 
and for this reason, if  one does not have the secret key, the data 
become useless. Therefore, a question and an issue were asked: 
Can mathematical operations apply to encrypted data without 
decrypting it, and from this, the idea of  using fully homomorphic 
systems (FHE) was raised. After that, several attempts were 
made to develop these systems, but most of  the research did not 
succeed as they received partially homomorphic schemes such as 
RSA and Goldwasser-Micali [8]. The algorithm that achieves the 
addition and multiplication properties can be considered as FHE, 
as it is regarded as a special algorithm that contains the feature of  
performing mathematical operations (addition and multiplication) 
on data without decrypting it and obtaining correct results [9]. 
FHE is an encryption technology that allows calculations to be 
performed on encrypted data without decrypting it, and this 
results in an encrypted result where when this result is decrypted 
we get a result similar to the result of  the calculations on the data 
without encrypting it [9]. The world of  computing is in constant 
progress, and the main challenge is to create a guarantee and 
trust among customers when storing their sensitive data on the 
cloud to ensure and respect their privacy. This is a new approach 
that cloud providers follow to encrypt users’ data, upload it to 
the cloud, and perform operations on it without decrypting it to 
ensure the integrity of  customer data [10]. This paper presents 
a fully homomorphic system (the correct numbers and texts) 
based on a new algorithm that will be explained later in this 
paper as this scheme relies on data encryption and operations 
performed on it without decrypting and reducing computational 
complications and the time used to encrypt and decrypt data 
and reduce energy consumption. Most of  the previous research 
in this field deals with data when encrypting after converting 
it to the binary system and this means more time. As for our 
current research, data operations are encrypted without the 
need to convert them to binary representation and this reduces 
mathematical operations and there is a reduction in the time of  
encryption and encryption solution, as well as a mathematical 
model has been suggested that deals with the inverse calculation 
and the process of  raising to the exponential and increases the 
complexity of  attacking the new system.

2. LITERATURE REVIEW

C. Gentry et al. (2012), this paper introduces contrast/
orientation techniques to transfer the elements of  plain text 
across these vectors very efficiently so that they are able to 
perform general calculations in a batch way without the need 
to decrypt the text and also make some improvements that 

can accelerate the normal homomorphic, where you can 
make homogeneous evaluation of  arithmetic operations 
using multi-arithmetic head only [11].

J. Fan et al. (2012), this paper concludes two copies of  the 
redefinition that lead to a quick calculation of  homogeneous 
processes using the parameter transformation trick, as this 
paper conveys Brakerski’s fully homomorphic scheme based on 
the learning with errors (LWE) problem to the ring-LWE [12].

Z. Brakerski et al. (2012), this paper introduces squash and 
bootstrapping techniques to convert a somewhat symmetric 
encryption scheme into an integrated symmetric encryption 
scheme [13].

X. Cao et al. (2014), this paper presents a completely symmetric 
encryption scheme using only a basic unit calculation as it 
relies on the technique of  using multiplication and addition 
instead of  using ideal clamps on a polynomial loop [14].

C. Xiang et al. (2014), this paper presents an entirely symmetric 
encryption scheme on integers, as it reduces the size of  the 
public key using the square model encryption method in 
public key elements instead of  using a linear model based on 
a stronger variant of  the approximate-GCD problem [15].

M. M. Potey et al. (2016), this paper presents a completely 
symmetric encryption system where it focuses on storing 
customer data on the cloud in an encrypted form so that 
customer data remain safe and when any data modification 
is made the system loads data on the customer’s device and 
modifies it and then stores it again on the cloud in encrypted 
form [16].

K. Gai et al. (2018), this paper proposes a new solution for 
mixing real numbers on a novel tensor-based FHE solution 
that uses tensor laws to reduce the risk of  unencrypted data 
storage [17].

S. S. Hamad et al. (2018), these heirs offer a completely 
symmetric encryption system, as it relies on the principle of  
encryption a number from the plain text with another number 
using a secret key without converting to binary format and 
then comparing the result with a DGHV and SDC system [18].

S. S. Hamad et al (2018), this paper presents a fully 
homomorphic encryption system based on Euler’s theory and 
the time complexity has been calculated and compared with 
other systems with an encrypt key size up to 512 bits while 
the size of  the key in our proposed scheme reaches more 



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UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1 89

than 2048 bits and the encrypting process is done through 
more complex and powerful mathematical equations [19]. 

V. Kumar et al (2018), this paper presents fully homomorphic 
encryption system with probabilistic encrypting and relies 
on Euler’s theory. The encrypting process is done through 
the following mathematical equation (C=Mk* 𝜇 (n) +1 mod x) 
while in our proposed scheme a more complex and difficult 
mathematical algorithm is used which helps to stand more 
against hacker attacks and deter them [20]. 

R. F. Hassan et al. (2019), this paper proposes a blueprint for 
building asymmetric cloud-based architecture to save user data 
in the form of  unusual text. This pattern uses the elliptic curve 
to create the secret key for data encryption. This pattern is a new 
algorithm that reduces processing time and storage space [21].

3. STATEMENT OF THE PROBLEM

Cloud providers provide many services, including applications 
and storage many companies and users do not trust the 
providers of  these services due to security concerns. Where 
the user does not upload his personal data to the cloud 
because the cloud providers are able to read and modify every 
bit loaded on the cloud and use it for personal purposes, and 
this thing does not comply with respecting the user’s privacy. 
Furthermore, some cloud providers still use traditional 
security techniques that are not secure with low-security level 
to protect user privacy. Some of  the cloud providers have 
started to use high-level technologies to protect the privacy 
of  users and the security of  their data, but there remains a 
problem that the provider of  the cloud itself  is still able to 
access user data, and this is not safe for users. This problem 
can be solved when following FHE systems when storing 
data on the cloud where these systems can encrypt the data 
and store it in the cloud in an encrypted form and thus the 
cloud provider or others cannot see the data and use it, so the 
privacy of  users and the security of  their data are protected.

4. PROPOSED FHE SYSTEM

The proposed scheme works as follows:
Generating the encryption key and then encrypting the numbers 
and texts and storing them in encrypted form on the cloud. 
In our work, we use a local cloud and experiment with the 
proposed scheme on it. The purpose of  this process is to save 
the data encrypted on the cloud so that no one can view the 
data and use it for personal purposes Therefore, when the data 
owner needs to perform an amendment of  the encrypted data 

on the cloud, an encrypted request is sent to the server, and the 
server performs mathematical operations on the encrypted data 
and returns an encrypted result where this encrypted result can 
only be decrypted through the private encryption key which is 
with the owner of  data only so that he can decrypt the encrypted 
result and see his data. In this way, we have been able to maintain 
the privacy and security of  the data when stored in the cloud. 
These procedures go through three stages. Generation the 
encryption key stage, the encryption stage, and the decryption 
stage. The model of  the proposed scheme is given in Fig. 1, 
and the flowchart of  the proposed scheme is given in Fig. 2. 
The proposed scheme performs several random examples with 
multiplication and addition as follows:
A. Key Generation:
 1. Generate two large Prime number p and q
 2. Compute n = p*q
 3. Calculate L=((P−1 mod q)*p)+((q−1 mod p)*q)
 4. Select r: Where r is a big random integer

B. B. Messages Encryption
The conditions:

(M
1
&M

2
), (M

1
+M

2
), and (M

1
*M

2
) < n

Where M1 and M
2
 are the Messages.

pK
sK

Storage

Key Generation

Encryption

Request

Decryption

Set to storage

Get from storage

Fig. 1. Model of proposed FHE scheme.



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90 UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1

The schema of  message encryption is:

  C = L * Mr µ (p) +1 mod n. (1)

Where 𝜇 (p) = (p-1), Euler function and C, the ciphers text.

C. Message Decryption
The schema of  cipher decryption is:

   M=C mod p (2)

Where M is the number or text that will be encrypt and C 
is the result of  the encrypted number or text we named it 
cipher text

D. Euler’s Theorem
All of  us know that Euler’s Theorem contains two-part they are:
1. M 𝜇 (p) ≡ 1(mod p), when p and m are prime to each other.
2. M r* 𝜇 (n) +1 ≡ M (mod n), when r is an integer, M<n and 

n=p*q where q and p are two primes number.

E. A simple example of  how to make an amendment 
to encrypted data

We have two values M1 = 3, M2 = 5. We encrypt them 
through a simple encryption equation that is multiplied by 
each value, so we get C1 = M1 * 2 and C2 = M2 * 2, so 
C1 = 6, C2 = 10 when we add the two values C1 + C2 = 

C3 so C3 = 16 We decrypt C3 so we get the result 16/2 = 8 
which is the same result when we add M1 + M2 = M3 where 
3 + 5 = 8 as shown in Fig. 3.

5. THE PROVE OF OUR SCHEMA IS FHE

We choose two numbers M
1
, M

2 
and encrypt them to get two 

encrypted or (ciphers) C
1
 and C

2
, respectively, and then we 

combine C
1
 + C

2
 to get a new ciphered result we name it C

3
 

then we decrypt C
3
 and compare the result with M

3
 which is 

the result of  combine M
1
 + M

2
 we also multiply C

1
 * C

2
 to 

get C
4
 and compare it to M

4
, which is the result of  M

1
 * M

2
.

A. The Prove of  Additive Homomorphic
If  the following condition is fulfilled, it becomes clear to us 
that the proposed scheme additive homomorphic:

M
1
+M

2
=dec [enc (M

1
) + enc (M

2
)] (4) 

Where dec is the decryption function and enc is the 
encryption function

Proof:

C
1
=L*(M

1
r µ (p) +1 mod n).

C
2
=L*(M

2
r µ (p) +1 mod n).

C
1
+C

2
= L*(M

1
r µ (p) +1 mod n) + L*(M

2
r µ (p) +1 mod n).

dec (C
1
+C

2
) = (C

1
+C

2
) mod p

= [L*(M
1
r µ (p) +1 mod n) + L*(M

2
r µ (p) +1 mod n)] mod p

= [(L mod p) + ((M
1
r µ (p) +1 mod n) mod p) + (L mod p) + 

((M
2
r µ (p) +1 mod n) mod p)]

= [(M
1
r µ (p) +1 mod p) mod n + (M

2
r µ (p) +1 mod p) mod n]

We know M
1
r µ (p) +1 mod p = M

1
 and M

2
r µ (p) +1 mod p = M

2
 

by Euler’s Theorem so

Fig. 2. Flowchart of proposed FHE scheme. Fig. 3. A simple example of how modify encrypted data.



 Omar and abed: Cloud Banking Data Security

UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1 91

= (M
1
 mod n) + (M

2
 mod n)

= (M
1
+M

2
) mod n 

Because M
1
+M

2
 less than < (n)

 = M
1
+M

2
 

dec (C
1
+C

2
) = M

1
+M

2
 so the condition is fulfilled

B. The Prove of  Multiplicative Homomorphic

If  the following condition is fulfilled, it becomes clear to 
us that the proposed scheme multiplicative homomorphic:

 M
1
*M

2
=dec [enc (M

1
) * enc (M

2
)] (5)

Where dec is the decryption function and enc is the 
encryption function 

Proof:
C

1
=L*(M

1
r µ (p) +1 mod n).

C
2
=L*(M

2
r µ (p) +1 mod n).

C
1
*C

2
= (L*(M

1
r µ (p) +1 mod n)) * (L*(M

2
r µ (p) +1 mod n)).

dec (C
1
*C

2
) = (C

1
*C

2
) mod p

= [(L*(M
1
r µ (p) +1 mod n)) * (L*(M

2
r µ (p) +1 mod n))] mod p

= [(L mod p) * ((M
1
rµ  (p) +1 mod n) mod p) * (L mod p) * 

((M
2
r µ (p) +1 mod n) mod p)]

= [(M
1
r µ (p) +1 mod p) mod n * (M

2
r µ (p) +1 mod p) mod n]

We know M
1
r µ (p) +1 mod p = M

1
 and M

2
r µ (p) +1 mod p = M

2
 

by Euler’s Theorem so
= (M

1
 mod n) * (M

2
 mod n)

= (M
1
*M

2
) mod n 

Because M
1
*M

2
 less than < (n)

= M
1
*M

2
 

dec (C
1
*C

2
) = M

1
*M

2
 so the condition is fulfilled

6. REAL EXAMPLE

Let us choose two different number M
1
= 10, M2 = 40, 

select two big prime numbers p=523, q=617, select random 

number r=100 and compute n, L where n = p*q and L = 
((P−1 mod q)*p) + ((q−1 mod p)*q), as in Fig. 1, so n = 322691 
and L = 322692 now we will compute C

1
, C

2
 as shown in 

Fig. 4 where

C
1
= L*(M

1
r µ (p) +1 mod n) 

C
1
= 322692 * (10100*(522) +1 mod 322691)

C
1
= 84555952836

C
2
= L*(M2r µ (p) +1 mod n)

C
2
= 322692 * (40100*(522) +1 mod 322691)

C
2
= 70220360736

A. Check the Additive Homomorphism

As shown in Fig. 5, Let us define C
3
 is the result of  C

1
+C

2
 

C
3
= C

1
+C

2
 

C
3
= 84555952836+70220360736

C
3
= 154776313572

M
3
= C

3
 mod p

M
3
= 154776313572 mod 523

M
3
= 50, which is the same of  M

1
+M

2
 = 10 + 40 =50

B. Check the Multiplication Homomorphism 

As shown in Fig. 6, Let us define C
4
 is the result of  C

1
*C

2
 

C
4
= C

1
*C

2
 

C
4
= 84555952836*70220360736

C
4
= 5937549510520122247296

M
4
= C

4
 mod p

M
4
= 5937549510520122247296 mod 523

M
4
= 50, which is the same of  M

1
*M

2
 = 10 * 40 =400

7. RESULTS

Our proposed method has been applied in Java Language 
on a laptop that has these characteristics Intel (R) core (TM) 

Fig. 4. Verification that the proposed scheme supports multiplicative homomorphic system.



 Omar and abed: Cloud Banking Data Security

92 UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1

8110011485075986472668526287650474047702785552627
7139605888244856948751484971356945255025501977455
2242450237953291087748249243514503675865792656993
93729838051811451

Q=1428710476741675056983014575571840561823434645
4308656139478728164897664839386811178089812726550
5708304317799826040708010919513590630000335514123
0450272776428691918542268804417638286844165397915
2025714562637864986328594073222682892055143305181
2687655466062902039677657892147970940904308293447
443717248390239707

R=365786518636912644776042065063644900157123708
343207168729026337822168443513411848955281137920
158798190812229338500124674534784650074194884515
2271827981943

N=2423607304574691011057220168339429745775510876
8568255735015912152074767485603430716960118055838
9243234428533681091865082478949426971733704964018
7576258686356978941473841479446251805425174083399

i7-8550U CPU @1.80GHz 2.00GHz, 8 GB Ram, 64-bit 
Operating System,x64-based processor, Windows 10 and Big 
Integer library of  java is used. We have previously seen that 
in section 5 our scheme achieves the two properties (addition 
and multiplication) on the correct numbers when encrypt in 
contrast to the two systems (RSA and Pailler) that produce a 
single property either multiplication or addition, we took as an 
example of  2048 bit A message containing several languages: 
English, Kurdish, Arabic and Chinese, to indicate that our 
scheme works in all languages. The message was:

The language considered at the university is English

ەییزیلگنیئ ینامز ەدنەسەپ ەب ادۆكناز ەل ەك یەنامز وەئ

ةيزيلكنالا يه ةعماجلا يف ةربتعملا ةغللا

大學考慮的語言是英語

P=16963600001744112018845147215300525136637986969
1606741862700184835051235683163815632346364513963
5084178686272336909107427580252972488626713138540

Fig. 5. Verification that the proposed scheme supports additive homomorphic system.

Fig. 6. A real example of generating an encryption key and encrypting two different numbers.



 Omar and abed: Cloud Banking Data Security

UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1 93

0

50000

100000

150000

200000

250000

300000

64
Bit

128
Bit

256
Bit

512
Bit

1024
Bit

2048
Bit

E
xc

ut
io

n 
Ti

m
e 

in
 m

s

Size of Key

Proposed
Method

RSA

Pailler

Fig. 7. Computation encryption time of various schema.

Fig. 8. Computation decryption time of various schema.

0

50000

100000

150000

200000

250000

300000

64
Bit

128
Bit

256
Bit

512
Bit

1024
Bit

2048
Bit

E
xc

ut
io

n 
Ti

m
e 

in
 m

s

Size of Key

Proposed
Method

RSA

Pailler

0064335766935428553190201256143433654205627755229
6773381542471828455818813480172653876483980783338
1523057539397742755088141082360135822895062302531
9405062251415063552873019444449238666440140085803
2829153319755489679960430558612883401366594381416
5468112883656495673094721811758386521739451237520
5070768701405826931878983152614067930454176175622
2924904444160392437762620644204922911348434700560
07271825256265091103199457484857

L=24236073045746910110572201683394297457755108
7685682557350159121520747674856034307169601180
5583892432344285336810918650824789494269717337
0496401875762586863569789414738414794462518054
2517408339900643357669354285531902012561434336
5420562775522967733815424718284558188134801726
5387648398078333815230575393977427550881410823
6013582289506230253194050622514150635528730194
4444923866644014008580328291533197554896799604
3055861288340136659438141654681128836564956730
9472181175838652173945123752050707687014058269
3187898315261406793045417617562229249044441603
9243776262064420492291134843470056007271825256
265091103199457484858

The Message after encryption (Cipher Text)

541476558809409702391337896786206578891371305860
691083047075666735305343010133163455201330600329

818224876828649953919527566237735831578747495518
661815006015094327373599324058140501637682523981
366081263444402953878958225004102881404987245214
085192130463968623162036132714218988345866733882
828903027959438577677193858956252126893602243322
002345822997903630750182808060329693726890973821
429052022147058264305295245097017754099269475380
968046201854139181624798301373478600684536391994
135042539217304792283425928429438405414943114956
731879603950076538717093967938918097476473355425
283428257417215267662967218064104960563636218183
044111151212122457871341575675158274986166996526
006578968820402465601212584511978294298514268554
125554995603375526132322574633145472359908234720
133081143881121000520379674740198817341417761860
826872691325817210768306765600237104658826101240
831563114649492567258100255788974674414548062825

TABLE  1: Computation encryption time of various 
schema
Key Size Proposed method RSA Pailler
64 Bit 88 ms 59 ms 103 ms
128 Bit 139 ms 100 ms 182 ms
256 Bit 218 ms 149 ms 727 ms
512 Bit 1141 ms 397 ms 4212 ms
1024 Bit 6058 ms 2185 ms 55139 ms
2048 Bit 65876 ms 29820 ms 263303 ms
Average 12253 ms 5451 ms 53944 ms

TABLE  2: Computation decryption time of various 
schema
Key Size Proposed Method RSA Pailler
64 Bit 31 ms 72 ms 193 ms
128 Bit 43 ms 116 ms 330 ms
256 Bit 50 ms 315 ms 1429 ms
512 Bit 60 ms 1450 ms 11441 ms
1024 Bit 131 ms 7829 ms 122628 ms
2048 Bit 260 ms 79609 ms 976289 ms
Average 95 ms 14898 ms 185385 ms



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94 UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1

289283723466283906129211351747505124028302482285
703983215028876622455291720747481357534432866979
561161051794214495384555564764420022771673904608
026921423801092986234452794686905395614250428215
39788299132797410163169266322544228501653889014
41231774699848323143262753973952981234912026166
08092930905934341723828737491536602463718665109
04460259954270328428583255617601007624795283333
12842498083186883479202672771030666642010819171
03871200835323397770355533934916679402150831209
71613731326031096116661094157439907155297740345
56154583520372539433462549143084673593882815487
33624326112691124298132589125000613618859548392
80194895402855066065235834892981371608451492075
898392646836063832420875791614210127746840887222
061576759203922203224378888374677613916469740136
215937279995273878941455335546570056409881117615
612427776918414604124368172979351492484034377939
232910419697167267189883148981938503891449737345
277644170563374412805408898899652315897930433017
221778569673211415882347553987827098592640370937
720688618264473231853293964905495556724277624311
697945653171210371750503583126470426057905397533
244577146375498719004689422402622745765224202206
710655778164805330785789281954819858081405410264
417267795724923069668706099902071….etc. Due to the 
length of  the encrypted text (Cipher Text), which reaches 67 
pages, it has been truncated. Where the encrypted time was 
1572 ms, and the decrypted time was 31 ms. We have also 
tested it on text with 8KB in its size and several different 
keys in terms of  size, and we compared the results with 
the planners from. In terms of  velocity, we obtained the 
following results: As shown in Tables 1 and 2, respectively, 
and the graph in Figs 7 and 8.

8. CONCLUSION

Our scheme relies on FHE on whole numbers, texts, and 
supports all languages such as English, Arabic, Kurdi, and 
Chinese and others. Very large prime numbers (up to 617 
digits, 2048 bit) represent the strength for the attack of  
our scheme because the proposed system depends on the 
problem of  factorization to the primary factors, which are 
considered mathematical problems under discussion at the 
present time when taking the time. We have come to the 
conclusion that our scheme is very effective in relation to 
the time when encrypt and decrypt numbers and texts in 
comparison with other techniques and approaches that are 
circulated and used at the present time.

REFERENCES

[1] L. A. Tawalbeh and G. Saldamli. “Reconsidering big data security 
and privacy in cloud and mobile cloud systems”. Journal of King 
Saud University Computer, vol. 40, pp. 1-7, 2019.

[2] J. Domingo-Ferrer, O. Farràs, J. Ribes-González and D. 
Sánchez. “Privacy-preserving cloud computing on sensitive data: 
A survey of methods, products and challenges”. Computer and 
Communications, vol. 140-141, no. 2018, pp. 38-60, 2019.

[3] S. Sakharkar, S. Karnuke, S. Doifode and V. Deshmukh. “A 
research homomorphic encryption scheme to secure data mining 
in cloud computing for banking system”. International Journal for 
Innovative Research in Multidisciplinary Field, vol. 4, no. 4, pp. 
276-280, 2018.

[4] J. H. Cheon, A. Kim, M. Kim and Y. Song. “Homomorphic encryption 
for arithmetic of approximate numbers”. In: Lecture Notes in 
Computer Science. Vol. 10624. Springer Science+Business 
Media, Berlin, Germany, pp. 409-437, 2017.

[5]	 P.	Sha	and	Z.	Zhu.	“The	modification	of	RSA	algorithm	to	adapt	
fully homomorphic encryption algorithm in cloud computing”. 
In: Proceeding 2016 4th IEEE International Conference Cloud 
Computing and Intelligence Systems. pp. 388-392, 2016.

[6] L. Chen and Z. Zhang. “Bootstrapping Fully Homomorphic 
Encryption with Ring Plaintexts Within Polynomial Noise. Vol. 2. 
Conference Paper, pp. 285-304, 2017.

[7] C. Gentry. “A Fully Homomorphic Encryption Scheme”. Dissertation, 
p. 169, 2009.

[8] V. Kumar and N. Srivastava. “Chinese Remainder Theorem 
based Fully Homomorphic Encryption over Integers”. International 
Journal of Applied Engineering Research, vol. 14, no. 2, pp. 203-
208, 2019.

[9] M. A. Mohammed and F. S. Abed. “A symmetric-based framework 
for securing cloud data at rest”. Turkish Journal of Electrical 
Engineering and Computer Sciences, vol. 1, pp. 347-361, 2019.

[10] K. Gai, M. Qiu, Y. Li and X. Y. Liu. “Advanced fully homomorphic 
encryption scheme over real numbers”. In: Proceeding 4th IEEE 
International Conference Cyber Secur Cloud Computing CSCloud 
2017 3rd IEEE Intertnational Conference Scalable Smart Cloud, 
SSC 2017, pp. 64-69, 2017.

[11] C. Gentry, S. Halevi and N. P. Smart. “Fully homomorphic 
encryption with polylog overhead”. In: Lecture Notes in Computer 
Science. Vol. 7237. Springer Science+Business Media, Berlin, 
Germany, pp. 465-482, 2012.

[12] J. Fan and F. Vercauteren. “Somewhat practical fully homomorphic 
encryption”. In: Proceeding 15th International Conference Practice 
Theory Public Key Cryptogr, pp. 1-16, 2012.

[13] Z. Brakerski and V. Vaikuntanathan. “Fully homomorphic encryption 
from ring-LWE and security for key dependent messages”. In: 
Lecture Notes in Computer Science. Vol. 6841. Springer, Berlin, 
Germany, pp. 505-524, 2011.

[14] X. Cao, C. Moore, M. O’Neill, N. Hanley and E. O’Sullivan. “High-
speed fully homomorphic encryption over the integers”. In: Lecture 
Notes in Computer Science. Vol. 8438. Springer, Berlin, Germany, 
pp. 169-180, 2014.

[15] C. Xiang and C. M. Tang. “Improved fully homomorphic encryption 
over the integers with shorter public keys”. International Journal of 
Security and its Applications, vol. 8, no. 6, pp. 365-374, 2014.

[16] M. M. Potey, C. A. Dhote and D. H. Sharma. “Homomorphic 
encryption for security of cloud data”. Procedia Computer Science, 



 Omar and abed: Cloud Banking Data Security

UHD Journal of Science and Technology | Jan 2020 | Vol 4 | Issue 1 95

vol. 79, pp. 175-181, 2016.
[17] K. Gai and M. Qiu. “Blend arithmetic operations on tensor-

based fully homomorphic encryption over real numbers”. IEEE 
Transactions on Industrial Informatics, vol. 14, no. 8, pp. 3590-
3598, 2018.

[18] S. S. Hamad and A. M. Sagheer. “Design of fully homomorphic 
encryption by prime modular operation”. Telfor Journal, vol. 10, no. 
2, pp. 118-122, 2018.

[19] S. S. Hamad and A. M. Sagheer. “Fully homomorphic encryption 
based on Euler’s theorem”. The International Journal of Information 

Security, vol. 9, no. 3, p. 83, 2018.
[20] V. Kumar, R. Kumar, S. K. Pandey and M. Alam. “Fully homomorphic 

encryption scheme with probabilistic encryption based on euler’s 
theorem and application in cloud computing”. In: Advances in 
Intelligent Systems and Computing. Vol. 654. Springer, Berlin, 
Germany, pp. 605-611, 2018.

[21] R. F. Hassan and A. M. Sagheer. “A proposed secure cloud 
environment based on homomorphic encryption”. International 
Advanced Research Journal in Science, Engineering and 
Technology, vol. 6, no. 5, pp. 166-175, 2019.