id	sid	tid	token	lemma	pos
ap-688	1	1	ap05_2.vp	ap05_2.vp	VERB
ap-688	1	2	1	1	NUM
ap-688	1	3	introduction	introduction	NOUN
ap-688	1	4	contemporary	contemporary	ADJ
ap-688	1	5	cryptographic	cryptographic	ADJ
ap-688	1	6	schemata	schemata	NOUN
ap-688	1	7	are	be	AUX
ap-688	1	8	frequently	frequently	ADV
ap-688	1	9	based	base	VERB
ap-688	1	10	on	on	ADP
ap-688	1	11	the	the	DET
ap-688	1	12	discrete	discrete	ADJ
ap-688	1	13	logarithm	logarithm	NOUN
ap-688	1	14	problem	problem	NOUN
ap-688	1	15	(	(	PUNCT
ap-688	1	16	dlp	dlp	NOUN
ap-688	1	17	):	):	PUNCT
ap-688	1	18	find	find	VERB
ap-688	1	19	integer	integer	NOUN
ap-688	1	20	k	k	PROPN
ap-688	2	1	such	such	ADJ
ap-688	2	2	that	that	PRON
ap-688	2	3	q	q	PROPN
ap-688	3	1	k	k	NOUN
ap-688	3	2	p	p	X
ap-688	3	3	p	p	X
ap-688	3	4	k	k	PROPN
ap-688	3	5	�	�	PROPN
ap-688	3	6	�	�	PROPN
ap-688	3	7	�	�	PROPN
ap-688	3	8	�	�	PROPN
ap-688	3	9	1	1	NUM
ap-688	3	10	(	(	PUNCT
ap-688	3	11	1	1	NUM
ap-688	3	12	)	)	PUNCT
ap-688	3	13	for	for	ADP
ap-688	3	14	given	give	VERB
ap-688	3	15	group	group	NOUN
ap-688	3	16	elements	element	NOUN
ap-688	3	17	p	p	NOUN
ap-688	3	18	and	and	CCONJ
ap-688	3	19	q.	q.	PROPN
ap-688	3	20	in	in	ADP
ap-688	3	21	elliptic	elliptic	ADJ
ap-688	3	22	curve	curve	NOUN
ap-688	3	23	cryptography	cryptography	NOUN
ap-688	3	24	(	(	PUNCT
ap-688	3	25	ecc	ecc	PROPN
ap-688	3	26	)	)	PUNCT
ap-688	3	27	,	,	PUNCT
ap-688	3	28	p	p	NOUN
ap-688	3	29	and	and	CCONJ
ap-688	3	30	q	q	NOUN
ap-688	3	31	are	be	AUX
ap-688	3	32	points	point	NOUN
ap-688	3	33	on	on	ADP
ap-688	3	34	a	a	DET
ap-688	3	35	chosen	choose	VERB
ap-688	3	36	elliptic	elliptic	ADJ
ap-688	3	37	curve	curve	NOUN
ap-688	3	38	over	over	ADP
ap-688	3	39	a	a	DET
ap-688	3	40	finite	finite	ADJ
ap-688	3	41	field	field	NOUN
ap-688	3	42	.	.	PUNCT
ap-688	4	1	we	we	PRON
ap-688	4	2	focus	focus	VERB
ap-688	4	3	on	on	ADP
ap-688	4	4	curves	curve	NOUN
ap-688	4	5	over	over	ADP
ap-688	4	6	gf(2	gf(2	PROPN
ap-688	4	7	m	m	NOUN
ap-688	4	8	)	)	PUNCT
ap-688	4	9	,	,	PUNCT
ap-688	4	10	where	where	SCONJ
ap-688	4	11	point	point	NOUN
ap-688	4	12	coordinates	coordinate	NOUN
ap-688	4	13	are	be	AUX
ap-688	4	14	expressed	express	VERB
ap-688	4	15	as	as	ADP
ap-688	4	16	m	m	NOUN
ap-688	4	17	-	-	PUNCT
ap-688	4	18	bit	bit	NOUN
ap-688	4	19	vectors	vector	NOUN
ap-688	4	20	.	.	PUNCT
ap-688	5	1	the	the	DET
ap-688	5	2	dlp	dlp	NOUN
ap-688	5	3	in	in	ADP
ap-688	5	4	such	such	DET
ap-688	5	5	a	a	DET
ap-688	5	6	group	group	NOUN
ap-688	5	7	is	be	AUX
ap-688	5	8	exponentially	exponentially	ADV
ap-688	5	9	hard	hard	ADJ
ap-688	5	10	in	in	ADP
ap-688	5	11	comparison	comparison	NOUN
ap-688	5	12	with	with	ADP
ap-688	5	13	dlp	dlp	NOUN
ap-688	5	14	in	in	ADP
ap-688	5	15	a	a	DET
ap-688	5	16	multiplicative	multiplicative	ADJ
ap-688	5	17	group	group	NOUN
ap-688	5	18	over	over	ADP
ap-688	5	19	a	a	DET
ap-688	5	20	finite	finite	ADJ
ap-688	5	21	field	field	NOUN
ap-688	5	22	.	.	PUNCT
ap-688	6	1	this	this	PRON
ap-688	6	2	means	mean	VERB
ap-688	6	3	that	that	SCONJ
ap-688	6	4	a	a	DET
ap-688	6	5	173	173	NUM
ap-688	6	6	bit	bit	NOUN
ap-688	6	7	key	key	NOUN
ap-688	6	8	provides	provide	VERB
ap-688	6	9	approximately	approximately	ADV
ap-688	6	10	the	the	DET
ap-688	6	11	same	same	ADJ
ap-688	6	12	security	security	NOUN
ap-688	6	13	level	level	NOUN
ap-688	6	14	as	as	ADP
ap-688	6	15	the	the	DET
ap-688	6	16	1024	1024	NUM
ap-688	6	17	-	-	PUNCT
ap-688	6	18	bit	bit	NOUN
ap-688	6	19	rsa	rsa	NOUN
ap-688	6	20	[	[	X
ap-688	6	21	7	7	NUM
ap-688	6	22	]	]	PUNCT
ap-688	6	23	.	.	PUNCT
ap-688	7	1	this	this	DET
ap-688	7	2	fact	fact	NOUN
ap-688	7	3	is	be	AUX
ap-688	7	4	very	very	ADV
ap-688	7	5	important	important	ADJ
ap-688	7	6	in	in	ADP
ap-688	7	7	applications	application	NOUN
ap-688	7	8	such	such	ADJ
ap-688	7	9	as	as	ADP
ap-688	7	10	chip	chip	NOUN
ap-688	7	11	cards	card	NOUN
ap-688	7	12	,	,	PUNCT
ap-688	7	13	where	where	SCONJ
ap-688	7	14	the	the	DET
ap-688	7	15	size	size	NOUN
ap-688	7	16	of	of	ADP
ap-688	7	17	the	the	DET
ap-688	7	18	hardware	hardware	NOUN
ap-688	7	19	and	and	CCONJ
ap-688	7	20	energy	energy	NOUN
ap-688	7	21	consumption	consumption	NOUN
ap-688	7	22	is	be	AUX
ap-688	7	23	crucial	crucial	ADJ
ap-688	7	24	.	.	PUNCT
ap-688	8	1	in	in	ADP
ap-688	8	2	algorithms	algorithm	NOUN
ap-688	8	3	such	such	ADJ
ap-688	8	4	as	as	ADP
ap-688	8	5	the	the	DET
ap-688	8	6	elliptic	elliptic	ADJ
ap-688	8	7	curve	curve	NOUN
ap-688	8	8	digital	digital	ADJ
ap-688	8	9	signature	signature	NOUN
ap-688	8	10	algorithm	algorithm	NOUN
ap-688	8	11	(	(	PUNCT
ap-688	8	12	ecdsa	ecdsa	PROPN
ap-688	8	13	)	)	PUNCT
ap-688	8	14	,	,	PUNCT
ap-688	8	15	k	k	PROPN
ap-688	8	16	is	be	AUX
ap-688	8	17	an	an	DET
ap-688	8	18	m	m	NOUN
ap-688	8	19	-	-	PUNCT
ap-688	8	20	bit	bit	NOUN
ap-688	8	21	integer	integer	NOUN
ap-688	8	22	,	,	PUNCT
ap-688	8	23	p	p	NOUN
ap-688	8	24	is	be	AUX
ap-688	8	25	a	a	DET
ap-688	8	26	chosen	choose	VERB
ap-688	8	27	point	point	NOUN
ap-688	8	28	and	and	CCONJ
ap-688	8	29	q	q	NOUN
ap-688	8	30	is	be	AUX
ap-688	8	31	computed	compute	VERB
ap-688	8	32	using	use	VERB
ap-688	8	33	eq	eq	ADP
ap-688	8	34	.	.	PROPN
ap-688	9	1	1	1	X
ap-688	9	2	.	.	PUNCT
ap-688	10	1	it	it	PRON
ap-688	10	2	requires	require	VERB
ap-688	10	3	addition	addition	NOUN
ap-688	10	4	,	,	PUNCT
ap-688	10	5	multiplication	multiplication	NOUN
ap-688	10	6	and	and	CCONJ
ap-688	10	7	inversion	inversion	NOUN
ap-688	10	8	over	over	ADP
ap-688	10	9	gf(2	gf(2	PROPN
ap-688	10	10	m	m	NOUN
ap-688	10	11	)	)	PUNCT
ap-688	10	12	.	.	PUNCT
ap-688	11	1	1.1	1.1	NUM
ap-688	11	2	finite	finite	ADJ
ap-688	11	3	field	field	NOUN
ap-688	11	4	operations	operation	NOUN
ap-688	11	5	the	the	DET
ap-688	11	6	implementation	implementation	NOUN
ap-688	11	7	of	of	ADP
ap-688	11	8	these	these	DET
ap-688	11	9	operations	operation	NOUN
ap-688	11	10	is	be	AUX
ap-688	11	11	determined	determine	VERB
ap-688	11	12	by	by	ADP
ap-688	11	13	the	the	DET
ap-688	11	14	representation	representation	NOUN
ap-688	11	15	of	of	ADP
ap-688	11	16	the	the	DET
ap-688	11	17	field	field	NOUN
ap-688	11	18	elements	element	NOUN
ap-688	11	19	in	in	ADP
ap-688	11	20	gf(2	gf(2	PROPN
ap-688	11	21	m	m	NOUN
ap-688	11	22	)	)	PUNCT
ap-688	12	1	[	[	X
ap-688	12	2	2	2	NUM
ap-688	12	3	]	]	PUNCT
ap-688	12	4	.	.	PUNCT
ap-688	13	1	in	in	ADP
ap-688	13	2	this	this	DET
ap-688	13	3	work	work	NOUN
ap-688	13	4	we	we	PRON
ap-688	13	5	focus	focus	VERB
ap-688	13	6	on	on	ADP
ap-688	13	7	the	the	DET
ap-688	13	8	normal	normal	ADJ
ap-688	13	9	basis	basis	NOUN
ap-688	13	10	representation	representation	NOUN
ap-688	13	11	.	.	PUNCT
ap-688	14	1	addition	addition	NOUN
ap-688	14	2	over	over	ADP
ap-688	14	3	elements	element	NOUN
ap-688	14	4	of	of	ADP
ap-688	14	5	gf(2	gf(2	PROPN
ap-688	14	6	m	m	X
ap-688	14	7	)	)	PUNCT
ap-688	14	8	is	be	AUX
ap-688	14	9	implemented	implement	VERB
ap-688	14	10	as	as	ADP
ap-688	14	11	a	a	DET
ap-688	14	12	bit	bit	NOUN
ap-688	14	13	-	-	PUNCT
ap-688	14	14	wise	wise	ADJ
ap-688	14	15	xor	xor	PROPN
ap-688	14	16	.	.	PUNCT
ap-688	15	1	squaring	square	VERB
ap-688	15	2	is	be	AUX
ap-688	15	3	realized	realize	VERB
ap-688	15	4	by	by	ADP
ap-688	15	5	rotation	rotation	NOUN
ap-688	15	6	(	(	PUNCT
ap-688	15	7	cyclic	cyclic	ADJ
ap-688	15	8	shift	shift	NOUN
ap-688	15	9	)	)	PUNCT
ap-688	15	10	one	one	NUM
ap-688	15	11	bit	bit	NOUN
ap-688	15	12	to	to	ADP
ap-688	15	13	the	the	DET
ap-688	15	14	right	right	NOUN
ap-688	15	15	.	.	PUNCT
ap-688	16	1	because	because	SCONJ
ap-688	16	2	it	it	PRON
ap-688	16	3	is	be	AUX
ap-688	16	4	so	so	ADV
ap-688	16	5	simple	simple	ADJ
ap-688	16	6	(	(	PUNCT
ap-688	16	7	one	one	NUM
ap-688	16	8	clock	clock	NOUN
ap-688	16	9	cycle	cycle	NOUN
ap-688	16	10	)	)	PUNCT
ap-688	16	11	,	,	PUNCT
ap-688	16	12	it	it	PRON
ap-688	16	13	is	be	AUX
ap-688	16	14	regarded	regard	VERB
ap-688	16	15	as	as	ADP
ap-688	16	16	a	a	DET
ap-688	16	17	special	special	ADJ
ap-688	16	18	case	case	NOUN
ap-688	16	19	.	.	PUNCT
ap-688	17	1	multiplication	multiplication	NOUN
ap-688	17	2	is	be	AUX
ap-688	17	3	based	base	VERB
ap-688	17	4	on	on	ADP
ap-688	17	5	matrix	matrix	NOUN
ap-688	17	6	multiplication	multiplication	NOUN
ap-688	17	7	over	over	ADP
ap-688	17	8	gf(2	gf(2	PROPN
ap-688	17	9	m	m	NOUN
ap-688	17	10	)	)	PUNCT
ap-688	17	11	.	.	PUNCT
ap-688	18	1	in	in	ADP
ap-688	18	2	hardware	hardware	NOUN
ap-688	18	3	,	,	PUNCT
ap-688	18	4	a	a	DET
ap-688	18	5	special	special	ADJ
ap-688	18	6	unit	unit	NOUN
ap-688	18	7	(	(	PUNCT
ap-688	18	8	multiplier	multiplier	ADV
ap-688	18	9	)	)	PUNCT
ap-688	18	10	is	be	AUX
ap-688	18	11	necessary	necessary	ADJ
ap-688	18	12	.	.	PUNCT
ap-688	19	1	the	the	DET
ap-688	19	2	best	well	ADV
ap-688	19	3	-	-	PUNCT
ap-688	19	4	known	know	VERB
ap-688	19	5	algorithm	algorithm	NOUN
ap-688	19	6	for	for	ADP
ap-688	19	7	inversion	inversion	NOUN
ap-688	19	8	in	in	ADP
ap-688	19	9	normal	normal	ADJ
ap-688	19	10	basis	basis	NOUN
ap-688	19	11	is	be	AUX
ap-688	19	12	the	the	DET
ap-688	19	13	algorithm	algorithm	NOUN
ap-688	19	14	of	of	ADP
ap-688	19	15	itoh	itoh	NOUN
ap-688	19	16	,	,	PUNCT
ap-688	19	17	teechai	teechai	NOUN
ap-688	19	18	and	and	CCONJ
ap-688	19	19	tsujii	tsujii	NOUN
ap-688	19	20	(	(	PUNCT
ap-688	19	21	itt	itt	INTJ
ap-688	19	22	)	)	PUNCT
ap-688	20	1	[	[	X
ap-688	20	2	3	3	X
ap-688	20	3	]	]	PUNCT
ap-688	20	4	based	base	VERB
ap-688	20	5	on	on	ADP
ap-688	20	6	multiplication	multiplication	NOUN
ap-688	20	7	and	and	CCONJ
ap-688	20	8	squaring	squaring	NOUN
ap-688	20	9	.	.	PUNCT
ap-688	21	1	1.2	1.2	NUM
ap-688	21	2	scalability	scalability	NOUN
ap-688	21	3	we	we	PRON
ap-688	21	4	understand	understand	VERB
ap-688	21	5	scalability	scalability	NOUN
ap-688	21	6	as	as	ADP
ap-688	21	7	the	the	DET
ap-688	21	8	ability	ability	NOUN
ap-688	21	9	to	to	PART
ap-688	21	10	change	change	VERB
ap-688	21	11	scale	scale	NOUN
ap-688	21	12	or	or	CCONJ
ap-688	21	13	to	to	PART
ap-688	21	14	be	be	AUX
ap-688	21	15	available	available	ADJ
ap-688	21	16	in	in	ADP
ap-688	21	17	various	various	ADJ
ap-688	21	18	versions	version	NOUN
ap-688	21	19	.	.	PUNCT
ap-688	22	1	the	the	DET
ap-688	22	2	term	term	NOUN
ap-688	22	3	‘	'	PUNCT
ap-688	22	4	scale	scale	NOUN
ap-688	22	5	’	'	PUNCT
ap-688	22	6	can	can	AUX
ap-688	22	7	be	be	AUX
ap-688	22	8	paraphrased	paraphrase	VERB
ap-688	22	9	as	as	ADP
ap-688	22	10	‘	'	PUNCT
ap-688	22	11	the	the	DET
ap-688	22	12	important	important	ADJ
ap-688	22	13	dimension	dimension	NOUN
ap-688	22	14	’	'	PUNCT
ap-688	22	15	and	and	CCONJ
ap-688	22	16	hence	hence	ADV
ap-688	22	17	is	be	AUX
ap-688	22	18	a	a	DET
ap-688	22	19	matter	matter	NOUN
ap-688	22	20	of	of	ADP
ap-688	22	21	viewpoint	viewpoint	NOUN
ap-688	22	22	.	.	PUNCT
ap-688	23	1	the	the	DET
ap-688	23	2	basic	basic	ADJ
ap-688	23	3	dimension	dimension	NOUN
ap-688	23	4	of	of	ADP
ap-688	23	5	cryptography	cryptography	NOUN
ap-688	23	6	is	be	AUX
ap-688	23	7	the	the	DET
ap-688	23	8	measure	measure	NOUN
ap-688	23	9	of	of	ADP
ap-688	23	10	security	security	NOUN
ap-688	23	11	,	,	PUNCT
ap-688	23	12	which	which	PRON
ap-688	23	13	translates	translate	VERB
ap-688	23	14	to	to	ADP
ap-688	23	15	key	key	ADJ
ap-688	23	16	length	length	NOUN
ap-688	23	17	.	.	PUNCT
ap-688	24	1	a	a	DET
ap-688	24	2	unit	unit	NOUN
ap-688	24	3	is	be	AUX
ap-688	24	4	scalable	scalable	ADJ
ap-688	24	5	if	if	SCONJ
ap-688	24	6	it	it	PRON
ap-688	24	7	can	can	AUX
ap-688	24	8	serve	serve	VERB
ap-688	24	9	for	for	ADP
ap-688	24	10	computations	computation	NOUN
ap-688	24	11	with	with	ADP
ap-688	24	12	varying	vary	VERB
ap-688	24	13	key	key	ADJ
ap-688	24	14	length	length	NOUN
ap-688	24	15	,	,	PUNCT
ap-688	24	16	provided	provide	VERB
ap-688	24	17	that	that	SCONJ
ap-688	24	18	the	the	DET
ap-688	24	19	internal	internal	ADJ
ap-688	24	20	memory	memory	NOUN
ap-688	24	21	is	be	AUX
ap-688	24	22	sufficient	sufficient	ADJ
ap-688	24	23	[	[	X
ap-688	24	24	5	5	NUM
ap-688	24	25	]	]	PUNCT
ap-688	24	26	.	.	PUNCT
ap-688	25	1	we	we	PRON
ap-688	25	2	suggest	suggest	AUX
ap-688	25	3	calling	call	VERB
ap-688	25	4	this	this	DET
ap-688	25	5	kind	kind	NOUN
ap-688	25	6	of	of	ADP
ap-688	25	7	scalability	scalability	NOUN
ap-688	25	8	scalability	scalability	NOUN
ap-688	25	9	in	in	ADP
ap-688	25	10	precision	precision	NOUN
ap-688	25	11	.	.	PUNCT
ap-688	26	1	in	in	ADP
ap-688	26	2	the	the	DET
ap-688	26	3	world	world	NOUN
ap-688	26	4	of	of	ADP
ap-688	26	5	parallel	parallel	ADJ
ap-688	26	6	processing	processing	NOUN
ap-688	26	7	and	and	CCONJ
ap-688	26	8	vlsi	vlsi	PROPN
ap-688	26	9	design	design	PROPN
ap-688	26	10	,	,	PUNCT
ap-688	26	11	the	the	DET
ap-688	26	12	important	important	ADJ
ap-688	26	13	dimension	dimension	NOUN
ap-688	26	14	is	be	AUX
ap-688	26	15	the	the	DET
ap-688	26	16	number	number	NOUN
ap-688	26	17	of	of	ADP
ap-688	26	18	processors	processor	NOUN
ap-688	26	19	or	or	CCONJ
ap-688	26	20	other	other	ADJ
ap-688	26	21	hardware	hardware	NOUN
ap-688	26	22	units	unit	NOUN
ap-688	26	23	.	.	PUNCT
ap-688	27	1	an	an	DET
ap-688	27	2	algorithm	algorithm	NOUN
ap-688	27	3	scales	scale	VERB
ap-688	27	4	well	well	ADV
ap-688	27	5	if	if	SCONJ
ap-688	27	6	we	we	PRON
ap-688	27	7	can	can	AUX
ap-688	27	8	obtain	obtain	VERB
ap-688	27	9	more	more	ADJ
ap-688	27	10	performance	performance	NOUN
ap-688	27	11	by	by	ADP
ap-688	27	12	assigning	assign	VERB
ap-688	27	13	more	more	ADJ
ap-688	27	14	resources	resource	NOUN
ap-688	27	15	(	(	PUNCT
ap-688	27	16	processors	processor	NOUN
ap-688	27	17	,	,	PUNCT
ap-688	27	18	chip	chip	NOUN
ap-688	27	19	area	area	NOUN
ap-688	27	20	)	)	PUNCT
ap-688	27	21	.	.	PUNCT
ap-688	28	1	we	we	PRON
ap-688	28	2	shall	shall	AUX
ap-688	28	3	speak	speak	VERB
ap-688	28	4	about	about	ADP
ap-688	28	5	scalability	scalability	NOUN
ap-688	28	6	in	in	ADP
ap-688	28	7	performance	performance	NOUN
ap-688	28	8	.	.	PUNCT
ap-688	29	1	as	as	SCONJ
ap-688	29	2	this	this	DET
ap-688	29	3	paper	paper	NOUN
ap-688	29	4	is	be	AUX
ap-688	29	5	focused	focus	VERB
ap-688	29	6	on	on	ADP
ap-688	29	7	this	this	DET
ap-688	29	8	kind	kind	NOUN
ap-688	29	9	of	of	ADP
ap-688	29	10	scalability	scalability	NOUN
ap-688	29	11	only	only	ADV
ap-688	29	12	,	,	PUNCT
ap-688	29	13	we	we	PRON
ap-688	29	14	will	will	AUX
ap-688	29	15	use	use	VERB
ap-688	29	16	just	just	ADV
ap-688	29	17	the	the	DET
ap-688	29	18	term	term	NOUN
ap-688	29	19	‘	'	PUNCT
ap-688	29	20	scalability	scalability	NOUN
ap-688	29	21	’	'	PUNCT
ap-688	29	22	.	.	PUNCT
ap-688	30	1	we	we	PRON
ap-688	30	2	need	need	VERB
ap-688	30	3	scalability	scalability	NOUN
ap-688	30	4	for	for	ADP
ap-688	30	5	two	two	NUM
ap-688	30	6	reasons	reason	NOUN
ap-688	30	7	.	.	PUNCT
ap-688	31	1	the	the	DET
ap-688	31	2	first	first	ADJ
ap-688	31	3	(	(	PUNCT
ap-688	31	4	and	and	CCONJ
ap-688	31	5	more	more	ADV
ap-688	31	6	important	important	ADJ
ap-688	31	7	)	)	PUNCT
ap-688	31	8	reason	reason	NOUN
ap-688	31	9	is	be	AUX
ap-688	31	10	practical	practical	ADJ
ap-688	31	11	:	:	PUNCT
ap-688	31	12	hardware	hardware	NOUN
ap-688	31	13	implementations	implementation	NOUN
ap-688	31	14	are	be	AUX
ap-688	31	15	needed	need	VERB
ap-688	31	16	for	for	ADP
ap-688	31	17	a	a	DET
ap-688	31	18	variety	variety	NOUN
ap-688	31	19	of	of	ADP
ap-688	31	20	contexts	context	NOUN
ap-688	31	21	,	,	PUNCT
ap-688	31	22	from	from	ADP
ap-688	31	23	smart	smart	ADJ
ap-688	31	24	-	-	PUNCT
ap-688	31	25	card	card	NOUN
ap-688	31	26	devices	device	NOUN
ap-688	31	27	to	to	ADP
ap-688	31	28	high	high	ADJ
ap-688	31	29	-	-	PUNCT
ap-688	31	30	throughput	throughput	NOUN
ap-688	31	31	servers	server	NOUN
ap-688	31	32	.	.	PUNCT
ap-688	32	1	the	the	DET
ap-688	32	2	second	second	ADJ
ap-688	32	3	reason	reason	NOUN
ap-688	32	4	is	be	AUX
ap-688	32	5	a	a	DET
ap-688	32	6	fair	fair	ADJ
ap-688	32	7	comparison	comparison	NOUN
ap-688	32	8	of	of	ADP
ap-688	32	9	design	design	NOUN
ap-688	32	10	versions	version	NOUN
ap-688	32	11	,	,	PUNCT
ap-688	32	12	where	where	SCONJ
ap-688	32	13	scaling	scale	VERB
ap-688	32	14	the	the	DET
ap-688	32	15	units	unit	NOUN
ap-688	32	16	to	to	PART
ap-688	32	17	match	match	VERB
ap-688	32	18	in	in	ADP
ap-688	32	19	one	one	NUM
ap-688	32	20	dimension	dimension	NOUN
ap-688	32	21	is	be	AUX
ap-688	32	22	preferable	preferable	ADJ
ap-688	32	23	to	to	ADP
ap-688	32	24	artificial	artificial	ADJ
ap-688	32	25	quality	quality	NOUN
ap-688	32	26	factors	factor	NOUN
ap-688	32	27	.	.	PUNCT
ap-688	33	1	to	to	PART
ap-688	33	2	scale	scale	VERB
ap-688	33	3	a	a	DET
ap-688	33	4	unit	unit	NOUN
ap-688	33	5	means	mean	VERB
ap-688	33	6	to	to	PART
ap-688	33	7	employ	employ	VERB
ap-688	33	8	parallelism	parallelism	NOUN
ap-688	33	9	at	at	ADP
ap-688	33	10	a	a	DET
ap-688	33	11	certain	certain	ADJ
ap-688	33	12	level	level	NOUN
ap-688	33	13	of	of	ADP
ap-688	33	14	abstraction	abstraction	NOUN
ap-688	33	15	.	.	PUNCT
ap-688	34	1	we	we	PRON
ap-688	34	2	can	can	AUX
ap-688	34	3	scale	scale	VERB
ap-688	34	4	at	at	ADP
ap-688	34	5	algorithmic	algorithmic	ADJ
ap-688	34	6	level	level	NOUN
ap-688	34	7	by	by	ADP
ap-688	34	8	selecting	select	VERB
ap-688	34	9	a	a	DET
ap-688	34	10	different	different	ADJ
ap-688	34	11	algorithm	algorithm	NOUN
ap-688	34	12	,	,	PUNCT
ap-688	34	13	at	at	ADP
ap-688	34	14	the	the	DET
ap-688	34	15	register	register	NOUN
ap-688	34	16	-	-	PUNCT
ap-688	34	17	transfer	transfer	NOUN
ap-688	34	18	level	level	NOUN
ap-688	34	19	,	,	PUNCT
ap-688	34	20	e.g.	e.g.	ADV
ap-688	34	21	,	,	PUNCT
ap-688	34	22	by	by	ADP
ap-688	34	23	changing	change	VERB
ap-688	34	24	the	the	DET
ap-688	34	25	data	datum	NOUN
ap-688	34	26	path	path	NOUN
ap-688	34	27	width	width	NOUN
ap-688	34	28	,	,	PUNCT
ap-688	34	29	or	or	CCONJ
ap-688	34	30	at	at	ADP
ap-688	34	31	the	the	DET
ap-688	34	32	gate	gate	NOUN
ap-688	34	33	level	level	NOUN
ap-688	34	34	by	by	ADP
ap-688	34	35	factoring	factor	VERB
ap-688	34	36	combinational	combinational	ADJ
ap-688	34	37	circuits	circuit	NOUN
ap-688	34	38	,	,	PUNCT
ap-688	34	39	or	or	CCONJ
ap-688	34	40	even	even	ADV
ap-688	34	41	at	at	ADP
ap-688	34	42	the	the	DET
ap-688	34	43	physical	physical	ADJ
ap-688	34	44	level	level	NOUN
ap-688	34	45	.	.	PUNCT
ap-688	35	1	this	this	DET
ap-688	35	2	work	work	NOUN
ap-688	35	3	aims	aim	VERB
ap-688	35	4	at	at	ADP
ap-688	35	5	the	the	DET
ap-688	35	6	seam	seam	NOUN
ap-688	35	7	between	between	ADP
ap-688	35	8	algorithmic	algorithmic	ADJ
ap-688	35	9	and	and	CCONJ
ap-688	35	10	register	register	ADJ
ap-688	35	11	-	-	PUNCT
ap-688	35	12	transfer	transfer	NOUN
ap-688	35	13	level	level	NOUN
ap-688	35	14	.	.	PUNCT
ap-688	36	1	units	unit	NOUN
ap-688	36	2	composed	compose	VERB
ap-688	36	3	of	of	ADP
ap-688	36	4	sub	sub	NOUN
ap-688	36	5	-	-	NOUN
ap-688	36	6	units	unit	NOUN
ap-688	36	7	are	be	AUX
ap-688	36	8	harder	hard	ADJ
ap-688	36	9	to	to	PART
ap-688	36	10	scale	scale	VERB
ap-688	36	11	.	.	PUNCT
ap-688	37	1	we	we	PRON
ap-688	37	2	might	might	AUX
ap-688	37	3	be	be	AUX
ap-688	37	4	lucky	lucky	ADJ
ap-688	37	5	and	and	CCONJ
ap-688	37	6	find	find	VERB
ap-688	37	7	a	a	DET
ap-688	37	8	unified	unified	ADJ
ap-688	37	9	scaling	scaling	NOUN
ap-688	37	10	parameter	parameter	NOUN
ap-688	37	11	,	,	PUNCT
ap-688	37	12	e.g.	e.g.	ADV
ap-688	37	13	,	,	PUNCT
ap-688	37	14	data	datum	NOUN
ap-688	37	15	path	path	NOUN
ap-688	37	16	width	width	NOUN
ap-688	37	17	.	.	PUNCT
ap-688	38	1	in	in	ADP
ap-688	38	2	the	the	DET
ap-688	38	3	general	general	ADJ
ap-688	38	4	case	case	NOUN
ap-688	38	5	,	,	PUNCT
ap-688	38	6	however	however	ADV
ap-688	38	7	,	,	PUNCT
ap-688	38	8	each	each	DET
ap-688	38	9	sub	sub	NOUN
ap-688	38	10	-	-	NOUN
ap-688	38	11	unit	unit	NOUN
ap-688	38	12	may	may	AUX
ap-688	38	13	have	have	VERB
ap-688	38	14	a	a	DET
ap-688	38	15	different	different	ADJ
ap-688	38	16	scaling	scaling	NOUN
ap-688	38	17	parameter	parameter	NOUN
ap-688	38	18	.	.	PUNCT
ap-688	39	1	the	the	DET
ap-688	39	2	sub	sub	ADJ
ap-688	39	3	-	-	ADJ
ap-688	39	4	units	unit	NOUN
ap-688	39	5	interact	interact	VERB
ap-688	39	6	.	.	PUNCT
ap-688	40	1	firstly	firstly	ADV
ap-688	40	2	,	,	PUNCT
ap-688	40	3	if	if	SCONJ
ap-688	40	4	there	there	PRON
ap-688	40	5	is	be	VERB
ap-688	40	6	a	a	DET
ap-688	40	7	common	common	ADJ
ap-688	40	8	clock	clock	NOUN
ap-688	40	9	(	(	PUNCT
ap-688	40	10	as	as	ADP
ap-688	40	11	preferred	prefer	VERB
ap-688	40	12	in	in	ADP
ap-688	40	13	practice	practice	NOUN
ap-688	40	14	)	)	PUNCT
ap-688	40	15	,	,	PUNCT
ap-688	40	16	it	it	PRON
ap-688	40	17	must	must	AUX
ap-688	40	18	suit	suit	VERB
ap-688	40	19	the	the	DET
ap-688	40	20	slowest	slow	ADJ
ap-688	40	21	sub	sub	NOUN
ap-688	40	22	-	-	NOUN
ap-688	40	23	unit	unit	NOUN
ap-688	40	24	.	.	PUNCT
ap-688	41	1	secondly	secondly	ADV
ap-688	41	2	,	,	PUNCT
ap-688	41	3	to	to	PART
ap-688	41	4	achieve	achieve	VERB
ap-688	41	5	the	the	DET
ap-688	41	6	best	good	ADJ
ap-688	41	7	global	global	ADJ
ap-688	41	8	area	area	NOUN
ap-688	41	9	-	-	PUNCT
ap-688	41	10	performance	performance	NOUN
ap-688	41	11	ratio	ratio	NOUN
ap-688	41	12	,	,	PUNCT
ap-688	41	13	local	local	ADJ
ap-688	41	14	area	area	NOUN
ap-688	41	15	-	-	PUNCT
ap-688	41	16	performance	performance	NOUN
ap-688	41	17	tradeoffs	tradeoff	NOUN
ap-688	41	18	are	be	AUX
ap-688	41	19	not	not	PART
ap-688	41	20	independent	independent	ADJ
ap-688	41	21	.	.	PUNCT
ap-688	42	1	the	the	DET
ap-688	42	2	above	above	ADJ
ap-688	42	3	sketched	sketched	ADJ
ap-688	42	4	elliptic	elliptic	ADJ
ap-688	42	5	curve	curve	NOUN
ap-688	42	6	operations	operation	NOUN
ap-688	42	7	offer	offer	VERB
ap-688	42	8	very	very	ADV
ap-688	42	9	limited	limited	ADJ
ap-688	42	10	parallelism	parallelism	NOUN
ap-688	42	11	and	and	CCONJ
ap-688	42	12	therefore	therefore	ADV
ap-688	42	13	can	can	AUX
ap-688	42	14	not	not	PART
ap-688	42	15	be	be	AUX
ap-688	42	16	a	a	DET
ap-688	42	17	major	major	ADJ
ap-688	42	18	source	source	NOUN
ap-688	42	19	of	of	ADP
ap-688	42	20	scalability	scalability	NOUN
ap-688	42	21	.	.	PUNCT
ap-688	43	1	scalability	scalability	NOUN
ap-688	43	2	must	must	AUX
ap-688	43	3	be	be	AUX
ap-688	43	4	sought	seek	VERB
ap-688	43	5	for	for	ADP
ap-688	43	6	in	in	ADP
ap-688	43	7	finite	finite	ADJ
ap-688	43	8	field	field	NOUN
ap-688	43	9	operations	operation	NOUN
ap-688	43	10	,	,	PUNCT
ap-688	43	11	and	and	CCONJ
ap-688	43	12	therefore	therefore	ADV
ap-688	43	13	the	the	DET
ap-688	43	14	most	most	ADV
ap-688	43	15	interesting	interesting	ADJ
ap-688	43	16	area	area	NOUN
ap-688	43	17	for	for	ADP
ap-688	43	18	scalability	scalability	NOUN
ap-688	43	19	in	in	ADP
ap-688	43	20	an	an	DET
ap-688	43	21	elliptic	elliptic	ADJ
ap-688	43	22	curve	curve	NOUN
ap-688	43	23	processor	processor	NOUN
ap-688	43	24	is	be	AUX
ap-688	43	25	the	the	DET
ap-688	43	26	finite	finite	ADJ
ap-688	43	27	field	field	NOUN
ap-688	43	28	unit	unit	NOUN
ap-688	43	29	.	.	PUNCT
ap-688	44	1	1.3	1.3	NUM
ap-688	44	2	metrics	metric	NOUN
ap-688	44	3	the	the	DET
ap-688	44	4	metrics	metric	NOUN
ap-688	44	5	used	use	VERB
ap-688	44	6	reflects	reflect	VERB
ap-688	44	7	the	the	DET
ap-688	44	8	abstraction	abstraction	ADJ
ap-688	44	9	level	level	NOUN
ap-688	44	10	of	of	ADP
ap-688	44	11	the	the	DET
ap-688	44	12	parallelism	parallelism	NOUN
ap-688	44	13	employed	employ	VERB
ap-688	44	14	.	.	PUNCT
ap-688	45	1	when	when	SCONJ
ap-688	45	2	the	the	DET
ap-688	45	3	data	data	NOUN
ap-688	45	4	path	path	NOUN
ap-688	45	5	units	unit	NOUN
ap-688	45	6	are	be	AUX
ap-688	45	7	simple	simple	ADJ
ap-688	45	8	and	and	CCONJ
ap-688	45	9	their	their	PRON
ap-688	45	10	implementations	implementation	NOUN
ap-688	45	11	are	be	AUX
ap-688	45	12	obvious	obvious	ADJ
ap-688	45	13	,	,	PUNCT
ap-688	45	14	we	we	PRON
ap-688	45	15	can	can	AUX
ap-688	45	16	get	get	VERB
ap-688	45	17	at	at	ADP
ap-688	45	18	a	a	DET
ap-688	45	19	lower	low	ADJ
ap-688	45	20	©	©	PROPN
ap-688	45	21	czech	czech	PROPN
ap-688	45	22	technical	technical	PROPN
ap-688	45	23	university	university	PROPN
ap-688	45	24	publishing	publishing	NOUN
ap-688	45	25	house	house	NOUN
ap-688	45	26	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	45	27	55	55	NUM
ap-688	45	28	czech	czech	PROPN
ap-688	45	29	technical	technical	PROPN
ap-688	45	30	university	university	PROPN
ap-688	45	31	in	in	ADP
ap-688	45	32	prague	prague	PROPN
ap-688	45	33	acta	acta	PROPN
ap-688	45	34	polytechnica	polytechnica	PROPN
ap-688	45	35	vol	vol	NOUN
ap-688	45	36	.	.	PROPN
ap-688	46	1	45	45	NUM
ap-688	46	2	no	no	NOUN
ap-688	46	3	.	.	PUNCT
ap-688	47	1	2/2005	2/2005	NUM
ap-688	47	2	scalable	scalable	ADJ
ap-688	47	3	normal	normal	ADJ
ap-688	47	4	basis	basis	NOUN
ap-688	47	5	arithmetic	arithmetic	ADJ
ap-688	47	6	unit	unit	NOUN
ap-688	47	7	for	for	ADP
ap-688	47	8	elliptic	elliptic	ADJ
ap-688	47	9	curve	curve	NOUN
ap-688	47	10	cryptography	cryptography	NOUN
ap-688	47	11	j.	j.	PROPN
ap-688	47	12	schmidt	schmidt	PROPN
ap-688	47	13	,	,	PUNCT
ap-688	47	14	m.	m.	NOUN
ap-688	47	15	novotný	novotný	VERB
ap-688	47	16	the	the	DET
ap-688	47	17	design	design	NOUN
ap-688	47	18	of	of	ADP
ap-688	47	19	a	a	DET
ap-688	47	20	scalable	scalable	ADJ
ap-688	47	21	arithmetic	arithmetic	ADJ
ap-688	47	22	unit	unit	NOUN
ap-688	47	23	for	for	ADP
ap-688	47	24	operations	operation	NOUN
ap-688	47	25	over	over	ADP
ap-688	47	26	elements	element	NOUN
ap-688	47	27	of	of	ADP
ap-688	47	28	gf(2	gf(2	PROPN
ap-688	47	29	m	m	NOUN
ap-688	47	30	)	)	PUNCT
ap-688	47	31	represented	represent	VERB
ap-688	47	32	in	in	ADP
ap-688	47	33	normal	normal	ADJ
ap-688	47	34	basis	basis	NOUN
ap-688	47	35	is	be	AUX
ap-688	47	36	presented	present	VERB
ap-688	47	37	.	.	PUNCT
ap-688	48	1	the	the	DET
ap-688	48	2	unit	unit	NOUN
ap-688	48	3	is	be	AUX
ap-688	48	4	applicable	applicable	ADJ
ap-688	48	5	in	in	ADP
ap-688	48	6	public	public	ADJ
ap-688	48	7	-	-	PUNCT
ap-688	48	8	key	key	NOUN
ap-688	48	9	cryptography	cryptography	NOUN
ap-688	48	10	.	.	PUNCT
ap-688	49	1	it	it	PRON
ap-688	49	2	comprises	comprise	VERB
ap-688	49	3	a	a	DET
ap-688	49	4	pipelined	pipelined	ADJ
ap-688	49	5	massey	massey	NOUN
ap-688	49	6	-	-	PUNCT
ap-688	49	7	omura	omura	NOUN
ap-688	49	8	multiplier	multipli	ADJ
ap-688	49	9	and	and	CCONJ
ap-688	49	10	a	a	DET
ap-688	49	11	shifter	shifter	NOUN
ap-688	49	12	.	.	PUNCT
ap-688	50	1	we	we	PRON
ap-688	50	2	equipped	equip	VERB
ap-688	50	3	the	the	DET
ap-688	50	4	multiplier	multipli	ADJ
ap-688	50	5	with	with	ADP
ap-688	50	6	additional	additional	ADJ
ap-688	50	7	data	datum	NOUN
ap-688	50	8	paths	path	NOUN
ap-688	50	9	to	to	PART
ap-688	50	10	enable	enable	VERB
ap-688	50	11	easy	easy	ADJ
ap-688	50	12	implementation	implementation	NOUN
ap-688	50	13	of	of	ADP
ap-688	50	14	both	both	DET
ap-688	50	15	multiplication	multiplication	NOUN
ap-688	50	16	and	and	CCONJ
ap-688	50	17	inversion	inversion	NOUN
ap-688	50	18	in	in	ADP
ap-688	50	19	a	a	DET
ap-688	50	20	single	single	ADJ
ap-688	50	21	arithmetic	arithmetic	ADJ
ap-688	50	22	unit	unit	NOUN
ap-688	50	23	.	.	PUNCT
ap-688	51	1	we	we	PRON
ap-688	51	2	discuss	discuss	VERB
ap-688	51	3	optimum	optimum	ADJ
ap-688	51	4	design	design	NOUN
ap-688	51	5	of	of	ADP
ap-688	51	6	the	the	DET
ap-688	51	7	shifter	shifter	NOUN
ap-688	51	8	with	with	ADP
ap-688	51	9	respect	respect	NOUN
ap-688	51	10	to	to	ADP
ap-688	51	11	the	the	DET
ap-688	51	12	inversion	inversion	NOUN
ap-688	51	13	algorithm	algorithm	NOUN
ap-688	51	14	and	and	CCONJ
ap-688	51	15	multiplier	multipli	ADJ
ap-688	51	16	performance	performance	NOUN
ap-688	51	17	.	.	PUNCT
ap-688	52	1	the	the	DET
ap-688	52	2	functionality	functionality	NOUN
ap-688	52	3	of	of	ADP
ap-688	52	4	the	the	DET
ap-688	52	5	multiplier	multipli	ADJ
ap-688	52	6	/	/	SYM
ap-688	52	7	inverter	inverter	NOUN
ap-688	52	8	has	have	AUX
ap-688	52	9	been	be	AUX
ap-688	52	10	tested	test	VERB
ap-688	52	11	by	by	ADP
ap-688	52	12	simulation	simulation	NOUN
ap-688	52	13	and	and	CCONJ
ap-688	52	14	implemented	implement	VERB
ap-688	52	15	in	in	ADP
ap-688	52	16	xilinx	xilinx	PROPN
ap-688	52	17	virtex	virtex	PROPN
ap-688	52	18	fpga	fpga	PROPN
ap-688	52	19	.	.	PUNCT
ap-688	53	1	we	we	PRON
ap-688	53	2	present	present	VERB
ap-688	53	3	implementation	implementation	NOUN
ap-688	53	4	data	datum	NOUN
ap-688	53	5	for	for	ADP
ap-688	53	6	various	various	ADJ
ap-688	53	7	digit	digit	NOUN
ap-688	53	8	widths	width	NOUN
ap-688	53	9	which	which	PRON
ap-688	53	10	exhibit	exhibit	VERB
ap-688	53	11	a	a	DET
ap-688	53	12	time	time	NOUN
ap-688	53	13	minimum	minimum	NOUN
ap-688	53	14	for	for	ADP
ap-688	53	15	digit	digit	NOUN
ap-688	53	16	width	width	PROPN
ap-688	53	17	d	d	X
ap-688	53	18	�	�	PROPN
ap-688	53	19	15	15	NUM
ap-688	53	20	.	.	PUNCT
ap-688	54	1	keywords	keyword	NOUN
ap-688	54	2	:	:	PUNCT
ap-688	54	3	finite	finite	PROPN
ap-688	54	4	fields	field	NOUN
ap-688	54	5	,	,	PUNCT
ap-688	54	6	normal	normal	ADJ
ap-688	54	7	base	base	NOUN
ap-688	54	8	,	,	PUNCT
ap-688	54	9	multiplication	multiplication	NOUN
ap-688	54	10	,	,	PUNCT
ap-688	54	11	inversion	inversion	NOUN
ap-688	54	12	,	,	PUNCT
ap-688	54	13	arithmetic	arithmetic	ADJ
ap-688	54	14	unit	unit	NOUN
ap-688	54	15	.	.	PUNCT
ap-688	55	1	level	level	NOUN
ap-688	55	2	.	.	PUNCT
ap-688	56	1	in	in	ADP
ap-688	56	2	this	this	DET
ap-688	56	3	work	work	NOUN
ap-688	56	4	,	,	PUNCT
ap-688	56	5	we	we	PRON
ap-688	56	6	use	use	VERB
ap-688	56	7	the	the	DET
ap-688	56	8	classical	classical	ADJ
ap-688	56	9	metrics	metric	NOUN
ap-688	56	10	of	of	ADP
ap-688	56	11	area	area	NOUN
ap-688	56	12	(	(	PUNCT
ap-688	56	13	which	which	PRON
ap-688	56	14	is	be	AUX
ap-688	56	15	connected	connect	VERB
ap-688	56	16	to	to	ADP
ap-688	56	17	power	power	NOUN
ap-688	56	18	consumption	consumption	NOUN
ap-688	56	19	)	)	PUNCT
ap-688	56	20	and	and	CCONJ
ap-688	56	21	time	time	NOUN
ap-688	56	22	.	.	PUNCT
ap-688	57	1	when	when	SCONJ
ap-688	57	2	a	a	DET
ap-688	57	3	unit	unit	NOUN
ap-688	57	4	is	be	AUX
ap-688	57	5	scaled	scale	VERB
ap-688	57	6	,	,	PUNCT
ap-688	57	7	its	its	PRON
ap-688	57	8	area	area	NOUN
ap-688	57	9	a	a	PRON
ap-688	57	10	and	and	CCONJ
ap-688	57	11	time	time	NOUN
ap-688	57	12	t	t	PROPN
ap-688	57	13	vary	vary	VERB
ap-688	57	14	in	in	ADP
ap-688	57	15	opposite	opposite	ADJ
ap-688	57	16	directions	direction	NOUN
ap-688	57	17	.	.	PUNCT
ap-688	58	1	time	time	NOUN
ap-688	58	2	t	t	PROPN
ap-688	58	3	depends	depend	VERB
ap-688	58	4	on	on	ADP
ap-688	58	5	the	the	DET
ap-688	58	6	number	number	NOUN
ap-688	58	7	of	of	ADP
ap-688	58	8	clock	clock	NOUN
ap-688	58	9	cycles	cycle	NOUN
ap-688	58	10	t	t	PROPN
ap-688	58	11	spent	spend	VERB
ap-688	58	12	in	in	ADP
ap-688	58	13	a	a	DET
ap-688	58	14	given	give	VERB
ap-688	58	15	calculation	calculation	NOUN
ap-688	58	16	and	and	CCONJ
ap-688	58	17	on	on	ADP
ap-688	58	18	the	the	DET
ap-688	58	19	critical	critical	ADJ
ap-688	58	20	path	path	NOUN
ap-688	58	21	length	length	NOUN
ap-688	58	22	�	�	PROPN
ap-688	58	23	in	in	ADP
ap-688	58	24	hardware	hardware	NOUN
ap-688	58	25	.	.	PUNCT
ap-688	59	1	to	to	PART
ap-688	59	2	compare	compare	VERB
ap-688	59	3	differently	differently	ADV
ap-688	59	4	scaled	scale	VERB
ap-688	59	5	units	unit	NOUN
ap-688	59	6	,	,	PUNCT
ap-688	59	7	we	we	PRON
ap-688	59	8	use	use	VERB
ap-688	59	9	the	the	DET
ap-688	59	10	quality	quality	NOUN
ap-688	59	11	measure	measure	NOUN
ap-688	59	12	q	q	PUNCT
ap-688	59	13	at	at	ADP
ap-688	59	14	at	at	ADP
ap-688	59	15	�	�	PROPN
ap-688	59	16	�	�	PROPN
ap-688	59	17	�	�	PROPN
ap-688	59	18	.	.	PROPN
ap-688	59	19	2	2	NUM
ap-688	59	20	previous	previous	ADJ
ap-688	59	21	work	work	NOUN
ap-688	59	22	massey	massey	NOUN
ap-688	59	23	and	and	CCONJ
ap-688	59	24	omura	omura	PROPN
ap-688	59	25	proposed	propose	VERB
ap-688	59	26	a	a	DET
ap-688	59	27	multiplier	multipli	ADJ
ap-688	59	28	[	[	X
ap-688	59	29	6	6	NUM
ap-688	59	30	]	]	PUNCT
ap-688	59	31	that	that	PRON
ap-688	59	32	employs	employ	VERB
ap-688	59	33	the	the	DET
ap-688	59	34	regularity	regularity	NOUN
ap-688	59	35	of	of	ADP
ap-688	59	36	equations	equation	NOUN
ap-688	59	37	for	for	ADP
ap-688	59	38	all	all	DET
ap-688	59	39	bits	bit	NOUN
ap-688	59	40	of	of	ADP
ap-688	59	41	a	a	DET
ap-688	59	42	result	result	NOUN
ap-688	59	43	.	.	PUNCT
ap-688	60	1	from	from	ADP
ap-688	60	2	the	the	DET
ap-688	60	3	equation	equation	NOUN
ap-688	60	4	for	for	ADP
ap-688	60	5	one	one	NUM
ap-688	60	6	bit	bit	NOUN
ap-688	60	7	of	of	ADP
ap-688	60	8	a	a	DET
ap-688	60	9	result	result	NOUN
ap-688	60	10	(	(	PUNCT
ap-688	60	11	e.g.	e.g.	ADV
ap-688	60	12	c0	c0	NOUN
ap-688	60	13	)	)	PUNCT
ap-688	60	14	,	,	PUNCT
ap-688	60	15	equations	equation	NOUN
ap-688	60	16	for	for	ADP
ap-688	60	17	other	other	ADJ
ap-688	60	18	bits	bit	NOUN
ap-688	60	19	can	can	AUX
ap-688	60	20	be	be	AUX
ap-688	60	21	derived	derive	VERB
ap-688	60	22	by	by	ADP
ap-688	60	23	rotating	rotate	VERB
ap-688	60	24	bits	bit	NOUN
ap-688	60	25	of	of	ADP
ap-688	60	26	the	the	DET
ap-688	60	27	arguments	argument	NOUN
ap-688	60	28	a	a	PRON
ap-688	60	29	and	and	CCONJ
ap-688	60	30	b	b	NOUN
ap-688	61	1	[	[	X
ap-688	61	2	2	2	NUM
ap-688	61	3	]	]	PUNCT
ap-688	61	4	.	.	PUNCT
ap-688	62	1	in	in	ADP
ap-688	62	2	this	this	DET
ap-688	62	3	multiplier	multipli	ADJ
ap-688	62	4	,	,	PUNCT
ap-688	62	5	one	one	NUM
ap-688	62	6	bit	bit	NOUN
ap-688	62	7	of	of	ADP
ap-688	62	8	the	the	DET
ap-688	62	9	result	result	NOUN
ap-688	62	10	is	be	AUX
ap-688	62	11	computed	compute	VERB
ap-688	62	12	completely	completely	ADV
ap-688	62	13	in	in	ADP
ap-688	62	14	one	one	NUM
ap-688	62	15	clock	clock	NOUN
ap-688	62	16	cycle	cycle	NOUN
ap-688	62	17	.	.	PUNCT
ap-688	63	1	then	then	ADV
ap-688	63	2	,	,	PUNCT
ap-688	63	3	registers	register	NOUN
ap-688	63	4	holding	hold	VERB
ap-688	63	5	the	the	DET
ap-688	63	6	arguments	argument	NOUN
ap-688	63	7	a	a	PRON
ap-688	63	8	and	and	CCONJ
ap-688	63	9	b	b	NOUN
ap-688	63	10	are	be	AUX
ap-688	63	11	rotated	rotate	VERB
ap-688	63	12	right	right	ADV
ap-688	63	13	one	one	NUM
ap-688	63	14	bit	bit	NOUN
ap-688	63	15	between	between	ADP
ap-688	63	16	cycles	cycle	NOUN
ap-688	63	17	.	.	PUNCT
ap-688	64	1	the	the	DET
ap-688	64	2	computation	computation	NOUN
ap-688	64	3	of	of	ADP
ap-688	64	4	m	m	PROPN
ap-688	64	5	bits	bit	NOUN
ap-688	64	6	of	of	ADP
ap-688	64	7	the	the	DET
ap-688	64	8	result	result	NOUN
ap-688	64	9	takes	take	VERB
ap-688	64	10	m	m	NOUN
ap-688	64	11	clock	clock	NOUN
ap-688	64	12	cycles	cycle	NOUN
ap-688	64	13	and	and	CCONJ
ap-688	64	14	hence	hence	ADV
ap-688	64	15	this	this	DET
ap-688	64	16	multiplier	multiplier	ADV
ap-688	64	17	is	be	AUX
ap-688	64	18	also	also	ADV
ap-688	64	19	called	call	VERB
ap-688	64	20	bit	bit	NOUN
ap-688	64	21	-	-	PUNCT
ap-688	64	22	serial	serial	NOUN
ap-688	64	23	.	.	PUNCT
ap-688	65	1	agnew	agnew	PROPN
ap-688	65	2	,	,	PUNCT
ap-688	65	3	mullin	mullin	PROPN
ap-688	65	4	,	,	PUNCT
ap-688	65	5	onyszchuk	onyszchuk	ADJ
ap-688	65	6	and	and	CCONJ
ap-688	65	7	vanstone	vanstone	NOUN
ap-688	65	8	introduced	introduce	VERB
ap-688	65	9	a	a	DET
ap-688	65	10	modification	modification	NOUN
ap-688	65	11	of	of	ADP
ap-688	65	12	the	the	DET
ap-688	65	13	massey	massey	NOUN
ap-688	65	14	-	-	PUNCT
ap-688	65	15	omura	omura	NOUN
ap-688	65	16	multiplier	multiplier	ADV
ap-688	65	17	[	[	X
ap-688	65	18	1	1	NUM
ap-688	65	19	]	]	PUNCT
ap-688	65	20	(	(	PUNCT
ap-688	65	21	in	in	ADP
ap-688	65	22	this	this	DET
ap-688	65	23	paper	paper	NOUN
ap-688	65	24	,	,	PUNCT
ap-688	65	25	we	we	PRON
ap-688	65	26	call	call	VERB
ap-688	65	27	it	it	PRON
ap-688	65	28	the	the	DET
ap-688	65	29	amov	amov	ADJ
ap-688	65	30	multiplier	multiplier	NOUN
ap-688	65	31	)	)	PUNCT
ap-688	65	32	.	.	PUNCT
ap-688	66	1	they	they	PRON
ap-688	66	2	divided	divide	VERB
ap-688	66	3	the	the	DET
ap-688	66	4	equation	equation	NOUN
ap-688	66	5	for	for	ADP
ap-688	66	6	each	each	DET
ap-688	66	7	bit	bit	NOUN
ap-688	66	8	ci	ci	NOUN
ap-688	66	9	into	into	ADP
ap-688	66	10	m	m	PROPN
ap-688	66	11	products	product	NOUN
ap-688	66	12	pi	pi	PROPN
ap-688	66	13	,	,	PUNCT
ap-688	66	14	j	j	NOUN
ap-688	66	15	:	:	PUNCT
ap-688	67	1	c	c	PROPN
ap-688	68	1	p	p	NOUN
ap-688	68	2	p	p	X
ap-688	68	3	p	p	X
ap-688	69	1	pi	pi	NOUN
ap-688	70	1	i	i	PRON
ap-688	71	1	i	i	INTJ
ap-688	72	1	i	i	PRON
ap-688	72	2	m	m	VERB
ap-688	72	3	i	i	NOUN
ap-688	72	4	m	m	VERB
ap-688	72	5	�	�	PROPN
ap-688	72	6	�	�	PROPN
ap-688	72	7	�	�	PROPN
ap-688	72	8	�	�	PROPN
ap-688	72	9	�	�	PROPN
ap-688	72	10	�	�	PROPN
ap-688	72	11	�	�	PROPN
ap-688	72	12	,	,	PUNCT
ap-688	72	13	,	,	PUNCT
ap-688	72	14	,	,	PUNCT
ap-688	72	15	,	,	PUNCT
ap-688	72	16	0	0	NUM
ap-688	72	17	1	1	NUM
ap-688	72	18	2	2	NUM
ap-688	72	19	1	1	NUM
ap-688	72	20	�	�	PROPN
ap-688	72	21	(	(	PUNCT
ap-688	72	22	2	2	NUM
ap-688	72	23	)	)	PUNCT
ap-688	72	24	in	in	ADP
ap-688	72	25	the	the	DET
ap-688	72	26	first	first	ADJ
ap-688	72	27	clock	clock	NOUN
ap-688	72	28	cycle	cycle	NOUN
ap-688	72	29	,	,	PUNCT
ap-688	72	30	the	the	DET
ap-688	72	31	product	product	NOUN
ap-688	72	32	pi	pi	NOUN
ap-688	72	33	,	,	PUNCT
ap-688	72	34	i+0	i+0	X
ap-688	72	35	of	of	ADP
ap-688	72	36	bit	bit	NOUN
ap-688	72	37	ci	ci	NOUN
ap-688	72	38	for	for	ADP
ap-688	72	39	all	all	PRON
ap-688	72	40	i	i	PRON
ap-688	72	41	�	�	PROPN
ap-688	72	42	�	�	PROPN
ap-688	72	43	0	0	NUM
ap-688	72	44	,	,	PUNCT
ap-688	72	45	m	m	VERB
ap-688	72	46	–	–	PUNCT
ap-688	72	47	1	1	NUM
ap-688	72	48	is	be	AUX
ap-688	72	49	evaluated	evaluate	VERB
ap-688	72	50	.	.	PUNCT
ap-688	73	1	in	in	ADP
ap-688	73	2	the	the	DET
ap-688	73	3	next	next	ADJ
ap-688	73	4	cycle	cycle	NOUN
ap-688	73	5	,	,	PUNCT
ap-688	73	6	the	the	DET
ap-688	73	7	product	product	NOUN
ap-688	73	8	pi	pi	NOUN
ap-688	73	9	,	,	PUNCT
ap-688	73	10	i+1	i+1	NUM
ap-688	73	11	(	(	PUNCT
ap-688	73	12	all	all	DET
ap-688	73	13	subscripts	subscript	NOUN
ap-688	73	14	are	be	AUX
ap-688	73	15	reduced	reduce	VERB
ap-688	73	16	mod	mod	PROPN
ap-688	73	17	m	m	PROPN
ap-688	73	18	)	)	PUNCT
ap-688	73	19	of	of	ADP
ap-688	73	20	bit	bit	NOUN
ap-688	73	21	ci	ci	NOUN
ap-688	73	22	for	for	ADP
ap-688	73	23	all	all	PRON
ap-688	73	24	i	i	PRON
ap-688	73	25	�	�	PROPN
ap-688	73	26	�	�	PROPN
ap-688	73	27	0	0	NUM
ap-688	73	28	,	,	PUNCT
ap-688	73	29	m	m	VERB
ap-688	73	30	–	–	PUNCT
ap-688	73	31	1	1	NUM
ap-688	73	32	is	be	AUX
ap-688	73	33	evaluated	evaluate	VERB
ap-688	73	34	and	and	CCONJ
ap-688	73	35	added	add	VERB
ap-688	73	36	to	to	ADP
ap-688	73	37	the	the	DET
ap-688	73	38	intermediate	intermediate	ADJ
ap-688	73	39	result	result	NOUN
ap-688	73	40	,	,	PUNCT
ap-688	73	41	and	and	CCONJ
ap-688	73	42	so	so	ADV
ap-688	73	43	on	on	ADV
ap-688	73	44	.	.	PUNCT
ap-688	74	1	all	all	DET
ap-688	74	2	bits	bit	NOUN
ap-688	74	3	of	of	ADP
ap-688	74	4	the	the	DET
ap-688	74	5	result	result	NOUN
ap-688	74	6	are	be	AUX
ap-688	74	7	successively	successively	ADV
ap-688	74	8	evaluated	evaluate	VERB
ap-688	74	9	in	in	ADP
ap-688	74	10	parallel	parallel	NOUN
ap-688	74	11	;	;	PUNCT
ap-688	74	12	the	the	DET
ap-688	74	13	computation	computation	NOUN
ap-688	74	14	is	be	AUX
ap-688	74	15	pipelined	pipeline	VERB
ap-688	74	16	.	.	PUNCT
ap-688	75	1	the	the	DET
ap-688	75	2	block	block	NOUN
ap-688	75	3	diagram	diagram	NOUN
ap-688	75	4	of	of	ADP
ap-688	75	5	the	the	DET
ap-688	75	6	amov	amov	ADJ
ap-688	75	7	multiplier	multipli	ADJ
ap-688	75	8	is	be	AUX
ap-688	75	9	in	in	ADP
ap-688	75	10	fig	fig	NOUN
ap-688	75	11	.	.	PUNCT
ap-688	76	1	1	1	X
ap-688	76	2	.	.	PUNCT
ap-688	76	3	the	the	DET
ap-688	76	4	multiplication	multiplication	NOUN
ap-688	76	5	is	be	AUX
ap-688	76	6	performed	perform	VERB
ap-688	76	7	as	as	SCONJ
ap-688	76	8	follows	follow	VERB
ap-688	76	9	:	:	PUNCT
ap-688	76	10	in	in	ADP
ap-688	76	11	the	the	DET
ap-688	76	12	first	first	ADJ
ap-688	76	13	step	step	NOUN
ap-688	76	14	,	,	PUNCT
ap-688	76	15	both	both	PRON
ap-688	76	16	operands	operand	VERB
ap-688	76	17	a	a	PRON
ap-688	76	18	and	and	CCONJ
ap-688	76	19	b	b	NOUN
ap-688	76	20	are	be	AUX
ap-688	76	21	loaded	load	VERB
ap-688	76	22	from	from	ADP
ap-688	76	23	inputs	input	NOUN
ap-688	76	24	in1	in1	NOUN
ap-688	76	25	and	and	CCONJ
ap-688	76	26	in2	in2	PROPN
ap-688	76	27	to	to	PART
ap-688	76	28	registers	register	VERB
ap-688	76	29	a	a	PRON
ap-688	76	30	and	and	CCONJ
ap-688	76	31	b	b	NOUN
ap-688	76	32	,	,	PUNCT
ap-688	76	33	respectively	respectively	ADV
ap-688	76	34	.	.	PUNCT
ap-688	77	1	then	then	ADV
ap-688	77	2	,	,	PUNCT
ap-688	77	3	in	in	ADP
ap-688	77	4	each	each	PRON
ap-688	77	5	of	of	ADP
ap-688	77	6	the	the	DET
ap-688	77	7	following	follow	VERB
ap-688	77	8	m	m	NOUN
ap-688	77	9	clock	clock	NOUN
ap-688	77	10	cycles	cycle	NOUN
ap-688	77	11	,	,	PUNCT
ap-688	77	12	both	both	CCONJ
ap-688	77	13	the	the	DET
ap-688	77	14	a	a	PRON
ap-688	77	15	and	and	CCONJ
ap-688	77	16	b	b	NOUN
ap-688	77	17	registers	register	NOUN
ap-688	77	18	are	be	AUX
ap-688	77	19	rotated	rotate	VERB
ap-688	77	20	right	right	INTJ
ap-688	77	21	(	(	PUNCT
ap-688	77	22	this	this	PRON
ap-688	77	23	is	be	AUX
ap-688	77	24	represented	represent	VERB
ap-688	77	25	by	by	ADP
ap-688	77	26	the	the	DET
ap-688	77	27	blocks	block	NOUN
ap-688	77	28	ror	ror	NOUN
ap-688	77	29	1	1	NUM
ap-688	77	30	)	)	PUNCT
ap-688	77	31	and	and	CCONJ
ap-688	77	32	the	the	DET
ap-688	77	33	result	result	NOUN
ap-688	77	34	c	c	NOUN
ap-688	77	35	in	in	ADP
ap-688	77	36	register	register	PROPN
ap-688	77	37	c	c	PROPN
ap-688	77	38	is	be	AUX
ap-688	77	39	evaluated	evaluate	VERB
ap-688	77	40	successively	successively	ADV
ap-688	77	41	by	by	ADP
ap-688	77	42	the	the	DET
ap-688	77	43	block	block	NOUN
ap-688	77	44	comb	comb	NOUN
ap-688	77	45	.	.	PUNCT
ap-688	78	1	logic	logic	NOUN
ap-688	78	2	,	,	PUNCT
ap-688	78	3	which	which	PRON
ap-688	78	4	implements	implement	VERB
ap-688	78	5	the	the	DET
ap-688	78	6	products	product	NOUN
ap-688	78	7	pi	pi	PROPN
ap-688	78	8	,	,	PUNCT
ap-688	78	9	j	j	PROPN
ap-688	78	10	from	from	ADP
ap-688	78	11	eq	eq	NOUN
ap-688	78	12	.	.	PROPN
ap-688	79	1	2	2	NUM
ap-688	79	2	.	.	X
ap-688	79	3	after	after	ADP
ap-688	79	4	m	m	PROPN
ap-688	79	5	clock	clock	NOUN
ap-688	79	6	cycles	cycle	NOUN
ap-688	79	7	,	,	PUNCT
ap-688	79	8	the	the	DET
ap-688	79	9	result	result	NOUN
ap-688	79	10	c	c	PROPN
ap-688	79	11	a	a	DET
ap-688	79	12	b	b	PROPN
ap-688	79	13	�	�	PROPN
ap-688	79	14	is	be	AUX
ap-688	79	15	available	available	ADJ
ap-688	79	16	at	at	ADP
ap-688	79	17	output	output	NOUN
ap-688	79	18	out	out	ADP
ap-688	79	19	.	.	PUNCT
ap-688	80	1	all	all	DET
ap-688	80	2	registers	register	NOUN
ap-688	80	3	and	and	CCONJ
ap-688	80	4	data	datum	NOUN
ap-688	80	5	paths	path	NOUN
ap-688	80	6	are	be	AUX
ap-688	80	7	m	m	PROPN
ap-688	80	8	bits	bit	NOUN
ap-688	80	9	wide	wide	ADJ
ap-688	80	10	.	.	PUNCT
ap-688	81	1	the	the	DET
ap-688	81	2	amount	amount	NOUN
ap-688	81	3	of	of	ADP
ap-688	81	4	hardware	hardware	NOUN
ap-688	81	5	is	be	AUX
ap-688	81	6	the	the	DET
ap-688	81	7	same	same	ADJ
ap-688	81	8	as	as	ADP
ap-688	81	9	for	for	ADP
ap-688	81	10	the	the	DET
ap-688	81	11	non	non	ADJ
ap-688	81	12	-	-	ADJ
ap-688	81	13	pipelined	pipelined	ADJ
ap-688	81	14	massey	massey	NOUN
ap-688	81	15	-	-	PUNCT
ap-688	81	16	omura	omura	NOUN
ap-688	81	17	multiplier	multiplier	ADV
ap-688	81	18	,	,	PUNCT
ap-688	81	19	but	but	CCONJ
ap-688	81	20	the	the	DET
ap-688	81	21	critical	critical	ADJ
ap-688	81	22	path	path	NOUN
ap-688	81	23	is	be	AUX
ap-688	81	24	short	short	ADJ
ap-688	81	25	and	and	CCONJ
ap-688	81	26	constant	constant	ADJ
ap-688	81	27	(	(	PUNCT
ap-688	81	28	it	it	PRON
ap-688	81	29	does	do	AUX
ap-688	81	30	not	not	PART
ap-688	81	31	depend	depend	VERB
ap-688	81	32	on	on	ADP
ap-688	81	33	m	m	PROPN
ap-688	81	34	)	)	PUNCT
ap-688	81	35	and	and	CCONJ
ap-688	81	36	so	so	ADV
ap-688	81	37	the	the	DET
ap-688	81	38	maximum	maximum	ADJ
ap-688	81	39	achievable	achievable	ADJ
ap-688	81	40	frequency	frequency	NOUN
ap-688	81	41	is	be	AUX
ap-688	81	42	higher	high	ADJ
ap-688	81	43	.	.	PUNCT
ap-688	82	1	this	this	DET
ap-688	82	2	multiplier	multiplier	ADV
ap-688	82	3	is	be	AUX
ap-688	82	4	widely	widely	ADV
ap-688	82	5	used	use	VERB
ap-688	82	6	.	.	PUNCT
ap-688	83	1	the	the	DET
ap-688	83	2	computation	computation	NOUN
ap-688	83	3	of	of	ADP
ap-688	83	4	an	an	DET
ap-688	83	5	inverse	inverse	NOUN
ap-688	83	6	element	element	NOUN
ap-688	83	7	(	(	PUNCT
ap-688	83	8	inversion	inversion	NOUN
ap-688	83	9	)	)	PUNCT
ap-688	83	10	by	by	ADP
ap-688	83	11	the	the	DET
ap-688	83	12	itt	itt	ADJ
ap-688	83	13	algorithm	algorithm	NOUN
ap-688	83	14	[	[	X
ap-688	83	15	3	3	X
ap-688	83	16	]	]	PUNCT
ap-688	83	17	is	be	AUX
ap-688	83	18	usually	usually	ADV
ap-688	83	19	controlled	control	VERB
ap-688	83	20	by	by	ADP
ap-688	83	21	a	a	DET
ap-688	83	22	microprogram	microprogram	NOUN
ap-688	83	23	[	[	X
ap-688	83	24	4	4	NUM
ap-688	83	25	]	]	PUNCT
ap-688	83	26	.	.	PUNCT
ap-688	84	1	when	when	SCONJ
ap-688	84	2	implementing	implement	VERB
ap-688	84	3	the	the	DET
ap-688	84	4	itt	itt	ADJ
ap-688	84	5	inversion	inversion	NOUN
ap-688	84	6	using	use	VERB
ap-688	84	7	a	a	DET
ap-688	84	8	classical	classical	ADJ
ap-688	84	9	amov	amov	ADJ
ap-688	84	10	multiplier	multipli	ADJ
ap-688	84	11	,	,	PUNCT
ap-688	84	12	additional	additional	ADJ
ap-688	84	13	registers	register	NOUN
ap-688	84	14	and	and	CCONJ
ap-688	84	15	data	datum	NOUN
ap-688	84	16	transfers	transfer	NOUN
ap-688	84	17	outside	outside	ADP
ap-688	84	18	the	the	DET
ap-688	84	19	multiplier	multipli	ADJ
ap-688	84	20	are	be	AUX
ap-688	84	21	necessary	necessary	ADJ
ap-688	84	22	.	.	PUNCT
ap-688	85	1	in	in	ADP
ap-688	85	2	this	this	DET
ap-688	85	3	work	work	NOUN
ap-688	85	4	we	we	PRON
ap-688	85	5	present	present	VERB
ap-688	85	6	a	a	DET
ap-688	85	7	modification	modification	NOUN
ap-688	85	8	of	of	ADP
ap-688	85	9	the	the	DET
ap-688	85	10	amov	amov	ADJ
ap-688	85	11	multiplier	multiplier	NOUN
ap-688	85	12	,	,	PUNCT
ap-688	85	13	which	which	PRON
ap-688	85	14	allows	allow	VERB
ap-688	85	15	efficient	efficient	ADJ
ap-688	85	16	implementation	implementation	NOUN
ap-688	85	17	of	of	ADP
ap-688	85	18	both	both	CCONJ
ap-688	85	19	the	the	DET
ap-688	85	20	multiplication	multiplication	NOUN
ap-688	85	21	and	and	CCONJ
ap-688	85	22	itt	itt	ADJ
ap-688	85	23	inversion	inversion	NOUN
ap-688	85	24	algorithms	algorithm	NOUN
ap-688	85	25	.	.	PUNCT
ap-688	86	1	in	in	ADP
ap-688	86	2	comparison	comparison	NOUN
ap-688	86	3	with	with	ADP
ap-688	86	4	the	the	DET
ap-688	86	5	microprogrammed	microprogramme	VERB
ap-688	86	6	inversion	inversion	NOUN
ap-688	86	7	,	,	PUNCT
ap-688	86	8	no	no	DET
ap-688	86	9	additional	additional	ADJ
ap-688	86	10	registers	register	NOUN
ap-688	86	11	or	or	CCONJ
ap-688	86	12	data	data	NOUN
ap-688	86	13	transfers	transfer	NOUN
ap-688	86	14	outside	outside	ADP
ap-688	86	15	the	the	DET
ap-688	86	16	multiplier	multipli	ADJ
ap-688	86	17	are	be	AUX
ap-688	86	18	necessary	necessary	ADJ
ap-688	86	19	.	.	PUNCT
ap-688	87	1	we	we	PRON
ap-688	87	2	also	also	ADV
ap-688	87	3	introduce	introduce	VERB
ap-688	87	4	several	several	ADJ
ap-688	87	5	improvements	improvement	NOUN
ap-688	87	6	to	to	ADP
ap-688	87	7	this	this	DET
ap-688	87	8	multiplication	multiplication	NOUN
ap-688	87	9	/	/	SYM
ap-688	87	10	inversion	inversion	NOUN
ap-688	87	11	unit	unit	NOUN
ap-688	87	12	,	,	PUNCT
ap-688	87	13	which	which	PRON
ap-688	87	14	lead	lead	VERB
ap-688	87	15	to	to	ADP
ap-688	87	16	increased	increase	VERB
ap-688	87	17	performance	performance	NOUN
ap-688	87	18	and	and	CCONJ
ap-688	87	19	a	a	DET
ap-688	87	20	better	well	ADJ
ap-688	87	21	performance	performance	NOUN
ap-688	87	22	/	/	SYM
ap-688	87	23	area	area	NOUN
ap-688	87	24	ratio	ratio	NOUN
ap-688	87	25	.	.	PUNCT
ap-688	88	1	3	3	NUM
ap-688	88	2	structure	structure	NOUN
ap-688	88	3	of	of	ADP
ap-688	88	4	the	the	DET
ap-688	88	5	unit	unit	NOUN
ap-688	88	6	the	the	DET
ap-688	88	7	data	data	NOUN
ap-688	88	8	path	path	NOUN
ap-688	88	9	of	of	ADP
ap-688	88	10	our	our	PRON
ap-688	88	11	arithmetic	arithmetic	ADJ
ap-688	88	12	unit	unit	NOUN
ap-688	88	13	is	be	AUX
ap-688	88	14	an	an	DET
ap-688	88	15	extension	extension	NOUN
ap-688	88	16	of	of	ADP
ap-688	88	17	the	the	DET
ap-688	88	18	amov	amov	ADJ
ap-688	88	19	multiplier	multiplier	ADV
ap-688	88	20	.	.	PUNCT
ap-688	89	1	by	by	ADP
ap-688	89	2	adding	add	VERB
ap-688	89	3	one	one	NUM
ap-688	89	4	more	more	ADJ
ap-688	89	5	input	input	NOUN
ap-688	89	6	to	to	ADP
ap-688	89	7	the	the	DET
ap-688	89	8	multiplexer	multiplexer	NOUN
ap-688	89	9	preceding	precede	VERB
ap-688	89	10	register	register	NOUN
ap-688	89	11	a	a	PRON
ap-688	89	12	and	and	CCONJ
ap-688	89	13	by	by	ADP
ap-688	89	14	redirecting	redirect	VERB
ap-688	89	15	some	some	DET
ap-688	89	16	data	datum	NOUN
ap-688	89	17	paths	path	NOUN
ap-688	89	18	(	(	PUNCT
ap-688	89	19	see	see	VERB
ap-688	89	20	bold	bold	ADJ
ap-688	89	21	lines	line	NOUN
ap-688	89	22	in	in	ADP
ap-688	89	23	fig	fig	NOUN
ap-688	89	24	.	.	PUNCT
ap-688	89	25	2	2	NUM
ap-688	89	26	)	)	PUNCT
ap-688	89	27	,	,	PUNCT
ap-688	89	28	we	we	PRON
ap-688	89	29	can	can	AUX
ap-688	89	30	simply	simply	ADV
ap-688	89	31	implement	implement	VERB
ap-688	89	32	both	both	DET
ap-688	89	33	multiplication	multiplication	NOUN
ap-688	89	34	and	and	CCONJ
ap-688	89	35	itt	itt	ADJ
ap-688	89	36	inversion	inversion	NOUN
ap-688	89	37	in	in	ADP
ap-688	89	38	the	the	DET
ap-688	89	39	unit	unit	NOUN
ap-688	89	40	and	and	CCONJ
ap-688	89	41	thus	thus	ADV
ap-688	89	42	save	save	VERB
ap-688	89	43	additional	additional	ADJ
ap-688	89	44	registers	register	NOUN
ap-688	89	45	and	and	CCONJ
ap-688	89	46	data	datum	NOUN
ap-688	89	47	transfers	transfer	NOUN
ap-688	89	48	outside	outside	ADP
ap-688	89	49	of	of	ADP
ap-688	89	50	the	the	DET
ap-688	89	51	multiplier	multiplier	NOUN
ap-688	89	52	.	.	PUNCT
ap-688	90	1	the	the	DET
ap-688	90	2	modified	modify	VERB
ap-688	90	3	amov	amov	ADJ
ap-688	90	4	multiplier	multiplier	ADV
ap-688	90	5	has	have	VERB
ap-688	90	6	a	a	DET
ap-688	90	7	dedicated	dedicated	ADJ
ap-688	90	8	control	control	NOUN
ap-688	90	9	unit	unit	NOUN
ap-688	90	10	based	base	VERB
ap-688	90	11	on	on	ADP
ap-688	90	12	a	a	DET
ap-688	90	13	finite	finite	ADJ
ap-688	90	14	state	state	NOUN
ap-688	90	15	machine	machine	NOUN
ap-688	90	16	,	,	PUNCT
ap-688	90	17	two	two	NUM
ap-688	90	18	counters	counter	NOUN
ap-688	90	19	count_inv	count_inv	NUM
ap-688	90	20	and	and	CCONJ
ap-688	90	21	count_k	count_k	VERB
ap-688	90	22	and	and	CCONJ
ap-688	90	23	the	the	DET
ap-688	90	24	shift	shift	NOUN
ap-688	90	25	register	register	NOUN
ap-688	90	26	m.	m.	NOUN
ap-688	90	27	it	it	PRON
ap-688	90	28	implements	implement	VERB
ap-688	90	29	the	the	DET
ap-688	90	30	commands	command	NOUN
ap-688	90	31	load_op	load_op	PROPN
ap-688	90	32	,	,	PUNCT
ap-688	90	33	multiply	multiply	ADV
ap-688	90	34	and	and	CCONJ
ap-688	90	35	invert	invert	VERB
ap-688	90	36	.	.	PUNCT
ap-688	91	1	3.1	3.1	NUM
ap-688	91	2	multiplication	multiplication	NOUN
ap-688	91	3	multiplication	multiplication	NOUN
ap-688	91	4	is	be	AUX
ap-688	91	5	performed	perform	VERB
ap-688	91	6	as	as	SCONJ
ap-688	91	7	follows	follow	VERB
ap-688	91	8	:	:	PUNCT
ap-688	91	9	in	in	ADP
ap-688	91	10	the	the	DET
ap-688	91	11	first	first	ADJ
ap-688	91	12	two	two	NUM
ap-688	91	13	steps	step	NOUN
ap-688	91	14	,	,	PUNCT
ap-688	91	15	both	both	PRON
ap-688	91	16	operands	operand	VERB
ap-688	91	17	a	a	PRON
ap-688	91	18	and	and	CCONJ
ap-688	91	19	b	b	NOUN
ap-688	91	20	are	be	AUX
ap-688	91	21	successively	successively	ADV
ap-688	91	22	loaded	load	VERB
ap-688	91	23	from	from	ADP
ap-688	91	24	input	input	NOUN
ap-688	91	25	in	in	ADP
ap-688	91	26	to	to	ADP
ap-688	91	27	registers	register	NOUN
ap-688	91	28	a	a	PRON
ap-688	91	29	and	and	CCONJ
ap-688	91	30	b.	b.	PROPN
ap-688	91	31	then	then	ADV
ap-688	91	32	,	,	PUNCT
ap-688	91	33	in	in	ADP
ap-688	91	34	m	m	NOUN
ap-688	91	35	clock	clock	NOUN
ap-688	91	36	cycles	cycle	NOUN
ap-688	91	37	,	,	PUNCT
ap-688	91	38	the	the	DET
ap-688	91	39	multiplication	multiplication	NOUN
ap-688	91	40	is	be	AUX
ap-688	91	41	performed	perform	VERB
ap-688	91	42	as	as	ADP
ap-688	91	43	in	in	ADP
ap-688	91	44	the	the	DET
ap-688	91	45	standard	standard	ADJ
ap-688	91	46	amov	amov	ADJ
ap-688	91	47	multiplier	multiplier	ADV
ap-688	91	48	.	.	PUNCT
ap-688	92	1	after	after	ADP
ap-688	92	2	its	its	PRON
ap-688	92	3	completion	completion	NOUN
ap-688	92	4	,	,	PUNCT
ap-688	92	5	the	the	DET
ap-688	92	6	result	result	NOUN
ap-688	92	7	c	c	PROPN
ap-688	92	8	a	a	DET
ap-688	92	9	b	b	PROPN
ap-688	92	10	�	�	PROPN
ap-688	92	11	is	be	AUX
ap-688	92	12	loaded	load	VERB
ap-688	92	13	from	from	ADP
ap-688	92	14	register	register	PROPN
ap-688	92	15	c	c	PROPN
ap-688	92	16	to	to	PART
ap-688	92	17	register	register	VERB
ap-688	92	18	a	a	PRON
ap-688	92	19	and	and	CCONJ
ap-688	92	20	is	be	AUX
ap-688	92	21	available	available	ADJ
ap-688	92	22	at	at	ADP
ap-688	92	23	output	output	NOUN
ap-688	92	24	out	out	ADP
ap-688	92	25	.	.	PUNCT
ap-688	93	1	56	56	NUM
ap-688	93	2	©	©	PROPN
ap-688	93	3	czech	czech	PROPN
ap-688	93	4	technical	technical	PROPN
ap-688	93	5	university	university	PROPN
ap-688	93	6	publishing	publishing	NOUN
ap-688	93	7	house	house	NOUN
ap-688	93	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	93	9	acta	acta	PROPN
ap-688	93	10	polytechnica	polytechnica	PROPN
ap-688	93	11	vol	vol	NOUN
ap-688	93	12	.	.	PROPN
ap-688	94	1	45	45	NUM
ap-688	94	2	no	no	NOUN
ap-688	94	3	.	.	PUNCT
ap-688	95	1	2/2005	2/2005	NUM
ap-688	95	2	czech	czech	PROPN
ap-688	95	3	technical	technical	PROPN
ap-688	95	4	university	university	PROPN
ap-688	95	5	in	in	ADP
ap-688	95	6	prague	prague	PROPN
ap-688	95	7	b	b	PROPN
ap-688	95	8	comb	comb	NOUN
ap-688	95	9	.	.	PUNCT
ap-688	96	1	logic	logic	NOUN
ap-688	96	2	ror	ror	NOUN
ap-688	96	3	1	1	NUM
ap-688	96	4	in1	in1	NOUN
ap-688	96	5	ror	ror	NOUN
ap-688	96	6	1	1	NUM
ap-688	96	7	in2	in2	PROPN
ap-688	96	8	a	a	DET
ap-688	96	9	c	c	X
ap-688	96	10	out	out	ADP
ap-688	96	11	fig	fig	NOUN
ap-688	96	12	.	.	PUNCT
ap-688	97	1	1	1	NUM
ap-688	97	2	:	:	PUNCT
ap-688	97	3	amov	amov	ADJ
ap-688	97	4	multiplier	multipli	ADJ
ap-688	97	5	b	b	NOUN
ap-688	97	6	comb	comb	NOUN
ap-688	97	7	.	.	PUNCT
ap-688	98	1	logic	logic	NOUN
ap-688	98	2	ror	ror	NOUN
ap-688	98	3	1	1	NUM
ap-688	98	4	in	in	ADP
ap-688	98	5	ror	ror	NOUN
ap-688	98	6	1	1	NUM
ap-688	98	7	a	a	DET
ap-688	98	8	c	c	NOUN
ap-688	98	9	out	out	ADP
ap-688	98	10	fig	fig	NOUN
ap-688	98	11	.	.	PUNCT
ap-688	99	1	2	2	NUM
ap-688	99	2	:	:	PUNCT
ap-688	99	3	modified	modify	VERB
ap-688	99	4	amov	amov	ADJ
ap-688	99	5	multiplier	multipli	ADJ
ap-688	99	6	3.2	3.2	NUM
ap-688	99	7	inversion	inversion	NOUN
ap-688	99	8	our	our	PRON
ap-688	99	9	unit	unit	NOUN
ap-688	99	10	computes	compute	VERB
ap-688	99	11	the	the	DET
ap-688	99	12	itt	itt	ADJ
ap-688	99	13	inversion	inversion	NOUN
ap-688	100	1	[	[	X
ap-688	100	2	2	2	NUM
ap-688	100	3	]	]	PUNCT
ap-688	100	4	,	,	PUNCT
ap-688	101	1	[	[	X
ap-688	101	2	3	3	X
ap-688	101	3	]	]	PUNCT
ap-688	101	4	by	by	ADP
ap-688	101	5	algorithm	algorithm	NOUN
ap-688	101	6	1	1	NUM
ap-688	101	7	.	.	PUNCT
ap-688	101	8	it	it	PRON
ap-688	101	9	comprises	comprise	VERB
ap-688	101	10	�	�	PROPN
ap-688	101	11	�	�	PROPN
ap-688	101	12	log	log	PROPN
ap-688	101	13	(	(	PUNCT
ap-688	101	14	)	)	PUNCT
ap-688	101	15	(	(	PUNCT
ap-688	101	16	)	)	SYM
ap-688	102	1	2	2	NUM
ap-688	102	2	1	1	NUM
ap-688	102	3	1	1	NUM
ap-688	102	4	1	1	NUM
ap-688	102	5	m	m	PROPN
ap-688	102	6	w	w	PROPN
ap-688	102	7	m	m	PROPN
ap-688	102	8	�	�	PROPN
ap-688	102	9	�	�	PROPN
ap-688	102	10	�	�	PROPN
ap-688	102	11	�	�	PROPN
ap-688	102	12	multiplications	multiplication	NOUN
ap-688	102	13	,	,	PUNCT
ap-688	102	14	where	where	SCONJ
ap-688	102	15	w(m	w(m	PROPN
ap-688	102	16	�	�	PROPN
ap-688	102	17	1	1	NUM
ap-688	102	18	)	)	PUNCT
ap-688	102	19	is	be	AUX
ap-688	102	20	the	the	DET
ap-688	102	21	number	number	NOUN
ap-688	102	22	of	of	ADP
ap-688	102	23	non	non	ADJ
ap-688	102	24	-	-	ADJ
ap-688	102	25	zero	zero	NUM
ap-688	102	26	bits	bit	NOUN
ap-688	102	27	in	in	ADP
ap-688	102	28	the	the	DET
ap-688	102	29	binary	binary	ADJ
ap-688	102	30	representation	representation	NOUN
ap-688	102	31	of	of	ADP
ap-688	102	32	m	m	PROPN
ap-688	102	33	�	�	PROPN
ap-688	102	34	1	1	NUM
ap-688	102	35	.	.	PUNCT
ap-688	103	1	furthermore	furthermore	ADV
ap-688	103	2	,	,	PUNCT
ap-688	103	3	it	it	PRON
ap-688	103	4	needs	need	VERB
ap-688	103	5	(	(	PUNCT
ap-688	103	6	m	m	VERB
ap-688	103	7	�	�	NOUN
ap-688	103	8	1	1	NUM
ap-688	103	9	)	)	PUNCT
ap-688	103	10	�	�	PROPN
ap-688	103	11	w(m	w(m	PROPN
ap-688	103	12	�	�	PROPN
ap-688	103	13	1	1	NUM
ap-688	103	14	)	)	PUNCT
ap-688	103	15	squarings	squaring	NOUN
ap-688	103	16	.	.	PUNCT
ap-688	104	1	the	the	DET
ap-688	104	2	total	total	ADJ
ap-688	104	3	number	number	NOUN
ap-688	104	4	of	of	ADP
ap-688	104	5	clock	clock	NOUN
ap-688	104	6	cycles	cycle	NOUN
ap-688	104	7	spent	spend	VERB
ap-688	104	8	for	for	ADP
ap-688	104	9	one	one	NUM
ap-688	104	10	inversion	inversion	NOUN
ap-688	104	11	is	be	AUX
ap-688	104	12	�	�	PROPN
ap-688	104	13	�	�	PROPN
ap-688	104	14	�	�	PROPN
ap-688	104	15	�	�	PROPN
ap-688	104	16	c	c	NOUN
ap-688	104	17	m	m	PROPN
ap-688	104	18	w	w	NOUN
ap-688	104	19	m	m	PROPN
ap-688	104	20	c	c	NOUN
ap-688	104	21	m	m	PROPN
ap-688	104	22	w	w	NOUN
ap-688	104	23	m	m	VERB
ap-688	104	24	c	c	AUX
ap-688	104	25	co	co	NOUN
ap-688	104	26	inv	inv	VERB
ap-688	104	27	mul	mul	PROPN
ap-688	104	28	sqr	sqr	PROPN
ap-688	104	29	�	�	PROPN
ap-688	104	30	�	�	PROPN
ap-688	104	31	�	�	PROPN
ap-688	104	32	�	�	PROPN
ap-688	104	33	�	�	PROPN
ap-688	104	34	�	�	PROPN
ap-688	104	35	�	�	PROPN
ap-688	104	36	�	�	PROPN
ap-688	104	37	�	�	PROPN
ap-688	104	38	�	�	PROPN
ap-688	104	39	�	�	PROPN
ap-688	104	40	�	�	PROPN
ap-688	104	41	�	�	PROPN
ap-688	104	42	log	log	PROPN
ap-688	104	43	(	(	PUNCT
ap-688	104	44	)	)	PUNCT
ap-688	104	45	(	(	PUNCT
ap-688	104	46	)	)	PUNCT
ap-688	104	47	(	(	PUNCT
ap-688	104	48	)	)	PUNCT
ap-688	104	49	(	(	PUNCT
ap-688	104	50	)	)	PUNCT
ap-688	104	51	2	2	NUM
ap-688	104	52	1	1	NUM
ap-688	104	53	1	1	NUM
ap-688	104	54	1	1	NUM
ap-688	104	55	1	1	NUM
ap-688	104	56	1	1	NUM
ap-688	104	57	nst	nst	NOUN
ap-688	104	58	,	,	PUNCT
ap-688	104	59	where	where	SCONJ
ap-688	104	60	cmul	cmul	PROPN
ap-688	104	61	is	be	AUX
ap-688	104	62	number	number	NOUN
ap-688	104	63	of	of	ADP
ap-688	104	64	clock	clock	NOUN
ap-688	104	65	cycles	cycle	NOUN
ap-688	104	66	of	of	ADP
ap-688	104	67	1	1	NUM
ap-688	104	68	multiplication	multiplication	NOUN
ap-688	104	69	(	(	PUNCT
ap-688	104	70	cmul	cmul	PROPN
ap-688	104	71	�	�	PROPN
ap-688	104	72	m	m	PROPN
ap-688	104	73	)	)	PUNCT
ap-688	104	74	and	and	CCONJ
ap-688	104	75	csqr	csqr	NOUN
ap-688	104	76	is	be	AUX
ap-688	104	77	number	number	NOUN
ap-688	104	78	of	of	ADP
ap-688	104	79	clock	clock	NOUN
ap-688	104	80	cycles	cycle	NOUN
ap-688	104	81	of	of	ADP
ap-688	104	82	one	one	NUM
ap-688	104	83	squaring	squaring	NOUN
ap-688	104	84	(	(	PUNCT
ap-688	104	85	csqr	csqr	PROPN
ap-688	104	86	�	�	PROPN
ap-688	104	87	1	1	NUM
ap-688	104	88	)	)	PUNCT
ap-688	104	89	.	.	PUNCT
ap-688	105	1	note	note	VERB
ap-688	105	2	that	that	SCONJ
ap-688	105	3	the	the	DET
ap-688	105	4	inverted	inverted	ADJ
ap-688	105	5	value	value	NOUN
ap-688	105	6	must	must	AUX
ap-688	105	7	be	be	AUX
ap-688	105	8	available	available	ADJ
ap-688	105	9	at	at	ADP
ap-688	105	10	input	input	NOUN
ap-688	105	11	in	in	ADP
ap-688	105	12	during	during	ADP
ap-688	105	13	the	the	DET
ap-688	105	14	whole	whole	ADJ
ap-688	105	15	process	process	NOUN
ap-688	105	16	of	of	ADP
ap-688	105	17	inversion	inversion	NOUN
ap-688	105	18	.	.	PUNCT
ap-688	106	1	the	the	DET
ap-688	106	2	rotation	rotation	NOUN
ap-688	106	3	capability	capability	NOUN
ap-688	106	4	of	of	ADP
ap-688	106	5	register	register	PROPN
ap-688	106	6	b	b	PROPN
ap-688	106	7	is	be	AUX
ap-688	106	8	used	use	VERB
ap-688	106	9	for	for	ADP
ap-688	106	10	the	the	DET
ap-688	106	11	computation	computation	NOUN
ap-688	106	12	of	of	ADP
ap-688	106	13	squarings	squaring	NOUN
ap-688	106	14	in	in	ADP
ap-688	106	15	steps	step	NOUN
ap-688	106	16	3.2.1	3.2.1	NUM
ap-688	106	17	and	and	CCONJ
ap-688	106	18	3.4.2	3.4.2	NUM
ap-688	106	19	.	.	NOUN
ap-688	106	20	4	4	NUM
ap-688	106	21	scaling	scale	VERB
ap-688	106	22	the	the	DET
ap-688	106	23	multiplication	multiplication	NOUN
ap-688	106	24	the	the	DET
ap-688	106	25	basic	basic	ADJ
ap-688	106	26	ecc	ecc	PROPN
ap-688	106	27	operation	operation	NOUN
ap-688	106	28	(	(	PUNCT
ap-688	106	29	eq	eq	NOUN
ap-688	106	30	.	.	NOUN
ap-688	106	31	1	1	NUM
ap-688	106	32	)	)	PUNCT
ap-688	106	33	is	be	AUX
ap-688	106	34	performed	perform	VERB
ap-688	106	35	by	by	ADP
ap-688	106	36	successive	successive	ADJ
ap-688	106	37	point	point	NOUN
ap-688	106	38	additions	addition	NOUN
ap-688	106	39	and	and	CCONJ
ap-688	106	40	point	point	PROPN
ap-688	106	41	doublings	doublings	PROPN
ap-688	106	42	.	.	PUNCT
ap-688	107	1	each	each	PRON
ap-688	107	2	of	of	ADP
ap-688	107	3	these	these	DET
ap-688	107	4	operations	operation	NOUN
ap-688	107	5	needs	need	VERB
ap-688	107	6	1	1	NUM
ap-688	107	7	inversion	inversion	NOUN
ap-688	107	8	,	,	PUNCT
ap-688	107	9	2	2	NUM
ap-688	107	10	multiplications	multiplication	NOUN
ap-688	107	11	and	and	CCONJ
ap-688	107	12	1	1	NUM
ap-688	107	13	squaring	square	VERB
ap-688	107	14	[	[	NOUN
ap-688	107	15	2	2	NUM
ap-688	107	16	]	]	PUNCT
ap-688	107	17	.	.	PUNCT
ap-688	108	1	the	the	DET
ap-688	108	2	number	number	NOUN
ap-688	108	3	of	of	ADP
ap-688	108	4	clock	clock	NOUN
ap-688	108	5	cycles	cycle	NOUN
ap-688	108	6	necessary	necessary	ADJ
ap-688	108	7	for	for	ADP
ap-688	108	8	one	one	NUM
ap-688	108	9	point	point	NOUN
ap-688	108	10	addition	addition	NOUN
ap-688	108	11	or	or	CCONJ
ap-688	108	12	doubling	doubling	NOUN
ap-688	108	13	is	be	AUX
ap-688	108	14	then	then	ADV
ap-688	108	15	:	:	PUNCT
ap-688	108	16	�	�	PROPN
ap-688	108	17	�	�	PROPN
ap-688	108	18	�	�	PROPN
ap-688	108	19	�	�	PROPN
ap-688	108	20	c	c	NOUN
ap-688	108	21	m	m	PROPN
ap-688	108	22	w	w	NOUN
ap-688	108	23	m	m	PROPN
ap-688	108	24	c	c	NOUN
ap-688	108	25	m	m	PROPN
ap-688	108	26	w	w	NOUN
ap-688	108	27	m	m	PROPN
ap-688	108	28	c	c	NOUN
ap-688	108	29	const	const	X
ap-688	108	30	padd	padd	PROPN
ap-688	108	31	mul	mul	PROPN
ap-688	108	32	sqr	sqr	PROPN
ap-688	108	33	�	�	PROPN
ap-688	108	34	�	�	PROPN
ap-688	108	35	�	�	PROPN
ap-688	108	36	�	�	PROPN
ap-688	108	37	�	�	PROPN
ap-688	108	38	�	�	PROPN
ap-688	108	39	�	�	PROPN
ap-688	108	40	�	�	PROPN
ap-688	108	41	�	�	PROPN
ap-688	108	42	�	�	PROPN
ap-688	108	43	�	�	PROPN
ap-688	108	44	�	�	PROPN
ap-688	108	45	log	log	PROPN
ap-688	108	46	(	(	PUNCT
ap-688	108	47	)	)	PUNCT
ap-688	108	48	(	(	PUNCT
ap-688	108	49	)	)	PUNCT
ap-688	108	50	(	(	PUNCT
ap-688	108	51	)	)	PUNCT
ap-688	108	52	2	2	NUM
ap-688	108	53	1	1	NUM
ap-688	108	54	1	1	NUM
ap-688	108	55	1	1	NUM
ap-688	108	56	1	1	NUM
ap-688	108	57	.	.	PUNCT
ap-688	109	1	(	(	PUNCT
ap-688	109	2	3	3	X
ap-688	109	3	)	)	PUNCT
ap-688	109	4	we	we	PRON
ap-688	109	5	can	can	AUX
ap-688	109	6	reduce	reduce	VERB
ap-688	109	7	the	the	DET
ap-688	109	8	number	number	NOUN
ap-688	109	9	of	of	ADP
ap-688	109	10	clock	clock	NOUN
ap-688	109	11	cycles	cycle	NOUN
ap-688	109	12	cpadd	cpadd	NOUN
ap-688	109	13	in	in	ADP
ap-688	109	14	two	two	NUM
ap-688	109	15	ways	way	NOUN
ap-688	109	16	:	:	PUNCT
ap-688	109	17	by	by	ADP
ap-688	109	18	reducing	reduce	VERB
ap-688	109	19	the	the	DET
ap-688	109	20	number	number	NOUN
ap-688	109	21	of	of	ADP
ap-688	109	22	clock	clock	NOUN
ap-688	109	23	cycles	cycle	NOUN
ap-688	109	24	cmul	cmul	ADJ
ap-688	109	25	of	of	ADP
ap-688	109	26	the	the	DET
ap-688	109	27	multiplications	multiplication	NOUN
ap-688	109	28	and	and	CCONJ
ap-688	109	29	the	the	DET
ap-688	109	30	number	number	NOUN
ap-688	109	31	of	of	ADP
ap-688	109	32	clock	clock	NOUN
ap-688	109	33	cycles	cycle	NOUN
ap-688	109	34	csqr	csqr	NOUN
ap-688	109	35	of	of	ADP
ap-688	109	36	the	the	DET
ap-688	109	37	iterative	iterative	NOUN
ap-688	109	38	squaring.0	squaring.0	PROPN
ap-688	109	39	both	both	CCONJ
ap-688	109	40	the	the	DET
ap-688	109	41	massey	massey	NOUN
ap-688	109	42	-	-	PUNCT
ap-688	109	43	omura	omura	PROPN
ap-688	109	44	and	and	CCONJ
ap-688	109	45	the	the	DET
ap-688	109	46	amov	amov	ADJ
ap-688	109	47	multipliers	multiplier	NOUN
ap-688	109	48	need	need	VERB
ap-688	109	49	m	m	NOUN
ap-688	109	50	clock	clock	NOUN
ap-688	109	51	cycles	cycle	NOUN
ap-688	109	52	for	for	ADP
ap-688	109	53	computing	compute	VERB
ap-688	109	54	all	all	DET
ap-688	109	55	m	m	NOUN
ap-688	109	56	bits	bit	NOUN
ap-688	109	57	of	of	ADP
ap-688	109	58	the	the	DET
ap-688	109	59	result	result	NOUN
ap-688	109	60	.	.	PUNCT
ap-688	110	1	some	some	DET
ap-688	110	2	authors	author	NOUN
ap-688	110	3	also	also	ADV
ap-688	110	4	call	call	VERB
ap-688	110	5	them	they	PRON
ap-688	110	6	bit	bit	NOUN
ap-688	110	7	-	-	PUNCT
ap-688	110	8	serial	serial	NOUN
ap-688	110	9	,	,	PUNCT
ap-688	110	10	because	because	SCONJ
ap-688	110	11	they	they	PRON
ap-688	110	12	compute	compute	VERB
ap-688	110	13	one	one	NUM
ap-688	110	14	bit	bit	NOUN
ap-688	110	15	of	of	ADP
ap-688	110	16	a	a	DET
ap-688	110	17	result	result	NOUN
ap-688	110	18	in	in	ADP
ap-688	110	19	one	one	NUM
ap-688	110	20	clock	clock	NOUN
ap-688	110	21	cycle	cycle	NOUN
ap-688	110	22	.	.	PUNCT
ap-688	111	1	there	there	PRON
ap-688	111	2	is	be	VERB
ap-688	111	3	a	a	DET
ap-688	111	4	digit	digit	NOUN
ap-688	111	5	-	-	PUNCT
ap-688	111	6	serial	serial	ADJ
ap-688	111	7	variant	variant	NOUN
ap-688	111	8	of	of	ADP
ap-688	111	9	the	the	DET
ap-688	111	10	massey	massey	NOUN
ap-688	111	11	-	-	PUNCT
ap-688	111	12	omura	omura	NOUN
ap-688	111	13	multiplier	multiplier	ADV
ap-688	111	14	(	(	PUNCT
ap-688	111	15	some	some	DET
ap-688	111	16	authors	author	NOUN
ap-688	111	17	call	call	VERB
ap-688	111	18	it	it	PRON
ap-688	111	19	sliced	slice	VERB
ap-688	111	20	or	or	CCONJ
ap-688	111	21	parallel	parallel	ADJ
ap-688	111	22	)	)	PUNCT
ap-688	111	23	.	.	PUNCT
ap-688	112	1	in	in	ADP
ap-688	112	2	this	this	DET
ap-688	112	3	multiplier	multipli	ADJ
ap-688	112	4	,	,	PUNCT
ap-688	112	5	d	d	PROPN
ap-688	112	6	bits	bit	NOUN
ap-688	112	7	(	(	PUNCT
ap-688	112	8	also	also	ADV
ap-688	112	9	called	call	VERB
ap-688	112	10	a	a	DET
ap-688	112	11	digit	digit	NOUN
ap-688	112	12	)	)	PUNCT
ap-688	112	13	are	be	AUX
ap-688	112	14	evaluated	evaluate	VERB
ap-688	112	15	in	in	ADP
ap-688	112	16	one	one	NUM
ap-688	112	17	clock	clock	NOUN
ap-688	112	18	cycle	cycle	NOUN
ap-688	112	19	.	.	PUNCT
ap-688	113	1	in	in	ADP
ap-688	113	2	the	the	DET
ap-688	113	3	case	case	NOUN
ap-688	113	4	of	of	ADP
ap-688	113	5	a	a	DET
ap-688	113	6	digit	digit	NOUN
ap-688	113	7	-	-	PUNCT
ap-688	113	8	serial	serial	ADJ
ap-688	113	9	amov	amov	ADJ
ap-688	113	10	multiplier	multiplier	ADV
ap-688	113	11	,	,	PUNCT
ap-688	113	12	d	d	PROPN
ap-688	113	13	products	product	NOUN
ap-688	113	14	pi	pi	NOUN
ap-688	113	15	,	,	PUNCT
ap-688	113	16	j	j	PROPN
ap-688	113	17	are	be	AUX
ap-688	113	18	evaluated	evaluate	VERB
ap-688	113	19	in	in	ADP
ap-688	113	20	one	one	NUM
ap-688	113	21	clock	clock	NOUN
ap-688	113	22	cycle	cycle	NOUN
ap-688	113	23	.	.	PUNCT
ap-688	114	1	all	all	DET
ap-688	114	2	m	m	VERB
ap-688	114	3	bits	bit	NOUN
ap-688	114	4	of	of	ADP
ap-688	114	5	the	the	DET
ap-688	114	6	result	result	NOUN
ap-688	114	7	are	be	AUX
ap-688	114	8	then	then	ADV
ap-688	114	9	evaluated	evaluate	VERB
ap-688	114	10	in	in	ADP
ap-688	114	11	�	�	PROPN
ap-688	114	12	�	�	PROPN
ap-688	114	13	c	c	PROPN
ap-688	114	14	m	m	PROPN
ap-688	114	15	dmul	dmul	PROPN
ap-688	114	16	�	�	PROPN
ap-688	114	17	cycles	cycle	NOUN
ap-688	114	18	.	.	PUNCT
ap-688	115	1	since	since	SCONJ
ap-688	115	2	more	more	ADJ
ap-688	115	3	products	product	NOUN
ap-688	115	4	are	be	AUX
ap-688	115	5	evaluated	evaluate	VERB
ap-688	115	6	in	in	ADP
ap-688	115	7	one	one	NUM
ap-688	115	8	clock	clock	NOUN
ap-688	115	9	cycle	cycle	NOUN
ap-688	115	10	,	,	PUNCT
ap-688	115	11	more	more	ADV
ap-688	115	12	combinational	combinational	ADJ
ap-688	115	13	logic	logic	NOUN
ap-688	115	14	is	be	AUX
ap-688	115	15	necessary	necessary	ADJ
ap-688	115	16	.	.	PUNCT
ap-688	116	1	the	the	DET
ap-688	116	2	size	size	NOUN
ap-688	116	3	of	of	ADP
ap-688	116	4	the	the	DET
ap-688	116	5	block	block	NOUN
ap-688	116	6	comb	comb	NOUN
ap-688	116	7	.	.	PUNCT
ap-688	117	1	logic	logic	NOUN
ap-688	117	2	in	in	ADP
ap-688	117	3	fig	fig	NOUN
ap-688	117	4	.	.	PUNCT
ap-688	118	1	2	2	NUM
ap-688	118	2	is	be	AUX
ap-688	118	3	proportional	proportional	ADJ
ap-688	118	4	to	to	ADP
ap-688	118	5	d	d	PROPN
ap-688	118	6	�	�	PROPN
ap-688	118	7	1	1	NUM
ap-688	118	8	.	.	PUNCT
ap-688	119	1	the	the	DET
ap-688	119	2	size	size	NOUN
ap-688	119	3	of	of	ADP
ap-688	119	4	other	other	ADJ
ap-688	119	5	blocks	block	NOUN
ap-688	119	6	remains	remain	VERB
ap-688	119	7	constant	constant	ADJ
ap-688	119	8	.	.	PUNCT
ap-688	120	1	as	as	SCONJ
ap-688	120	2	the	the	DET
ap-688	120	3	combinational	combinational	ADJ
ap-688	120	4	logic	logic	NOUN
ap-688	120	5	becomes	become	VERB
ap-688	120	6	more	more	ADV
ap-688	120	7	complex	complex	ADJ
ap-688	120	8	,	,	PUNCT
ap-688	120	9	the	the	DET
ap-688	120	10	length	length	NOUN
ap-688	120	11	of	of	ADP
ap-688	120	12	the	the	DET
ap-688	120	13	critical	critical	ADJ
ap-688	120	14	path	path	NOUN
ap-688	120	15	grows	grow	VERB
ap-688	120	16	proportionally	proportionally	ADV
ap-688	120	17	to	to	PART
ap-688	120	18	log	log	VERB
ap-688	120	19	d.	d.	NOUN
ap-688	120	20	since	since	SCONJ
ap-688	120	21	one	one	NUM
ap-688	120	22	multiplication	multiplication	NOUN
ap-688	120	23	needs	need	VERB
ap-688	120	24	m	m	PROPN
ap-688	120	25	/	/	SYM
ap-688	120	26	d	d	PROPN
ap-688	120	27	clock	clock	NOUN
ap-688	120	28	cycles	cycle	NOUN
ap-688	120	29	,	,	PUNCT
ap-688	120	30	the	the	DET
ap-688	120	31	total	total	ADJ
ap-688	120	32	time	time	NOUN
ap-688	120	33	necessary	necessary	ADJ
ap-688	120	34	for	for	SCONJ
ap-688	120	35	one	one	NUM
ap-688	120	36	multiplication	multiplication	NOUN
ap-688	120	37	is	be	AUX
ap-688	120	38	�	�	NOUN
ap-688	120	39	o	o	NOUN
ap-688	120	40	m	m	PROPN
ap-688	120	41	d	d	X
ap-688	120	42	d	d	PROPN
ap-688	120	43	(	(	PUNCT
ap-688	120	44	)	)	PUNCT
ap-688	120	45	log	log	VERB
ap-688	120	46	,	,	PUNCT
ap-688	120	47	and	and	CCONJ
ap-688	120	48	the	the	DET
ap-688	120	49	total	total	ADJ
ap-688	120	50	time	time	NOUN
ap-688	120	51	of	of	ADP
ap-688	120	52	one	one	NUM
ap-688	120	53	inversion	inversion	NOUN
ap-688	120	54	(	(	PUNCT
ap-688	120	55	or	or	CCONJ
ap-688	120	56	point	point	VERB
ap-688	120	57	addition	addition	NOUN
ap-688	120	58	on	on	ADP
ap-688	120	59	elliptic	elliptic	ADJ
ap-688	120	60	curve	curve	NOUN
ap-688	120	61	)	)	PUNCT
ap-688	120	62	is	be	AUX
ap-688	120	63	t	t	NOUN
ap-688	120	64	o	o	NOUN
ap-688	120	65	m	m	VERB
ap-688	120	66	m	m	VERB
ap-688	120	67	d	d	NOUN
ap-688	120	68	m	m	NOUN
ap-688	120	69	dpadd	dpadd	NOUN
ap-688	120	70	�	�	PROPN
ap-688	120	71	�	�	PROPN
ap-688	120	72	�	�	PROPN
ap-688	120	73	�	�	PROPN
ap-688	120	74	�	�	PROPN
ap-688	120	75	�	�	PROPN
ap-688	120	76	�	�	PROPN
ap-688	120	77	�	�	PROPN
ap-688	120	78	�	�	PROPN
ap-688	120	79	(	(	PUNCT
ap-688	120	80	log	log	PROPN
ap-688	120	81	)	)	PUNCT
ap-688	120	82	.	.	PUNCT
ap-688	121	1	log	log	VERB
ap-688	121	2	.	.	PUNCT
ap-688	122	1	(	(	PUNCT
ap-688	122	2	4	4	X
ap-688	122	3	)	)	PUNCT
ap-688	122	4	5	5	NUM
ap-688	122	5	scaling	scale	VERB
ap-688	122	6	the	the	DET
ap-688	122	7	iterative	iterative	NOUN
ap-688	122	8	squarings	squaring	NOUN
ap-688	122	9	another	another	DET
ap-688	122	10	way	way	NOUN
ap-688	122	11	to	to	PART
ap-688	122	12	improve	improve	VERB
ap-688	122	13	the	the	DET
ap-688	122	14	performance	performance	NOUN
ap-688	122	15	of	of	ADP
ap-688	122	16	the	the	DET
ap-688	122	17	itt	itt	ADJ
ap-688	122	18	inversion	inversion	NOUN
ap-688	122	19	(	(	PUNCT
ap-688	122	20	and	and	CCONJ
ap-688	122	21	consequently	consequently	ADV
ap-688	122	22	the	the	DET
ap-688	122	23	point	point	NOUN
ap-688	122	24	addition	addition	NOUN
ap-688	122	25	)	)	PUNCT
ap-688	122	26	is	be	AUX
ap-688	122	27	to	to	PART
ap-688	122	28	reduce	reduce	VERB
ap-688	122	29	the	the	DET
ap-688	122	30	number	number	NOUN
ap-688	122	31	of	of	ADP
ap-688	122	32	clock	clock	NOUN
ap-688	122	33	cycles	cycle	NOUN
ap-688	122	34	necessary	necessary	ADJ
ap-688	122	35	for	for	ADP
ap-688	122	36	the	the	DET
ap-688	122	37	iterative	iterative	NOUN
ap-688	122	38	squarings	squaring	NOUN
ap-688	122	39	in	in	ADP
ap-688	122	40	step	step	NOUN
ap-688	122	41	3.2.1	3.2.1	NUM
ap-688	122	42	of	of	ADP
ap-688	122	43	algorithm	algorithm	NOUN
ap-688	122	44	1	1	NUM
ap-688	122	45	.	.	PUNCT
ap-688	122	46	adding	add	VERB
ap-688	122	47	one	one	NUM
ap-688	122	48	or	or	CCONJ
ap-688	122	49	more	more	ADJ
ap-688	122	50	blocks	block	NOUN
ap-688	122	51	performing	perform	VERB
ap-688	122	52	“	"	PUNCT
ap-688	122	53	long	long	ADJ
ap-688	122	54	distance	distance	NOUN
ap-688	122	55	”	"	PUNCT
ap-688	122	56	rotations	rotation	NOUN
ap-688	122	57	can	can	AUX
ap-688	122	58	reduce	reduce	VERB
ap-688	122	59	the	the	DET
ap-688	122	60	number	number	NOUN
ap-688	122	61	of	of	ADP
ap-688	122	62	clock	clock	NOUN
ap-688	122	63	cycles	cycle	NOUN
ap-688	122	64	required	require	VERB
ap-688	122	65	for	for	ADP
ap-688	122	66	all	all	DET
ap-688	122	67	iterative	iterative	NOUN
ap-688	122	68	squarings	squaring	NOUN
ap-688	122	69	(	(	PUNCT
ap-688	122	70	fig	fig	NOUN
ap-688	122	71	.	.	PUNCT
ap-688	123	1	3	3	NUM
ap-688	123	2	)	)	PUNCT
ap-688	123	3	.	.	PUNCT
ap-688	124	1	we	we	PRON
ap-688	124	2	shall	shall	AUX
ap-688	124	3	refer	refer	VERB
ap-688	124	4	to	to	ADP
ap-688	124	5	the	the	DET
ap-688	124	6	hardware	hardware	NOUN
ap-688	124	7	realizing	realize	VERB
ap-688	124	8	these	these	DET
ap-688	124	9	rotations	rotation	NOUN
ap-688	124	10	as	as	ADP
ap-688	124	11	the	the	DET
ap-688	124	12	shifter	shifter	NOUN
ap-688	124	13	.	.	PUNCT
ap-688	125	1	let	let	VERB
ap-688	125	2	m	m	PRON
ap-688	125	3	be	be	AUX
ap-688	125	4	the	the	DET
ap-688	125	5	degree	degree	NOUN
ap-688	125	6	of	of	ADP
ap-688	125	7	the	the	DET
ap-688	125	8	finite	finite	ADJ
ap-688	125	9	field	field	NOUN
ap-688	125	10	we	we	PRON
ap-688	125	11	work	work	VERB
ap-688	125	12	in	in	ADP
ap-688	125	13	,	,	PUNCT
ap-688	125	14	gf(2	gf(2	PROPN
ap-688	125	15	m	m	NOUN
ap-688	125	16	)	)	PUNCT
ap-688	125	17	.	.	PUNCT
ap-688	126	1	let	let	VERB
ap-688	126	2	m	m	PROPN
ap-688	126	3	b	b	PROPN
ap-688	126	4	b	b	PROPN
ap-688	126	5	b	b	PROPN
ap-688	126	6	br	br	NOUN
ap-688	126	7	r	r	PROPN
ap-688	126	8	�	�	PROPN
ap-688	126	9	�	�	PROPN
ap-688	126	10	�	�	PROPN
ap-688	126	11	1	1	NUM
ap-688	126	12	1	1	NUM
ap-688	126	13	1	1	NUM
ap-688	126	14	0	0	NUM
ap-688	126	15	(	(	PUNCT
ap-688	126	16	)	)	PUNCT
ap-688	126	17	�	�	PROPN
ap-688	126	18	be	be	AUX
ap-688	126	19	the	the	DET
ap-688	126	20	binary	binary	ADJ
ap-688	126	21	representation	representation	NOUN
ap-688	126	22	of	of	ADP
ap-688	126	23	m-1	m-1	PROPN
ap-688	126	24	such	such	ADJ
ap-688	126	25	that	that	SCONJ
ap-688	126	26	the	the	DET
ap-688	126	27	most	most	ADV
ap-688	126	28	significant	significant	ADJ
ap-688	126	29	bit	bit	NOUN
ap-688	126	30	br=1	br=1	NOUN
ap-688	126	31	.	.	PUNCT
ap-688	127	1	the	the	DET
ap-688	127	2	rotations	rotation	NOUN
ap-688	127	3	required	require	VERB
ap-688	127	4	by	by	ADP
ap-688	127	5	the	the	DET
ap-688	127	6	itoh	itoh	NOUN
ap-688	127	7	-	-	PUNCT
ap-688	127	8	teechaji	teechaji	NOUN
ap-688	127	9	-	-	PUNCT
ap-688	127	10	tsujii	tsujii	NOUN
ap-688	127	11	algorithm	algorithm	NOUN
ap-688	127	12	are	be	AUX
ap-688	127	13	�	�	PROPN
ap-688	127	14	�	�	PROPN
ap-688	127	15	k	k	PROPN
ap-688	128	1	k	k	PROPN
ap-688	129	1	i	i	PRON
ap-688	129	2	r	r	VERB
ap-688	129	3	k	k	PROPN
ap-688	129	4	b	b	PROPN
ap-688	129	5	bi	bi	INTJ
ap-688	130	1	i	i	NOUN
ap-688	130	2	r	r	VERB
ap-688	130	3	i	i	PROPN
ap-688	130	4	�	�	PROPN
ap-688	130	5	�	�	PROPN
ap-688	130	6	�	�	PROPN
ap-688	130	7	,	,	PUNCT
ap-688	130	8	,	,	PUNCT
ap-688	130	9	(	(	PUNCT
ap-688	130	10	)	)	PUNCT
ap-688	130	11	1	1	NUM
ap-688	130	12	�	�	PROPN
ap-688	130	13	�	�	PROPN
ap-688	130	14	.	.	PUNCT
ap-688	131	1	the	the	DET
ap-688	131	2	binary	binary	PROPN
ap-688	131	3	representation	representation	NOUN
ap-688	131	4	of	of	ADP
ap-688	131	5	ki	ki	PROPN
ap-688	131	6	is	be	AUX
ap-688	131	7	br	br	NOUN
ap-688	131	8	…	…	PUNCT
ap-688	131	9	bi	bi	NOUN
ap-688	131	10	.	.	PUNCT
ap-688	132	1	each	each	PRON
ap-688	132	2	of	of	ADP
ap-688	132	3	the	the	DET
ap-688	132	4	shifts	shift	NOUN
ap-688	132	5	is	be	AUX
ap-688	132	6	performed	perform	VERB
ap-688	132	7	exactly	exactly	ADV
ap-688	132	8	once	once	ADV
ap-688	132	9	in	in	ADP
ap-688	132	10	an	an	DET
ap-688	132	11	inversion	inversion	NOUN
ap-688	132	12	operation	operation	NOUN
ap-688	132	13	.	.	PUNCT
ap-688	133	1	let	let	VERB
ap-688	133	2	a	a	DET
ap-688	133	3	,	,	PUNCT
ap-688	133	4	t	t	PROPN
ap-688	133	5	,	,	PUNCT
ap-688	133	6	and	and	CCONJ
ap-688	133	7	�	�	PROPN
ap-688	133	8	be	be	AUX
ap-688	133	9	the	the	DET
ap-688	133	10	area	area	NOUN
ap-688	133	11	,	,	PUNCT
ap-688	133	12	the	the	DET
ap-688	133	13	total	total	ADJ
ap-688	133	14	number	number	NOUN
ap-688	133	15	of	of	ADP
ap-688	133	16	clock	clock	NOUN
ap-688	133	17	cycles	cycle	NOUN
ap-688	133	18	spent	spend	VERB
ap-688	133	19	in	in	ADP
ap-688	133	20	rotations	rotation	NOUN
ap-688	133	21	,	,	PUNCT
ap-688	133	22	and	and	CCONJ
ap-688	133	23	the	the	DET
ap-688	133	24	critical	critical	ADJ
ap-688	133	25	path	path	NOUN
ap-688	133	26	of	of	ADP
ap-688	133	27	the	the	DET
ap-688	133	28	shifter	shifter	NOUN
ap-688	133	29	.	.	PUNCT
ap-688	134	1	let	let	VERB
ap-688	134	2	a0	a0	PROPN
ap-688	134	3	,	,	PUNCT
ap-688	134	4	t0	t0	PROPN
ap-688	134	5	,	,	PUNCT
ap-688	134	6	and	and	CCONJ
ap-688	134	7	�	�	PROPN
ap-688	134	8	0	0	NUM
ap-688	134	9	be	be	VERB
ap-688	134	10	the	the	DET
ap-688	134	11	area	area	NOUN
ap-688	134	12	,	,	PUNCT
ap-688	134	13	total	total	ADJ
ap-688	134	14	number	number	NOUN
ap-688	134	15	of	of	ADP
ap-688	134	16	clock	clock	NOUN
ap-688	134	17	cycles	cycle	NOUN
ap-688	134	18	spent	spend	VERB
ap-688	134	19	in	in	ADP
ap-688	134	20	©	©	PROPN
ap-688	134	21	czech	czech	PROPN
ap-688	134	22	technical	technical	PROPN
ap-688	134	23	university	university	PROPN
ap-688	134	24	publishing	publishing	NOUN
ap-688	134	25	house	house	NOUN
ap-688	134	26	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	134	27	57	57	NUM
ap-688	134	28	czech	czech	PROPN
ap-688	134	29	technical	technical	PROPN
ap-688	134	30	university	university	PROPN
ap-688	134	31	in	in	ADP
ap-688	134	32	prague	prague	PROPN
ap-688	134	33	acta	acta	PROPN
ap-688	134	34	polytechnica	polytechnica	PROPN
ap-688	134	35	vol	vol	NOUN
ap-688	134	36	.	.	PROPN
ap-688	135	1	45	45	NUM
ap-688	135	2	no	no	NOUN
ap-688	135	3	.	.	PUNCT
ap-688	136	1	2/2005	2/2005	NUM
ap-688	136	2	1	1	NUM
ap-688	136	3	.	.	PUNCT
ap-688	137	1	mr	mr	PROPN
ap-688	137	2	...	...	PROPN
ap-688	137	3	m0	m0	PROPN
ap-688	137	4	�	�	PROPN
ap-688	137	5	m	m	PROPN
ap-688	137	6	–	–	PUNCT
ap-688	137	7	1	1	NUM
ap-688	137	8	;	;	PUNCT
ap-688	137	9	2	2	NUM
ap-688	137	10	.	.	X
ap-688	137	11	a	a	DET
ap-688	137	12	�	�	PROPN
ap-688	137	13	in	in	ADP
ap-688	137	14	;	;	PUNCT
ap-688	137	15	3	3	X
ap-688	137	16	.	.	X
ap-688	137	17	for	for	ADP
ap-688	137	18	count_inv	count_inv	NUM
ap-688	137	19	in	in	ADP
ap-688	137	20	r	r	NOUN
ap-688	137	21	–	–	PUNCT
ap-688	137	22	1	1	NUM
ap-688	137	23	down	down	ADP
ap-688	137	24	to	to	ADP
ap-688	137	25	0	0	NUM
ap-688	137	26	do	do	VERB
ap-688	137	27	3.1	3.1	NUM
ap-688	137	28	b	b	PROPN
ap-688	137	29	�	�	PROPN
ap-688	137	30	a	a	PRON
ap-688	137	31	;	;	PUNCT
ap-688	137	32	3.2	3.2	NUM
ap-688	137	33	for	for	ADP
ap-688	137	34	count_k	count_k	VERB
ap-688	137	35	in	in	ADP
ap-688	137	36	m2r	m2r	PROPN
ap-688	137	37	�	�	NOUN
ap-688	137	38	1	1	NUM
ap-688	137	39	…	…	PUNCT
ap-688	137	40	mr	mr	PROPN
ap-688	137	41	down	down	ADV
ap-688	137	42	to	to	ADP
ap-688	137	43	1	1	NUM
ap-688	137	44	do	do	AUX
ap-688	137	45	3.2.1	3.2.1	NUM
ap-688	137	46	.	.	PUNCT
ap-688	138	1	b	b	X
ap-688	138	2	�	�	PROPN
ap-688	138	3	b	b	PROPN
ap-688	138	4	ror	ror	PROPN
ap-688	138	5	1	1	NUM
ap-688	138	6	;	;	PUNCT
ap-688	138	7	3.3	3.3	NUM
ap-688	138	8	c	c	NOUN
ap-688	138	9	�	�	PROPN
ap-688	139	1	b	b	PROPN
ap-688	140	1	a	a	PROPN
ap-688	140	2	;	;	PUNCT
ap-688	140	3	3.3a	3.3a	NUM
ap-688	140	4	a	a	DET
ap-688	140	5	�	�	PROPN
ap-688	140	6	c	c	NOUN
ap-688	140	7	;	;	PUNCT
ap-688	140	8	3.3b	3.3b	NUM
ap-688	140	9	m	m	PROPN
ap-688	140	10	�	�	PROPN
ap-688	140	11	m	m	PROPN
ap-688	140	12	shl	shl	ADJ
ap-688	140	13	1	1	NUM
ap-688	140	14	;	;	PUNCT
ap-688	140	15	3.4	3.4	NUM
ap-688	140	16	if	if	SCONJ
ap-688	140	17	mr	mr	PROPN
ap-688	140	18	=	=	PROPN
ap-688	140	19	,	,	PUNCT
ap-688	140	20	1	1	NUM
ap-688	140	21	’	'	PUNCT
ap-688	140	22	then	then	ADV
ap-688	140	23	3.4.1	3.4.1	NUM
ap-688	140	24	b	b	PROPN
ap-688	140	25	�	�	PROPN
ap-688	140	26	a	a	PRON
ap-688	140	27	;	;	PUNCT
ap-688	140	28	3.4.2	3.4.2	NUM
ap-688	140	29	b	b	PROPN
ap-688	140	30	�	�	PROPN
ap-688	140	31	b	b	PROPN
ap-688	140	32	ror	ror	PROPN
ap-688	140	33	1	1	NUM
ap-688	140	34	;	;	PUNCT
ap-688	140	35	a	a	DET
ap-688	140	36	�	�	PROPN
ap-688	140	37	in	in	ADP
ap-688	140	38	;	;	PUNCT
ap-688	140	39	3.4.3	3.4.3	PROPN
ap-688	140	40	c	c	PROPN
ap-688	140	41	�	�	PROPN
ap-688	140	42	b	b	PROPN
ap-688	140	43	a	a	PROPN
ap-688	140	44	;	;	PUNCT
ap-688	140	45	3.4.4	3.4.4	NUM
ap-688	140	46	a	a	DET
ap-688	140	47	�	�	PROPN
ap-688	140	48	c	c	NOUN
ap-688	140	49	;	;	PUNCT
ap-688	140	50	4	4	X
ap-688	140	51	.	.	X
ap-688	141	1	a	a	DET
ap-688	141	2	�	�	PROPN
ap-688	141	3	a	a	DET
ap-688	141	4	ror	ror	NOUN
ap-688	141	5	1	1	NUM
ap-688	141	6	;	;	PUNCT
ap-688	141	7	algorithm	algorithm	NOUN
ap-688	141	8	1	1	NUM
ap-688	141	9	:	:	PUNCT
ap-688	141	10	an	an	DET
ap-688	141	11	implementation	implementation	NOUN
ap-688	141	12	of	of	ADP
ap-688	141	13	the	the	DET
ap-688	141	14	itt	itt	ADJ
ap-688	141	15	inversion	inversion	NOUN
ap-688	141	16	in	in	ADP
ap-688	141	17	the	the	DET
ap-688	141	18	modified	modify	VERB
ap-688	141	19	amov	amov	ADJ
ap-688	141	20	multiplier	multipli	ADJ
ap-688	141	21	b	b	NOUN
ap-688	141	22	comb	comb	NOUN
ap-688	141	23	.	.	PUNCT
ap-688	142	1	logic	logic	NOUN
ap-688	142	2	ror	ror	NOUN
ap-688	142	3	1	1	NUM
ap-688	142	4	in	in	ADP
ap-688	142	5	ror	ror	NOUN
ap-688	142	6	1	1	NUM
ap-688	142	7	a	a	DET
ap-688	142	8	c	c	NOUN
ap-688	142	9	out	out	ADP
ap-688	142	10	ror	ror	NOUN
ap-688	142	11	q	q	X
ap-688	142	12	ror	ror	NOUN
ap-688	142	13	r	r	NOUN
ap-688	142	14	fig	fig	NOUN
ap-688	142	15	.	.	PUNCT
ap-688	143	1	3	3	NUM
ap-688	143	2	:	:	PUNCT
ap-688	143	3	“	"	PUNCT
ap-688	143	4	long	long	ADJ
ap-688	143	5	distance	distance	NOUN
ap-688	143	6	”	"	PUNCT
ap-688	143	7	rotations	rotation	NOUN
ap-688	143	8	form	form	VERB
ap-688	143	9	a	a	DET
ap-688	143	10	shifter	shifter	NOUN
ap-688	143	11	that	that	PRON
ap-688	143	12	saves	save	VERB
ap-688	143	13	clock	clock	NOUN
ap-688	143	14	cycles	cycle	NOUN
ap-688	143	15	necessary	necessary	ADJ
ap-688	143	16	for	for	ADP
ap-688	143	17	squarings	squaring	NOUN
ap-688	143	18	in	in	ADP
ap-688	143	19	itt	itt	ADJ
ap-688	143	20	inversion	inversion	NOUN
ap-688	143	21	multiplications	multiplication	NOUN
ap-688	143	22	,	,	PUNCT
ap-688	143	23	and	and	CCONJ
ap-688	143	24	the	the	DET
ap-688	143	25	critical	critical	ADJ
ap-688	143	26	path	path	NOUN
ap-688	143	27	of	of	ADP
ap-688	143	28	the	the	DET
ap-688	143	29	rest	rest	NOUN
ap-688	143	30	of	of	ADP
ap-688	143	31	the	the	DET
ap-688	143	32	arithmetic	arithmetic	ADJ
ap-688	143	33	unit	unit	NOUN
ap-688	143	34	.	.	PUNCT
ap-688	144	1	the	the	DET
ap-688	144	2	quality	quality	NOUN
ap-688	144	3	measure	measure	NOUN
ap-688	144	4	of	of	ADP
ap-688	144	5	the	the	DET
ap-688	144	6	entire	entire	ADJ
ap-688	144	7	unit	unit	NOUN
ap-688	144	8	,	,	PUNCT
ap-688	144	9	and	and	CCONJ
ap-688	144	10	hence	hence	ADV
ap-688	144	11	our	our	PRON
ap-688	144	12	optimization	optimization	NOUN
ap-688	144	13	criterion	criterion	NOUN
ap-688	144	14	,	,	PUNCT
ap-688	144	15	is	be	AUX
ap-688	144	16	�	�	PROPN
ap-688	144	17	�	�	PROPN
ap-688	144	18	q	q	PROPN
ap-688	144	19	a	a	DET
ap-688	144	20	a	a	DET
ap-688	144	21	t	t	NOUN
ap-688	144	22	t	t	PROPN
ap-688	144	23	�	�	PROPN
ap-688	144	24	�	�	PROPN
ap-688	144	25	�	�	PROPN
ap-688	144	26	�	�	PROPN
ap-688	144	27	(	(	PUNCT
ap-688	144	28	)	)	PUNCT
ap-688	144	29	(	(	PUNCT
ap-688	144	30	)	)	PUNCT
ap-688	144	31	max	max	PROPN
ap-688	144	32	,	,	PUNCT
ap-688	144	33	0	0	NUM
ap-688	144	34	0	0	NUM
ap-688	144	35	0	0	NUM
ap-688	144	36	�	�	PROPN
ap-688	144	37	�	�	PROPN
ap-688	144	38	(	(	PUNCT
ap-688	144	39	5	5	NUM
ap-688	144	40	)	)	PUNCT
ap-688	144	41	this	this	DET
ap-688	144	42	equation	equation	NOUN
ap-688	144	43	also	also	ADV
ap-688	144	44	shows	show	VERB
ap-688	144	45	the	the	DET
ap-688	144	46	two	two	NUM
ap-688	144	47	dependencies	dependency	NOUN
ap-688	144	48	between	between	ADP
ap-688	144	49	the	the	DET
ap-688	144	50	shifter	shifter	NOUN
ap-688	144	51	and	and	CCONJ
ap-688	144	52	the	the	DET
ap-688	144	53	multiplier	multipli	ADJ
ap-688	144	54	.	.	PUNCT
ap-688	145	1	firstly	firstly	ADV
ap-688	145	2	,	,	PUNCT
ap-688	145	3	the	the	DET
ap-688	145	4	ratio	ratio	NOUN
ap-688	145	5	of	of	ADP
ap-688	145	6	the	the	DET
ap-688	145	7	shifter	shifter	NOUN
ap-688	145	8	’s	’s	PART
ap-688	145	9	area	area	NOUN
ap-688	145	10	and	and	CCONJ
ap-688	145	11	time	time	NOUN
ap-688	145	12	must	must	AUX
ap-688	145	13	be	be	AUX
ap-688	145	14	‘	'	PUNCT
ap-688	145	15	the	the	DET
ap-688	145	16	right	right	ADJ
ap-688	145	17	one	one	NOUN
ap-688	145	18	’	'	PUNCT
ap-688	145	19	.	.	PUNCT
ap-688	146	1	for	for	ADP
ap-688	146	2	each	each	DET
ap-688	146	3	a0	a0	NOUN
ap-688	146	4	,	,	PUNCT
ap-688	146	5	t0	t0	PROPN
ap-688	146	6	and	and	CCONJ
ap-688	146	7	�	�	PROPN
ap-688	146	8	0	0	NUM
ap-688	146	9	,	,	PUNCT
ap-688	146	10	the	the	DET
ap-688	146	11	area	area	NOUN
ap-688	146	12	and	and	CCONJ
ap-688	146	13	time	time	NOUN
ap-688	146	14	of	of	ADP
ap-688	146	15	the	the	DET
ap-688	146	16	shifter	shifter	NOUN
ap-688	146	17	shall	shall	AUX
ap-688	146	18	be	be	AUX
ap-688	146	19	adjusted	adjust	VERB
ap-688	146	20	to	to	PART
ap-688	146	21	achieve	achieve	VERB
ap-688	146	22	minimum	minimum	ADJ
ap-688	146	23	q	q	NOUN
ap-688	146	24	of	of	ADP
ap-688	146	25	the	the	DET
ap-688	146	26	entire	entire	ADJ
ap-688	146	27	unit	unit	NOUN
ap-688	146	28	.	.	PUNCT
ap-688	147	1	secondly	secondly	ADV
ap-688	147	2	,	,	PUNCT
ap-688	147	3	the	the	DET
ap-688	147	4	shifter	shifter	NOUN
ap-688	147	5	may	may	AUX
ap-688	147	6	slow	slow	VERB
ap-688	147	7	down	down	ADP
ap-688	147	8	the	the	DET
ap-688	147	9	au	au	ADJ
ap-688	147	10	clock	clock	NOUN
ap-688	147	11	.	.	PUNCT
ap-688	148	1	in	in	ADP
ap-688	148	2	this	this	DET
ap-688	148	3	case	case	NOUN
ap-688	148	4	,	,	PUNCT
ap-688	148	5	not	not	PART
ap-688	148	6	only	only	ADV
ap-688	148	7	the	the	DET
ap-688	148	8	time	time	NOUN
ap-688	148	9	t	t	PROPN
ap-688	148	10	�	�	PROPN
ap-688	148	11	is	be	AUX
ap-688	148	12	longer	long	ADJ
ap-688	148	13	,	,	PUNCT
ap-688	148	14	but	but	CCONJ
ap-688	148	15	also	also	ADV
ap-688	148	16	the	the	DET
ap-688	148	17	multiplication	multiplication	NOUN
ap-688	148	18	time	time	NOUN
ap-688	148	19	is	be	AUX
ap-688	148	20	t0	t0	NOUN
ap-688	148	21	�	�	PROPN
ap-688	148	22	instead	instead	ADV
ap-688	148	23	of	of	ADP
ap-688	148	24	t0	t0	PROPN
ap-688	148	25	�	�	PROPN
ap-688	148	26	0	0	NUM
ap-688	148	27	.	.	PUNCT
ap-688	149	1	as	as	SCONJ
ap-688	149	2	the	the	DET
ap-688	149	3	multiplier	multipli	ADJ
ap-688	149	4	dominates	dominate	VERB
ap-688	149	5	,	,	PUNCT
ap-688	149	6	the	the	DET
ap-688	149	7	penalty	penalty	NOUN
ap-688	149	8	may	may	AUX
ap-688	149	9	become	become	VERB
ap-688	149	10	unacceptable	unacceptable	ADJ
ap-688	149	11	.	.	PUNCT
ap-688	150	1	the	the	DET
ap-688	150	2	multiplier	multipli	ADJ
ap-688	150	3	is	be	AUX
ap-688	150	4	scaled	scale	VERB
ap-688	150	5	by	by	ADP
ap-688	150	6	manipulating	manipulate	VERB
ap-688	150	7	the	the	DET
ap-688	150	8	digit	digit	NOUN
ap-688	150	9	size	size	NOUN
ap-688	150	10	,	,	PUNCT
ap-688	150	11	which	which	PRON
ap-688	150	12	affects	affect	VERB
ap-688	150	13	a0	a0	PROPN
ap-688	150	14	,	,	PUNCT
ap-688	150	15	t0	t0	PROPN
ap-688	150	16	and	and	CCONJ
ap-688	150	17	�	�	PROPN
ap-688	150	18	0	0	NUM
ap-688	150	19	,	,	PUNCT
ap-688	150	20	while	while	SCONJ
ap-688	150	21	changing	change	VERB
ap-688	150	22	the	the	DET
ap-688	150	23	number	number	NOUN
ap-688	150	24	of	of	ADP
ap-688	150	25	rotations	rotation	NOUN
ap-688	150	26	in	in	ADP
ap-688	150	27	the	the	DET
ap-688	150	28	shifter	shifter	NOUN
ap-688	150	29	varies	vary	VERB
ap-688	150	30	a	a	DET
ap-688	150	31	,	,	PUNCT
ap-688	150	32	t	t	PROPN
ap-688	150	33	,	,	PUNCT
ap-688	150	34	and	and	CCONJ
ap-688	150	35	�	�	PROPN
ap-688	150	36	�	�	PROPN
ap-688	150	37	thus	thus	ADV
ap-688	150	38	the	the	DET
ap-688	150	39	optimization	optimization	NOUN
ap-688	150	40	problem	problem	NOUN
ap-688	150	41	becomes	become	VERB
ap-688	150	42	multi	multi	ADJ
ap-688	150	43	-	-	ADJ
ap-688	150	44	parametric	parametric	ADJ
ap-688	150	45	.	.	PUNCT
ap-688	151	1	because	because	SCONJ
ap-688	151	2	the	the	DET
ap-688	151	3	multiplier	multipli	ADJ
ap-688	151	4	logic	logic	NOUN
ap-688	151	5	dominates	dominate	VERB
ap-688	151	6	in	in	ADP
ap-688	151	7	both	both	DET
ap-688	151	8	area	area	NOUN
ap-688	151	9	and	and	CCONJ
ap-688	151	10	time	time	NOUN
ap-688	151	11	,	,	PUNCT
ap-688	151	12	we	we	PRON
ap-688	151	13	solve	solve	VERB
ap-688	151	14	it	it	PRON
ap-688	151	15	in	in	ADP
ap-688	151	16	a	a	DET
ap-688	151	17	pareto	pareto	NOUN
ap-688	151	18	-	-	PUNCT
ap-688	151	19	optimal	optimal	ADJ
ap-688	151	20	way	way	NOUN
ap-688	151	21	:	:	PUNCT
ap-688	151	22	we	we	PRON
ap-688	151	23	modify	modify	VERB
ap-688	151	24	the	the	DET
ap-688	151	25	shifter	shifter	NOUN
ap-688	151	26	to	to	PART
ap-688	151	27	achieve	achieve	VERB
ap-688	151	28	optimum	optimum	ADJ
ap-688	151	29	total	total	NOUN
ap-688	151	30	q	q	NOUN
ap-688	151	31	for	for	ADP
ap-688	151	32	a	a	DET
ap-688	151	33	given	give	VERB
ap-688	151	34	multiplier	multipli	ADJ
ap-688	151	35	digit	digit	NOUN
ap-688	151	36	width	width	NOUN
ap-688	151	37	.	.	PUNCT
ap-688	152	1	5.1	5.1	NUM
ap-688	152	2	decomposition	decomposition	NOUN
ap-688	152	3	in	in	ADP
ap-688	152	4	time	time	NOUN
ap-688	152	5	and	and	CCONJ
ap-688	152	6	space	space	NOUN
ap-688	152	7	to	to	PART
ap-688	152	8	implement	implement	VERB
ap-688	152	9	a	a	DET
ap-688	152	10	set	set	NOUN
ap-688	152	11	of	of	ADP
ap-688	152	12	rotations	rotation	NOUN
ap-688	152	13	,	,	PUNCT
ap-688	152	14	one	one	PRON
ap-688	152	15	might	might	AUX
ap-688	152	16	use	use	VERB
ap-688	152	17	:	:	PUNCT
ap-688	152	18	�	�	PROPN
ap-688	152	19	a	a	DET
ap-688	152	20	multiplexer	multiplexer	NOUN
ap-688	152	21	structure	structure	NOUN
ap-688	152	22	,	,	PUNCT
ap-688	152	23	such	such	ADJ
ap-688	152	24	as	as	ADP
ap-688	152	25	the	the	DET
ap-688	152	26	barrel	barrel	NOUN
ap-688	152	27	shifter	shifter	NOUN
ap-688	152	28	,	,	PUNCT
ap-688	152	29	spending	spend	VERB
ap-688	152	30	a	a	DET
ap-688	152	31	single	single	ADJ
ap-688	152	32	clock	clock	NOUN
ap-688	152	33	cycle	cycle	NOUN
ap-688	152	34	for	for	ADP
ap-688	152	35	each	each	DET
ap-688	152	36	rotation	rotation	NOUN
ap-688	152	37	,	,	PUNCT
ap-688	152	38	or	or	CCONJ
ap-688	152	39	�	�	PROPN
ap-688	152	40	hardware	hardware	NOUN
ap-688	152	41	providing	provide	VERB
ap-688	152	42	the	the	DET
ap-688	152	43	rotation	rotation	NOUN
ap-688	152	44	by	by	ADP
ap-688	152	45	1	1	NUM
ap-688	152	46	only	only	ADV
ap-688	152	47	,	,	PUNCT
ap-688	152	48	requiring	require	VERB
ap-688	152	49	k	k	PROPN
ap-688	152	50	clock	clock	NOUN
ap-688	152	51	cycles	cycle	NOUN
ap-688	152	52	to	to	PART
ap-688	152	53	rotate	rotate	VERB
ap-688	152	54	by	by	ADP
ap-688	152	55	k.	k.	PROPN
ap-688	152	56	these	these	DET
ap-688	152	57	options	option	NOUN
ap-688	152	58	can	can	AUX
ap-688	152	59	be	be	AUX
ap-688	152	60	seen	see	VERB
ap-688	152	61	as	as	ADP
ap-688	152	62	decompositions	decomposition	NOUN
ap-688	152	63	in	in	ADP
ap-688	152	64	space	space	NOUN
ap-688	152	65	and	and	CCONJ
ap-688	152	66	in	in	ADP
ap-688	152	67	time	time	NOUN
ap-688	152	68	,	,	PUNCT
ap-688	152	69	respectively	respectively	ADV
ap-688	152	70	.	.	PUNCT
ap-688	153	1	in	in	ADP
ap-688	153	2	a	a	DET
ap-688	153	3	more	more	ADV
ap-688	153	4	general	general	ADJ
ap-688	153	5	approach	approach	NOUN
ap-688	153	6	,	,	PUNCT
ap-688	153	7	we	we	PRON
ap-688	153	8	construct	construct	VERB
ap-688	153	9	hardware	hardware	NOUN
ap-688	153	10	providing	provide	VERB
ap-688	153	11	a	a	DET
ap-688	153	12	limited	limited	ADJ
ap-688	153	13	set	set	NOUN
ap-688	153	14	of	of	ADP
ap-688	153	15	rotations	rotation	NOUN
ap-688	153	16	,	,	PUNCT
ap-688	153	17	and	and	CCONJ
ap-688	153	18	we	we	PRON
ap-688	153	19	use	use	VERB
ap-688	153	20	it	it	PRON
ap-688	153	21	in	in	ADP
ap-688	153	22	multiple	multiple	ADJ
ap-688	153	23	clock	clock	NOUN
ap-688	153	24	cycles	cycle	NOUN
ap-688	153	25	to	to	PART
ap-688	153	26	realize	realize	VERB
ap-688	153	27	the	the	DET
ap-688	153	28	given	give	VERB
ap-688	153	29	rotations	rotation	NOUN
ap-688	153	30	.	.	PUNCT
ap-688	154	1	the	the	DET
ap-688	154	2	solution	solution	NOUN
ap-688	154	3	of	of	ADP
ap-688	154	4	our	our	PRON
ap-688	154	5	problem	problem	NOUN
ap-688	154	6	can	can	AUX
ap-688	154	7	be	be	AUX
ap-688	154	8	decomposed	decompose	VERB
ap-688	154	9	as	as	SCONJ
ap-688	154	10	follows	follow	VERB
ap-688	154	11	:	:	PUNCT
ap-688	154	12	�	�	NOUN
ap-688	154	13	find	find	VERB
ap-688	154	14	rotations	rotation	NOUN
ap-688	154	15	s	s	VERB
ap-688	154	16	j	j	PROPN
ap-688	154	17	nj	nj	PROPN
ap-688	154	18	�	�	PROPN
ap-688	154	19	�	�	PROPN
ap-688	154	20	�	�	PROPN
ap-688	154	21	z	z	PROPN
ap-688	154	22	,	,	PUNCT
ap-688	154	23	1	1	NUM
ap-688	154	24	�	�	NOUN
ap-688	154	25	and	and	CCONJ
ap-688	154	26	factors	factor	NOUN
ap-688	154	27	tij	tij	PROPN
ap-688	154	28	�	�	PROPN
ap-688	154	29	�	�	PROPN
ap-688	154	30	z	z	PROPN
ap-688	154	31	,	,	PUNCT
ap-688	154	32	i	i	PRON
ap-688	154	33	r	r	VERB
ap-688	154	34	j	j	PROPN
ap-688	154	35	n	n	CCONJ
ap-688	154	36	�	�	PROPN
ap-688	154	37	�	�	PROPN
ap-688	154	38	1	1	NUM
ap-688	154	39	1	1	NUM
ap-688	154	40	�	�	PROPN
ap-688	154	41	�	�	PROPN
ap-688	154	42	,	,	PUNCT
ap-688	154	43	such	such	ADJ
ap-688	154	44	that	that	PRON
ap-688	154	45	s	s	X
ap-688	154	46	t	t	X
ap-688	154	47	k	k	PROPN
ap-688	154	48	mj	mj	PROPN
ap-688	155	1	ij	ij	INTJ
ap-688	155	2	j	j	PROPN
ap-688	156	1	n	n	CCONJ
ap-688	156	2	i	i	PROPN
ap-688	156	3	�	�	PROPN
ap-688	156	4	�	�	PROPN
ap-688	156	5	�	�	PROPN
ap-688	156	6	1	1	NUM
ap-688	156	7	mod	mod	NOUN
ap-688	156	8	(	(	PUNCT
ap-688	156	9	6	6	NUM
ap-688	156	10	)	)	PUNCT
ap-688	156	11	(	(	PUNCT
ap-688	156	12	the	the	DET
ap-688	156	13	time	time	NOUN
ap-688	156	14	domain	domain	NOUN
ap-688	156	15	problem	problem	NOUN
ap-688	156	16	)	)	PUNCT
ap-688	156	17	.	.	PUNCT
ap-688	157	1	�	�	PROPN
ap-688	157	2	implement	implement	VERB
ap-688	157	3	the	the	DET
ap-688	157	4	rotations	rotation	NOUN
ap-688	157	5	sj	sj	INTJ
ap-688	157	6	under	under	ADP
ap-688	157	7	the	the	DET
ap-688	157	8	optimality	optimality	NOUN
ap-688	157	9	criterion	criterion	NOUN
ap-688	157	10	in	in	ADP
ap-688	157	11	eq	eq	NOUN
ap-688	157	12	.	.	PROPN
ap-688	157	13	5	5	NUM
ap-688	157	14	(	(	PUNCT
ap-688	157	15	the	the	DET
ap-688	157	16	space	space	NOUN
ap-688	157	17	domain	domain	NOUN
ap-688	157	18	problem	problem	NOUN
ap-688	157	19	)	)	PUNCT
ap-688	157	20	.	.	PUNCT
ap-688	158	1	for	for	ADP
ap-688	158	2	such	such	DET
ap-688	158	3	a	a	DET
ap-688	158	4	sequential	sequential	ADJ
ap-688	158	5	decomposition	decomposition	NOUN
ap-688	158	6	to	to	ADP
ap-688	158	7	work	work	VERB
ap-688	158	8	,	,	PUNCT
ap-688	158	9	the	the	DET
ap-688	158	10	first	first	ADJ
ap-688	158	11	step	step	NOUN
ap-688	158	12	must	must	AUX
ap-688	158	13	estimate	estimate	VERB
ap-688	158	14	the	the	DET
ap-688	158	15	quality	quality	NOUN
ap-688	158	16	of	of	ADP
ap-688	158	17	the	the	DET
ap-688	158	18	result	result	NOUN
ap-688	158	19	of	of	ADP
ap-688	158	20	the	the	DET
ap-688	158	21	second	second	ADJ
ap-688	158	22	step	step	NOUN
ap-688	158	23	.	.	PUNCT
ap-688	159	1	in	in	ADP
ap-688	159	2	our	our	PRON
ap-688	159	3	case	case	NOUN
ap-688	159	4	,	,	PUNCT
ap-688	159	5	we	we	PRON
ap-688	159	6	need	need	VERB
ap-688	159	7	the	the	DET
ap-688	159	8	estimation	estimation	NOUN
ap-688	159	9	of	of	ADP
ap-688	159	10	area	area	NOUN
ap-688	159	11	,	,	PUNCT
ap-688	159	12	clock	clock	NOUN
ap-688	159	13	cycles	cycle	NOUN
ap-688	159	14	,	,	PUNCT
ap-688	159	15	and	and	CCONJ
ap-688	159	16	critical	critical	ADJ
ap-688	159	17	path	path	NOUN
ap-688	159	18	of	of	ADP
ap-688	159	19	a	a	DET
ap-688	159	20	circuit	circuit	NOUN
ap-688	159	21	realizing	realize	VERB
ap-688	159	22	a	a	DET
ap-688	159	23	given	give	VERB
ap-688	159	24	set	set	NOUN
ap-688	159	25	of	of	ADP
ap-688	159	26	rotations	rotation	NOUN
ap-688	159	27	.	.	PUNCT
ap-688	160	1	thanks	thank	NOUN
ap-688	160	2	to	to	ADP
ap-688	160	3	the	the	DET
ap-688	160	4	special	special	ADJ
ap-688	160	5	nature	nature	NOUN
ap-688	160	6	of	of	ADP
ap-688	160	7	rotations	rotation	NOUN
ap-688	160	8	ki	ki	PROPN
ap-688	160	9	,	,	PUNCT
ap-688	160	10	we	we	PRON
ap-688	160	11	can	can	AUX
ap-688	160	12	have	have	AUX
ap-688	160	13	made	make	VERB
ap-688	160	14	reasonable	reasonable	ADJ
ap-688	160	15	assumptions	assumption	NOUN
ap-688	160	16	about	about	ADP
ap-688	160	17	them	they	PRON
ap-688	160	18	.	.	PUNCT
ap-688	161	1	the	the	DET
ap-688	161	2	decomposition	decomposition	NOUN
ap-688	161	3	of	of	ADP
ap-688	161	4	the	the	DET
ap-688	161	5	problem	problem	NOUN
ap-688	161	6	is	be	AUX
ap-688	161	7	summarized	summarize	VERB
ap-688	161	8	in	in	ADP
ap-688	161	9	fig	fig	NOUN
ap-688	161	10	.	.	PUNCT
ap-688	162	1	4	4	NUM
ap-688	162	2	.	.	X
ap-688	162	3	5.2	5.2	NUM
ap-688	162	4	space	space	NOUN
ap-688	162	5	domain	domain	NOUN
ap-688	162	6	problem	problem	NOUN
ap-688	162	7	let	let	VERB
ap-688	162	8	nmux	nmux	NOUN
ap-688	162	9	be	be	AUX
ap-688	162	10	the	the	DET
ap-688	162	11	number	number	NOUN
ap-688	162	12	of	of	ADP
ap-688	162	13	two	two	NUM
ap-688	162	14	-	-	PUNCT
ap-688	162	15	input	input	NOUN
ap-688	162	16	multiplexers	multiplexer	NOUN
ap-688	162	17	in	in	ADP
ap-688	162	18	a	a	DET
ap-688	162	19	circuit	circuit	NOUN
ap-688	162	20	implementing	implement	VERB
ap-688	162	21	n	n	ADP
ap-688	162	22	rotations	rotation	NOUN
ap-688	162	23	.	.	PUNCT
ap-688	163	1	for	for	ADP
ap-688	163	2	a	a	DET
ap-688	163	3	given	give	VERB
ap-688	163	4	n	n	CCONJ
ap-688	163	5	,	,	PUNCT
ap-688	163	6	nmux	nmux	NOUN
ap-688	163	7	has	have	VERB
ap-688	163	8	the	the	DET
ap-688	163	9	following	follow	VERB
ap-688	163	10	bounds	bound	NOUN
ap-688	163	11	:	:	PUNCT
ap-688	163	12	�	�	PROPN
ap-688	163	13	nmux	nmux	NOUN
ap-688	163	14	is	be	AUX
ap-688	163	15	o(n	o(n	NUM
ap-688	163	16	)	)	PUNCT
ap-688	163	17	.	.	PUNCT
ap-688	164	1	any	any	DET
ap-688	164	2	set	set	NOUN
ap-688	164	3	of	of	ADP
ap-688	164	4	rotations	rotation	NOUN
ap-688	164	5	can	can	AUX
ap-688	164	6	be	be	AUX
ap-688	164	7	implemented	implement	VERB
ap-688	164	8	using	use	VERB
ap-688	164	9	an	an	DET
ap-688	164	10	n	n	CCONJ
ap-688	164	11	-	-	PUNCT
ap-688	164	12	input	input	NOUN
ap-688	164	13	multiplexer	multiplexer	NOUN
ap-688	164	14	,	,	PUNCT
ap-688	164	15	which	which	PRON
ap-688	164	16	in	in	ADP
ap-688	164	17	turn	turn	NOUN
ap-688	164	18	is	be	AUX
ap-688	164	19	a	a	DET
ap-688	164	20	tree	tree	NOUN
ap-688	164	21	of	of	ADP
ap-688	164	22	n	n	DET
ap-688	164	23	2	2	NUM
ap-688	164	24	-	-	PUNCT
ap-688	164	25	input	input	NOUN
ap-688	164	26	multiplexers	multiplexer	NOUN
ap-688	164	27	.	.	PUNCT
ap-688	165	1	�	�	PROPN
ap-688	165	2	nmux	nmux	PROPN
ap-688	165	3	is	be	AUX
ap-688	165	4	�	�	PROPN
ap-688	165	5	(	(	PUNCT
ap-688	165	6	log	log	NOUN
ap-688	165	7	n	n	CCONJ
ap-688	165	8	)	)	PUNCT
ap-688	165	9	.	.	PUNCT
ap-688	166	1	this	this	PRON
ap-688	166	2	is	be	AUX
ap-688	166	3	the	the	DET
ap-688	166	4	minimum	minimum	ADJ
ap-688	166	5	number	number	NOUN
ap-688	166	6	of	of	ADP
ap-688	166	7	bits	bit	NOUN
ap-688	166	8	specifying	specify	VERB
ap-688	166	9	one	one	NUM
ap-688	166	10	number	number	NOUN
ap-688	166	11	out	out	ADP
ap-688	166	12	of	of	ADP
ap-688	166	13	n.	n.	NOUN
ap-688	166	14	note	note	VERB
ap-688	166	15	that	that	SCONJ
ap-688	166	16	in	in	ADP
ap-688	166	17	both	both	DET
ap-688	166	18	cases	case	NOUN
ap-688	166	19	,	,	PUNCT
ap-688	166	20	the	the	DET
ap-688	166	21	critical	critical	ADJ
ap-688	166	22	path	path	NOUN
ap-688	166	23	length	length	NOUN
ap-688	166	24	is	be	AUX
ap-688	166	25	logarithmic	logarithmic	ADJ
ap-688	166	26	.	.	PUNCT
ap-688	167	1	a	a	DET
ap-688	167	2	circuit	circuit	NOUN
ap-688	167	3	intermediate	intermediate	ADJ
ap-688	167	4	between	between	ADP
ap-688	167	5	these	these	DET
ap-688	167	6	two	two	NUM
ap-688	167	7	extremes	extreme	NOUN
ap-688	167	8	can	can	AUX
ap-688	167	9	be	be	AUX
ap-688	167	10	represented	represent	VERB
ap-688	167	11	as	as	ADP
ap-688	167	12	a	a	DET
ap-688	167	13	network	network	NOUN
ap-688	167	14	of	of	ADP
ap-688	167	15	2	2	NUM
ap-688	167	16	-	-	PUNCT
ap-688	167	17	input	input	NOUN
ap-688	167	18	multiplexers	multiplexer	NOUN
ap-688	167	19	.	.	PUNCT
ap-688	168	1	we	we	PRON
ap-688	168	2	have	have	AUX
ap-688	168	3	proven	prove	VERB
ap-688	168	4	that	that	SCONJ
ap-688	168	5	:	:	PUNCT
ap-688	168	6	�	�	PROPN
ap-688	168	7	unless	unless	SCONJ
ap-688	168	8	there	there	PRON
ap-688	168	9	are	be	VERB
ap-688	168	10	distinct	distinct	ADJ
ap-688	168	11	indices	index	NOUN
ap-688	168	12	a	a	DET
ap-688	168	13	,	,	PUNCT
ap-688	168	14	b	b	PROPN
ap-688	168	15	,	,	PUNCT
ap-688	168	16	c	c	NOUN
ap-688	168	17	,	,	PUNCT
ap-688	168	18	d	d	X
ap-688	168	19	such	such	ADJ
ap-688	168	20	that	that	PRON
ap-688	168	21	s	s	VERB
ap-688	168	22	s	s	X
ap-688	168	23	s	s	PROPN
ap-688	168	24	sa	sa	PROPN
ap-688	168	25	b	b	PROPN
ap-688	168	26	c	c	NOUN
ap-688	168	27	d	d	PUNCT
ap-688	168	28	�	�	PROPN
ap-688	168	29	�	�	PROPN
ap-688	168	30	�	�	PROPN
ap-688	168	31	,	,	PUNCT
ap-688	168	32	the	the	DET
ap-688	168	33	circuit	circuit	NOUN
ap-688	168	34	optimal	optimal	ADJ
ap-688	168	35	in	in	ADP
ap-688	168	36	area	area	NOUN
ap-688	168	37	and	and	CCONJ
ap-688	168	38	critical	critical	ADJ
ap-688	168	39	path	path	NOUN
ap-688	168	40	is	be	AUX
ap-688	168	41	an	an	DET
ap-688	168	42	n	n	CCONJ
ap-688	168	43	-	-	PUNCT
ap-688	168	44	input	input	NOUN
ap-688	168	45	multiplexer	multiplexer	NOUN
ap-688	168	46	;	;	PUNCT
ap-688	168	47	�	�	PROPN
ap-688	168	48	the	the	DET
ap-688	168	49	original	original	ADJ
ap-688	168	50	set	set	NOUN
ap-688	168	51	of	of	ADP
ap-688	168	52	rotations	rotation	NOUN
ap-688	168	53	ki	ki	PROPN
ap-688	168	54	does	do	AUX
ap-688	168	55	not	not	PART
ap-688	168	56	have	have	VERB
ap-688	168	57	the	the	DET
ap-688	168	58	above	above	ADJ
ap-688	168	59	property	property	NOUN
ap-688	168	60	.	.	PUNCT
ap-688	169	1	these	these	DET
ap-688	169	2	facts	fact	NOUN
ap-688	169	3	lead	lead	VERB
ap-688	169	4	us	we	PRON
ap-688	169	5	to	to	ADP
ap-688	169	6	the	the	DET
ap-688	169	7	tentative	tentative	ADJ
ap-688	169	8	assumption	assumption	NOUN
ap-688	169	9	that	that	SCONJ
ap-688	169	10	the	the	DET
ap-688	169	11	solution	solution	NOUN
ap-688	169	12	of	of	ADP
ap-688	169	13	the	the	DET
ap-688	169	14	space	space	NOUN
ap-688	169	15	domain	domain	NOUN
ap-688	169	16	problem	problem	NOUN
ap-688	169	17	can	can	AUX
ap-688	169	18	be	be	AUX
ap-688	169	19	approximated	approximate	VERB
ap-688	169	20	as	as	ADP
ap-688	169	21	an	an	DET
ap-688	169	22	n	n	CCONJ
ap-688	169	23	-	-	PUNCT
ap-688	169	24	input	input	NOUN
ap-688	169	25	multiplexer	multiplexer	NOUN
ap-688	169	26	.	.	PUNCT
ap-688	170	1	the	the	DET
ap-688	170	2	overall	overall	ADJ
ap-688	170	3	quality	quality	NOUN
ap-688	170	4	measure	measure	NOUN
ap-688	170	5	is	be	AUX
ap-688	170	6	then	then	ADV
ap-688	170	7	�	�	PROPN
ap-688	170	8	q	q	PROPN
ap-688	170	9	na	na	ADP
ap-688	170	10	n	n	PROPN
ap-688	170	11	a	a	DET
ap-688	170	12	t	t	NOUN
ap-688	170	13	t	t	PROPN
ap-688	170	14	nij	nij	PROPN
ap-688	170	15	j	j	PROPN
ap-688	171	1	n	n	CCONJ
ap-688	171	2	i	i	PRON
ap-688	171	3	r	r	NOUN
ap-688	171	4	�	�	PROPN
ap-688	171	5	�	�	PROPN
ap-688	171	6	�	�	PROPN
ap-688	171	7	�	�	PROPN
ap-688	171	8	�	�	PROPN
ap-688	171	9	�	�	PROPN
ap-688	171	10	�	�	PROPN
ap-688	171	11	�	�	PROPN
ap-688	171	12	�	�	PROPN
ap-688	171	13	�	�	PROPN
ap-688	171	14	�	�	PROPN
ap-688	171	15	�	�	PROPN
ap-688	171	16	�	�	PROPN
ap-688	171	17	�	�	PROPN
ap-688	171	18	�	�	PROPN
ap-688	171	19	�	�	PROPN
ap-688	171	20	�	�	PROPN
ap-688	171	21	�	�	PROPN
ap-688	171	22	�	�	PROPN
ap-688	171	23	mux	mux	PROPN
ap-688	171	24	mux	mux	PROPN
ap-688	171	25	(	(	PUNCT
ap-688	171	26	)	)	PUNCT
ap-688	171	27	max	max	PROPN
ap-688	171	28	(	(	PUNCT
ap-688	171	29	0	0	NUM
ap-688	171	30	1	1	NUM
ap-688	171	31	0	0	NUM
ap-688	171	32	1	1	NUM
ap-688	171	33	�	�	PROPN
ap-688	171	34	�	�	PROPN
ap-688	171	35	�	�	PROPN
ap-688	171	36	)	)	PUNCT
ap-688	171	37	,	,	PUNCT
ap-688	171	38	.	.	PUNCT
ap-688	172	1	�	�	PROPN
ap-688	172	2	0	0	NUM
ap-688	172	3	the	the	DET
ap-688	172	4	area	area	NOUN
ap-688	172	5	amux(n	amux(n	PROPN
ap-688	172	6	)	)	PUNCT
ap-688	172	7	and	and	CCONJ
ap-688	172	8	critical	critical	ADJ
ap-688	172	9	path	path	NOUN
ap-688	172	10	�	�	PROPN
ap-688	172	11	mux(n	mux(n	PROPN
ap-688	172	12	)	)	PUNCT
ap-688	172	13	of	of	ADP
ap-688	172	14	an	an	DET
ap-688	172	15	n	n	CCONJ
ap-688	172	16	-	-	PUNCT
ap-688	172	17	input	input	NOUN
ap-688	172	18	multiplexer	multiplexer	NOUN
ap-688	172	19	can	can	AUX
ap-688	172	20	be	be	AUX
ap-688	172	21	expressed	express	VERB
ap-688	172	22	in	in	ADP
ap-688	172	23	terms	term	NOUN
ap-688	172	24	of	of	ADP
ap-688	172	25	primitive	primitive	ADJ
ap-688	172	26	gates	gate	NOUN
ap-688	172	27	,	,	PUNCT
ap-688	172	28	if	if	SCONJ
ap-688	172	29	such	such	DET
ap-688	172	30	a	a	DET
ap-688	172	31	measure	measure	NOUN
ap-688	172	32	is	be	AUX
ap-688	172	33	used	use	VERB
ap-688	172	34	for	for	ADP
ap-688	172	35	the	the	DET
ap-688	172	36	rest	rest	NOUN
ap-688	172	37	of	of	ADP
ap-688	172	38	the	the	DET
ap-688	172	39	unit	unit	NOUN
ap-688	172	40	.	.	PUNCT
ap-688	173	1	alternatively	alternatively	ADV
ap-688	173	2	,	,	PUNCT
ap-688	173	3	these	these	DET
ap-688	173	4	values	value	NOUN
ap-688	173	5	can	can	AUX
ap-688	173	6	be	be	AUX
ap-688	173	7	measured	measure	VERB
ap-688	173	8	in	in	ADP
ap-688	173	9	terms	term	NOUN
ap-688	173	10	of	of	ADP
ap-688	173	11	implementation	implementation	NOUN
ap-688	173	12	technology	technology	NOUN
ap-688	173	13	(	(	PUNCT
ap-688	173	14	transistors	transistor	NOUN
ap-688	173	15	,	,	PUNCT
ap-688	173	16	programmable	programmable	ADJ
ap-688	173	17	blocks	block	NOUN
ap-688	173	18	)	)	PUNCT
ap-688	173	19	and	and	CCONJ
ap-688	173	20	as	as	SCONJ
ap-688	173	21	such	such	ADJ
ap-688	173	22	obtained	obtain	VERB
ap-688	173	23	from	from	ADP
ap-688	173	24	the	the	DET
ap-688	173	25	synthesis	synthesis	NOUN
ap-688	173	26	tools	tool	NOUN
ap-688	173	27	used	use	VERB
ap-688	173	28	.	.	PUNCT
ap-688	174	1	5.3	5.3	NUM
ap-688	174	2	time	time	NOUN
ap-688	174	3	domain	domain	NOUN
ap-688	174	4	problem	problem	NOUN
ap-688	174	5	due	due	ADP
ap-688	174	6	to	to	ADP
ap-688	174	7	the	the	DET
ap-688	174	8	modularity	modularity	NOUN
ap-688	174	9	of	of	ADP
ap-688	174	10	eq	eq	PROPN
ap-688	174	11	.	.	PROPN
ap-688	174	12	6	6	NUM
ap-688	174	13	,	,	PUNCT
ap-688	174	14	the	the	DET
ap-688	174	15	value	value	NOUN
ap-688	174	16	of	of	ADP
ap-688	174	17	all	all	DET
ap-688	174	18	sj	sj	INTJ
ap-688	174	19	and	and	CCONJ
ap-688	174	20	tij	tij	PROPN
ap-688	174	21	can	can	AUX
ap-688	174	22	be	be	AUX
ap-688	174	23	restricted	restrict	VERB
ap-688	174	24	to	to	ADP
ap-688	174	25	(	(	PUNCT
ap-688	174	26	0	0	NUM
ap-688	174	27	,	,	PUNCT
ap-688	174	28	m	m	NOUN
ap-688	174	29	)	)	PUNCT
ap-688	174	30	without	without	ADP
ap-688	174	31	loss	loss	NOUN
ap-688	174	32	of	of	ADP
ap-688	174	33	generality	generality	NOUN
ap-688	174	34	.	.	PUNCT
ap-688	175	1	this	this	PRON
ap-688	175	2	still	still	ADV
ap-688	175	3	represents	represent	VERB
ap-688	175	4	,	,	PUNCT
ap-688	175	5	however	however	ADV
ap-688	175	6	,	,	PUNCT
ap-688	175	7	a	a	DET
ap-688	175	8	large	large	ADJ
ap-688	175	9	solution	solution	NOUN
ap-688	175	10	space	space	NOUN
ap-688	175	11	.	.	PUNCT
ap-688	176	1	to	to	PART
ap-688	176	2	reduce	reduce	VERB
ap-688	176	3	it	it	PRON
ap-688	176	4	,	,	PUNCT
ap-688	176	5	further	further	ADJ
ap-688	176	6	decomposition	decomposition	NOUN
ap-688	176	7	is	be	AUX
ap-688	176	8	used	use	VERB
ap-688	176	9	:	:	PUNCT
ap-688	176	10	1	1	X
ap-688	176	11	.	.	X
ap-688	176	12	choose	choose	VERB
ap-688	176	13	a	a	DET
ap-688	176	14	set	set	NOUN
ap-688	176	15	of	of	ADP
ap-688	176	16	rotations	rotation	NOUN
ap-688	176	17	sj	sj	VERB
ap-688	176	18	.	.	NOUN
ap-688	176	19	2	2	NUM
ap-688	176	20	.	.	X
ap-688	176	21	obtain	obtain	VERB
ap-688	176	22	a	a	DET
ap-688	176	23	set	set	NOUN
ap-688	176	24	of	of	ADP
ap-688	176	25	factors	factor	NOUN
ap-688	177	1	tij	tij	INTJ
ap-688	177	2	giving	give	VERB
ap-688	177	3	optimum	optimum	ADJ
ap-688	177	4	quality	quality	NOUN
ap-688	177	5	q.	q.	NOUN
ap-688	177	6	because	because	SCONJ
ap-688	177	7	no	no	DET
ap-688	177	8	reliable	reliable	ADJ
ap-688	177	9	estimate	estimate	NOUN
ap-688	177	10	can	can	AUX
ap-688	177	11	be	be	AUX
ap-688	177	12	made	make	VERB
ap-688	177	13	in	in	ADP
ap-688	177	14	step	step	NOUN
ap-688	177	15	1	1	NUM
ap-688	177	16	,	,	PUNCT
ap-688	177	17	both	both	DET
ap-688	177	18	steps	step	NOUN
ap-688	177	19	are	be	AUX
ap-688	177	20	performed	perform	VERB
ap-688	177	21	iteratively	iteratively	ADV
ap-688	177	22	.	.	PUNCT
ap-688	178	1	in	in	ADP
ap-688	178	2	other	other	ADJ
ap-688	178	3	words	word	NOUN
ap-688	178	4	,	,	PUNCT
ap-688	178	5	we	we	PRON
ap-688	178	6	use	use	VERB
ap-688	178	7	step	step	NOUN
ap-688	178	8	2	2	NUM
ap-688	178	9	as	as	ADP
ap-688	178	10	the	the	DET
ap-688	178	11	evaluation	evaluation	NOUN
ap-688	178	12	function	function	NOUN
ap-688	178	13	for	for	ADP
ap-688	178	14	the	the	DET
ap-688	178	15	local	local	ADJ
ap-688	178	16	search	search	NOUN
ap-688	178	17	in	in	ADP
ap-688	178	18	step	step	NOUN
ap-688	178	19	1	1	NUM
ap-688	178	20	.	.	PUNCT
ap-688	178	21	5.4	5.4	NUM
ap-688	178	22	optimal	optimal	ADJ
ap-688	178	23	factors	factor	NOUN
ap-688	178	24	by	by	ADP
ap-688	178	25	dynamic	dynamic	ADJ
ap-688	178	26	programming	programming	NOUN
ap-688	178	27	in	in	ADP
ap-688	178	28	step	step	NOUN
ap-688	178	29	2	2	NUM
ap-688	178	30	above	above	ADV
ap-688	178	31	,	,	PUNCT
ap-688	178	32	n	n	X
ap-688	178	33	is	be	AUX
ap-688	178	34	fixed	fix	VERB
ap-688	178	35	,	,	PUNCT
ap-688	178	36	and	and	CCONJ
ap-688	178	37	so	so	ADV
ap-688	178	38	are	be	AUX
ap-688	178	39	the	the	DET
ap-688	178	40	parameters	parameter	NOUN
ap-688	178	41	of	of	ADP
ap-688	178	42	the	the	DET
ap-688	178	43	multiplexer	multiplexer	NOUN
ap-688	178	44	implementing	implement	VERB
ap-688	178	45	sj	sj	X
ap-688	178	46	.	.	PUNCT
ap-688	179	1	furthermore	furthermore	ADV
ap-688	179	2	,	,	PUNCT
ap-688	179	3	note	note	VERB
ap-688	179	4	that	that	SCONJ
ap-688	179	5	the	the	DET
ap-688	179	6	equations	equation	NOUN
ap-688	179	7	for	for	ADP
ap-688	179	8	different	different	ADJ
ap-688	179	9	values	value	NOUN
ap-688	179	10	of	of	ADP
ap-688	179	11	j	j	PROPN
ap-688	179	12	in	in	ADP
ap-688	179	13	eq	eq	PROPN
ap-688	179	14	.	.	PROPN
ap-688	179	15	6	6	NUM
ap-688	179	16	are	be	AUX
ap-688	179	17	independent	independent	ADJ
ap-688	179	18	,	,	PUNCT
ap-688	179	19	that	that	ADV
ap-688	179	20	is	is	ADV
ap-688	179	21	,	,	PUNCT
ap-688	179	22	we	we	PRON
ap-688	179	23	have	have	VERB
ap-688	179	24	r	r	NOUN
ap-688	179	25	primitive	primitive	ADJ
ap-688	179	26	problems	problem	NOUN
ap-688	179	27	of	of	ADP
ap-688	179	28	the	the	DET
ap-688	179	29	following	follow	VERB
ap-688	179	30	form	form	NOUN
ap-688	179	31	.	.	PUNCT
ap-688	180	1	58	58	NUM
ap-688	181	1	©	©	PROPN
ap-688	181	2	czech	czech	PROPN
ap-688	181	3	technical	technical	PROPN
ap-688	181	4	university	university	PROPN
ap-688	181	5	publishing	publishing	NOUN
ap-688	181	6	house	house	NOUN
ap-688	181	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	181	8	acta	acta	PROPN
ap-688	181	9	polytechnica	polytechnica	PROPN
ap-688	181	10	vol	vol	NOUN
ap-688	181	11	.	.	PROPN
ap-688	182	1	45	45	NUM
ap-688	182	2	no	no	NOUN
ap-688	182	3	.	.	PUNCT
ap-688	183	1	2/2005	2/2005	NUM
ap-688	183	2	czech	czech	PROPN
ap-688	183	3	technical	technical	PROPN
ap-688	183	4	university	university	PROPN
ap-688	183	5	in	in	ADP
ap-688	183	6	prague	prague	PROPN
ap-688	183	7	s	s	PART
ap-688	183	8	k	k	PROPN
ap-688	183	9	time	time	NOUN
ap-688	183	10	domain	domain	NOUN
ap-688	183	11	problem	problem	NOUN
ap-688	183	12	space	space	NOUN
ap-688	183	13	domain	domain	NOUN
ap-688	183	14	problem	problem	NOUN
ap-688	183	15	t	t	NOUN
ap-688	183	16	step	step	NOUN
ap-688	183	17	2	2	NUM
ap-688	183	18	step	step	NOUN
ap-688	183	19	1	1	NUM
ap-688	183	20	estimation	estimation	NOUN
ap-688	183	21	s	s	PART
ap-688	183	22	muxes	muxes	PROPN
ap-688	184	1	i	i	PRON
ap-688	184	2	ij	ij	INTJ
ap-688	185	1	i	i	PRON
ap-688	185	2	obtain	obtain	VERB
ap-688	185	3	tij	tij	PROPN
ap-688	185	4	i	i	PRON
ap-688	185	5	by	by	ADP
ap-688	185	6	dynamic	dynamic	ADJ
ap-688	185	7	programming	programming	NOUN
ap-688	185	8	genetic	genetic	ADJ
ap-688	185	9	algorithm	algorithm	NOUN
ap-688	185	10	choose	choose	VERB
ap-688	185	11	s	s	X
ap-688	185	12	i	i	NOUN
ap-688	185	13	fig	fig	NOUN
ap-688	185	14	.	.	PUNCT
ap-688	186	1	4	4	NUM
ap-688	186	2	:	:	PUNCT
ap-688	186	3	decomposition	decomposition	NOUN
ap-688	186	4	for	for	ADP
ap-688	186	5	a	a	DET
ap-688	186	6	given	give	VERB
ap-688	186	7	c	c	PROPN
ap-688	186	8	c	c	PROPN
ap-688	186	9	m	m	PROPN
ap-688	186	10	�	�	PROPN
ap-688	186	11	�	�	PROPN
ap-688	186	12	�	�	PROPN
ap-688	186	13	z	z	PROPN
ap-688	186	14	,	,	PUNCT
ap-688	186	15	and	and	CCONJ
ap-688	186	16	h	h	PROPN
ap-688	186	17	�	�	PROPN
ap-688	186	18	�	�	PROPN
ap-688	186	19	z	z	PROPN
ap-688	186	20	,	,	PUNCT
ap-688	186	21	find	find	VERB
ap-688	186	22	t	t	PROPN
ap-688	186	23	j	j	PROPN
ap-688	186	24	hij	hij	PROPN
ap-688	186	25	�	�	PROPN
ap-688	186	26	�	�	PROPN
ap-688	186	27	�	�	PROPN
ap-688	186	28	z	z	PROPN
ap-688	186	29	,	,	PUNCT
ap-688	186	30	1	1	NUM
ap-688	186	31	�	�	PROPN
ap-688	186	32	such	such	ADJ
ap-688	186	33	that	that	PRON
ap-688	186	34	s	s	X
ap-688	186	35	t	t	X
ap-688	186	36	c	c	PROPN
ap-688	186	37	mj	mj	PROPN
ap-688	186	38	j	j	PROPN
ap-688	186	39	j	j	PROPN
ap-688	186	40	h	h	PROPN
ap-688	186	41	�	�	PROPN
ap-688	186	42	�	�	PROPN
ap-688	186	43	�	�	PROPN
ap-688	186	44	1	1	NUM
ap-688	186	45	mod	mod	NOUN
ap-688	186	46	while	while	SCONJ
ap-688	186	47	minimizing	minimize	VERB
ap-688	186	48	q	q	PROPN
ap-688	186	49	tj	tj	PROPN
ap-688	186	50	j	j	PROPN
ap-688	186	51	n	n	PROPN
ap-688	186	52	�	�	PROPN
ap-688	186	53	�	�	PROPN
ap-688	186	54	�	�	PROPN
ap-688	186	55	1	1	NUM
ap-688	186	56	.	.	PUNCT
ap-688	187	1	let	let	VERB
ap-688	187	2	f(h	f(h	PROPN
ap-688	187	3	,	,	PUNCT
ap-688	187	4	c	c	AUX
ap-688	187	5	)	)	PUNCT
ap-688	187	6	be	be	AUX
ap-688	187	7	a	a	DET
ap-688	187	8	function	function	NOUN
ap-688	187	9	giving	give	VERB
ap-688	187	10	minimum	minimum	NOUN
ap-688	187	11	q	q	NOUN
ap-688	187	12	for	for	ADP
ap-688	187	13	the	the	DET
ap-688	187	14	above	above	ADJ
ap-688	187	15	problem	problem	NOUN
ap-688	187	16	.	.	PUNCT
ap-688	188	1	let	let	VERB
ap-688	188	2	f(0	f(0	NOUN
ap-688	188	3	,	,	PUNCT
ap-688	188	4	0	0	NUM
ap-688	188	5	)	)	PUNCT
ap-688	188	6	=	=	SYM
ap-688	188	7	0	0	NUM
ap-688	188	8	and	and	CCONJ
ap-688	188	9	f(0	f(0	NOUN
ap-688	188	10	,	,	PUNCT
ap-688	188	11	c	c	NOUN
ap-688	188	12	)	)	PUNCT
ap-688	188	13	=	=	SYM
ap-688	188	14	�	�	PROPN
ap-688	188	15	for	for	ADP
ap-688	188	16	c	c	PROPN
ap-688	188	17	>	>	X
ap-688	188	18	0	0	PROPN
ap-688	188	19	.	.	PUNCT
ap-688	189	1	then	then	ADV
ap-688	189	2	f(h	f(h	PROPN
ap-688	189	3	,	,	PUNCT
ap-688	189	4	c	c	NOUN
ap-688	189	5	)	)	PUNCT
ap-688	189	6	is	be	AUX
ap-688	189	7	,	,	PUNCT
ap-688	189	8	for	for	ADP
ap-688	189	9	0	0	NUM
ap-688	189	10	<	<	X
ap-688	189	11	h	h	PROPN
ap-688	189	12	�	�	PROPN
ap-688	189	13	r	r	PROPN
ap-688	189	14	,	,	PUNCT
ap-688	189	15	�	�	PROPN
ap-688	189	16	�	�	PROPN
ap-688	189	17	�	�	PROPN
ap-688	189	18	f	f	PROPN
ap-688	189	19	h	h	NOUN
ap-688	190	1	c	c	NOUN
ap-688	190	2	f	f	PROPN
ap-688	190	3	h	h	NOUN
ap-688	191	1	c	c	NOUN
ap-688	191	2	ds	ds	PROPN
ap-688	191	3	m	m	NOUN
ap-688	191	4	d	d	PROPN
ap-688	191	5	d	d	X
ap-688	191	6	h	h	NOUN
ap-688	191	7	(	(	PUNCT
ap-688	191	8	,	,	PUNCT
ap-688	191	9	)	)	PUNCT
ap-688	191	10	min	min	NOUN
ap-688	191	11	,	,	PUNCT
ap-688	191	12	(	(	PUNCT
ap-688	191	13	)	)	PUNCT
ap-688	191	14	mod	mod	PROPN
ap-688	191	15	�	�	PROPN
ap-688	191	16	�	�	PROPN
ap-688	191	17	�	�	PROPN
ap-688	191	18	�	�	PROPN
ap-688	191	19	1	1	NUM
ap-688	191	20	,	,	PUNCT
ap-688	191	21	where	where	SCONJ
ap-688	191	22	d	d	NOUN
ap-688	191	23	ranges	range	VERB
ap-688	191	24	between	between	ADP
ap-688	191	25	0	0	NUM
ap-688	191	26	and	and	CCONJ
ap-688	191	27	the	the	DET
ap-688	191	28	order	order	NOUN
ap-688	191	29	of	of	ADP
ap-688	191	30	sh	sh	PROPN
ap-688	191	31	in	in	ADP
ap-688	191	32	zm	zm	PROPN
ap-688	191	33	,	,	PUNCT
ap-688	191	34	that	that	PRON
ap-688	191	35	is	is	ADV
ap-688	191	36	0	0	NUM
ap-688	191	37	�	�	PROPN
ap-688	191	38	d	d	PROPN
ap-688	191	39	�	�	PROPN
ap-688	191	40	m	m	PROPN
ap-688	191	41	/	/	SYM
ap-688	191	42	gcd	gcd	PROPN
ap-688	191	43	(	(	PUNCT
ap-688	191	44	sh	sh	PROPN
ap-688	191	45	,	,	PUNCT
ap-688	191	46	m	m	PROPN
ap-688	191	47	)	)	PUNCT
ap-688	191	48	the	the	DET
ap-688	191	49	values	value	NOUN
ap-688	191	50	of	of	ADP
ap-688	191	51	f(h	f(h	PROPN
ap-688	191	52	,	,	PUNCT
ap-688	191	53	c	c	NOUN
ap-688	191	54	)	)	PUNCT
ap-688	191	55	are	be	AUX
ap-688	191	56	computed	compute	VERB
ap-688	191	57	for	for	ADP
ap-688	191	58	increasing	increase	VERB
ap-688	191	59	h	h	NOUN
ap-688	191	60	and	and	CCONJ
ap-688	191	61	are	be	AUX
ap-688	191	62	stored	store	VERB
ap-688	191	63	in	in	ADP
ap-688	191	64	a	a	DET
ap-688	191	65	two	two	NUM
ap-688	191	66	-	-	PUNCT
ap-688	191	67	dimensional	dimensional	ADJ
ap-688	191	68	array	array	NOUN
ap-688	191	69	with	with	ADP
ap-688	191	70	r	r	NOUN
ap-688	191	71	columns	column	NOUN
ap-688	191	72	and	and	CCONJ
ap-688	191	73	m	m	NOUN
ap-688	191	74	rows	row	NOUN
ap-688	191	75	.	.	PUNCT
ap-688	192	1	after	after	ADP
ap-688	192	2	that	that	PRON
ap-688	192	3	,	,	PUNCT
ap-688	192	4	the	the	DET
ap-688	192	5	element	element	NOUN
ap-688	192	6	(	(	PUNCT
ap-688	192	7	r	r	NOUN
ap-688	192	8	,	,	PUNCT
ap-688	192	9	ki	ki	PROPN
ap-688	192	10	)	)	PUNCT
ap-688	192	11	contains	contain	VERB
ap-688	192	12	the	the	DET
ap-688	192	13	contribution	contribution	NOUN
ap-688	192	14	of	of	ADP
ap-688	192	15	the	the	DET
ap-688	192	16	i	i	PROPN
ap-688	192	17	-	-	PUNCT
ap-688	192	18	th	th	X
ap-688	192	19	primitive	primitive	ADJ
ap-688	192	20	problem	problem	NOUN
ap-688	192	21	to	to	ADP
ap-688	192	22	the	the	DET
ap-688	192	23	optimization	optimization	NOUN
ap-688	192	24	criterion	criterion	NOUN
ap-688	192	25	,	,	PUNCT
ap-688	192	26	for	for	ADP
ap-688	192	27	1	1	NUM
ap-688	192	28	<	<	X
ap-688	192	29	i	i	PROPN
ap-688	192	30	�	�	PROPN
ap-688	192	31	r.	r.	PROPN
ap-688	192	32	eventually	eventually	ADV
ap-688	192	33	,	,	PUNCT
ap-688	192	34	all	all	PRON
ap-688	192	35	values	value	NOUN
ap-688	192	36	tij	tij	INTJ
ap-688	192	37	and	and	CCONJ
ap-688	192	38	therefore	therefore	ADV
ap-688	192	39	the	the	DET
ap-688	192	40	solution	solution	NOUN
ap-688	192	41	of	of	ADP
ap-688	192	42	step	step	NOUN
ap-688	192	43	2	2	NUM
ap-688	192	44	can	can	AUX
ap-688	192	45	be	be	AUX
ap-688	192	46	reconstructed	reconstruct	VERB
ap-688	192	47	from	from	ADP
ap-688	192	48	the	the	DET
ap-688	192	49	array	array	NOUN
ap-688	192	50	.	.	PUNCT
ap-688	193	1	this	this	PRON
ap-688	193	2	means	mean	VERB
ap-688	193	3	that	that	SCONJ
ap-688	193	4	one	one	NUM
ap-688	193	5	pass	pass	VERB
ap-688	193	6	only	only	ADV
ap-688	193	7	of	of	ADP
ap-688	193	8	the	the	DET
ap-688	193	9	above	above	ADJ
ap-688	193	10	outlined	outline	VERB
ap-688	193	11	dynamic	dynamic	ADJ
ap-688	193	12	programming	programming	NOUN
ap-688	193	13	procedure	procedure	NOUN
ap-688	193	14	is	be	AUX
ap-688	193	15	required	require	VERB
ap-688	193	16	to	to	PART
ap-688	193	17	solve	solve	VERB
ap-688	193	18	the	the	DET
ap-688	193	19	entire	entire	ADJ
ap-688	193	20	step	step	NOUN
ap-688	193	21	2	2	NUM
ap-688	193	22	.	.	PUNCT
ap-688	194	1	as	as	SCONJ
ap-688	194	2	r	r	NOUN
ap-688	194	3	is	be	AUX
ap-688	194	4	o(log	o(log	PROPN
ap-688	194	5	m	m	PROPN
ap-688	194	6	)	)	PUNCT
ap-688	194	7	,	,	PUNCT
ap-688	194	8	the	the	DET
ap-688	194	9	complexity	complexity	NOUN
ap-688	194	10	of	of	ADP
ap-688	194	11	this	this	DET
ap-688	194	12	algorithm	algorithm	NOUN
ap-688	194	13	is	be	AUX
ap-688	194	14	o(m2log	o(m2log	PROPN
ap-688	194	15	m	m	PROPN
ap-688	194	16	)	)	PUNCT
ap-688	194	17	.	.	PUNCT
ap-688	195	1	5.5	5.5	NUM
ap-688	195	2	optimal	optimal	ADJ
ap-688	195	3	rotation	rotation	NOUN
ap-688	195	4	set	set	VERB
ap-688	195	5	by	by	ADP
ap-688	195	6	a	a	DET
ap-688	195	7	genetic	genetic	ADJ
ap-688	195	8	algorithm	algorithm	NOUN
ap-688	195	9	the	the	DET
ap-688	195	10	search	search	NOUN
ap-688	195	11	process	process	NOUN
ap-688	195	12	in	in	ADP
ap-688	195	13	step	step	NOUN
ap-688	195	14	1	1	NUM
ap-688	195	15	is	be	AUX
ap-688	195	16	performed	perform	VERB
ap-688	195	17	by	by	ADP
ap-688	195	18	a	a	DET
ap-688	195	19	genetic	genetic	ADJ
ap-688	195	20	algorithm	algorithm	NOUN
ap-688	195	21	,	,	PUNCT
ap-688	195	22	which	which	PRON
ap-688	195	23	in	in	ADP
ap-688	195	24	turn	turn	NOUN
ap-688	195	25	uses	use	VERB
ap-688	195	26	the	the	DET
ap-688	195	27	above	above	ADJ
ap-688	195	28	procedure	procedure	NOUN
ap-688	195	29	to	to	PART
ap-688	195	30	evaluate	evaluate	VERB
ap-688	195	31	the	the	DET
ap-688	195	32	solution	solution	NOUN
ap-688	195	33	.	.	PUNCT
ap-688	196	1	thanks	thank	NOUN
ap-688	196	2	to	to	ADP
ap-688	196	3	the	the	DET
ap-688	196	4	decomposition	decomposition	NOUN
ap-688	196	5	in	in	ADP
ap-688	196	6	subsection	subsection	NOUN
ap-688	196	7	5.1	5.1	NUM
ap-688	196	8	,	,	PUNCT
ap-688	196	9	a	a	DET
ap-688	196	10	configuration	configuration	NOUN
ap-688	196	11	of	of	ADP
ap-688	196	12	the	the	DET
ap-688	196	13	search	search	NOUN
ap-688	196	14	problem	problem	NOUN
ap-688	196	15	is	be	AUX
ap-688	196	16	determined	determine	VERB
ap-688	196	17	by	by	ADP
ap-688	196	18	the	the	DET
ap-688	196	19	value	value	NOUN
ap-688	196	20	of	of	ADP
ap-688	196	21	n	n	PRON
ap-688	196	22	�	�	PROPN
ap-688	196	23	r	r	NOUN
ap-688	196	24	variables	variable	NOUN
ap-688	196	25	si	si	PROPN
ap-688	196	26	�	�	PROPN
ap-688	196	27	(	(	PUNCT
ap-688	196	28	0	0	NUM
ap-688	196	29	,	,	PUNCT
ap-688	196	30	m	m	NOUN
ap-688	196	31	)	)	PUNCT
ap-688	196	32	.	.	PUNCT
ap-688	197	1	this	this	PRON
ap-688	197	2	is	be	AUX
ap-688	197	3	the	the	DET
ap-688	197	4	phenotype	phenotype	NOUN
ap-688	197	5	of	of	ADP
ap-688	197	6	the	the	DET
ap-688	197	7	genetic	genetic	ADJ
ap-688	197	8	algorithm	algorithm	NOUN
ap-688	197	9	.	.	PUNCT
ap-688	198	1	the	the	DET
ap-688	198	2	genotype	genotype	NOUN
ap-688	198	3	(	(	PUNCT
ap-688	198	4	chromosome	chromosome	NOUN
ap-688	198	5	)	)	PUNCT
ap-688	198	6	is	be	AUX
ap-688	198	7	a	a	DET
ap-688	198	8	fixed	fix	VERB
ap-688	198	9	structure	structure	NOUN
ap-688	198	10	of	of	ADP
ap-688	198	11	r	r	NOUN
ap-688	198	12	variables	variable	NOUN
ap-688	198	13	from	from	ADP
ap-688	198	14	�	�	PROPN
ap-688	198	15	0,m	0,m	NUM
ap-688	198	16	)	)	PUNCT
ap-688	198	17	.	.	PUNCT
ap-688	199	1	a	a	DET
ap-688	199	2	zero	zero	NUM
ap-688	199	3	value	value	NOUN
ap-688	199	4	is	be	AUX
ap-688	199	5	omitted	omit	VERB
ap-688	199	6	from	from	ADP
ap-688	199	7	the	the	DET
ap-688	199	8	phenotype	phenotype	NOUN
ap-688	199	9	,	,	PUNCT
ap-688	199	10	and	and	CCONJ
ap-688	199	11	equal	equal	ADJ
ap-688	199	12	values	value	NOUN
ap-688	199	13	of	of	ADP
ap-688	199	14	two	two	NUM
ap-688	199	15	or	or	CCONJ
ap-688	199	16	more	more	ADJ
ap-688	199	17	variables	variable	NOUN
ap-688	199	18	in	in	ADP
ap-688	199	19	the	the	DET
ap-688	199	20	genotype	genotype	NOUN
ap-688	199	21	constitute	constitute	VERB
ap-688	199	22	a	a	DET
ap-688	199	23	single	single	ADJ
ap-688	199	24	shift	shift	NOUN
ap-688	199	25	in	in	ADP
ap-688	199	26	the	the	DET
ap-688	199	27	phenotype	phenotype	NOUN
ap-688	199	28	.	.	PUNCT
ap-688	200	1	all	all	DET
ap-688	200	2	permutations	permutation	NOUN
ap-688	200	3	of	of	ADP
ap-688	200	4	the	the	DET
ap-688	200	5	genotype	genotype	NOUN
ap-688	200	6	are	be	AUX
ap-688	200	7	considered	consider	VERB
ap-688	200	8	equivalent	equivalent	ADJ
ap-688	200	9	.	.	PUNCT
ap-688	201	1	this	this	DET
ap-688	201	2	decoder	decoder	NOUN
ap-688	201	3	avoids	avoid	VERB
ap-688	201	4	the	the	DET
ap-688	201	5	necessity	necessity	NOUN
ap-688	201	6	to	to	PART
ap-688	201	7	store	store	VERB
ap-688	201	8	n	n	PRON
ap-688	201	9	as	as	ADP
ap-688	201	10	a	a	DET
ap-688	201	11	separate	separate	ADJ
ap-688	201	12	variable	variable	NOUN
ap-688	201	13	and	and	CCONJ
ap-688	201	14	the	the	DET
ap-688	201	15	need	need	NOUN
ap-688	201	16	to	to	PART
ap-688	201	17	work	work	VERB
ap-688	201	18	with	with	ADP
ap-688	201	19	a	a	DET
ap-688	201	20	variable	variable	ADJ
ap-688	201	21	-	-	PUNCT
ap-688	201	22	length	length	NOUN
ap-688	201	23	genotype	genotype	NOUN
ap-688	201	24	.	.	PUNCT
ap-688	202	1	constrained	constrain	VERB
ap-688	202	2	optimization	optimization	NOUN
ap-688	202	3	was	be	AUX
ap-688	202	4	implemented	implement	VERB
ap-688	202	5	using	use	VERB
ap-688	202	6	a	a	DET
ap-688	202	7	penalty	penalty	NOUN
ap-688	202	8	for	for	ADP
ap-688	202	9	each	each	DET
ap-688	202	10	rotation	rotation	NOUN
ap-688	202	11	ki	ki	PROPN
ap-688	202	12	,	,	PUNCT
ap-688	202	13	which	which	PRON
ap-688	202	14	the	the	DET
ap-688	202	15	individual	individual	NOUN
ap-688	202	16	in	in	ADP
ap-688	202	17	question	question	NOUN
ap-688	202	18	can	can	AUX
ap-688	202	19	not	not	PART
ap-688	202	20	realize	realize	VERB
ap-688	202	21	.	.	PUNCT
ap-688	203	1	due	due	ADP
ap-688	203	2	to	to	ADP
ap-688	203	3	the	the	DET
ap-688	203	4	modularity	modularity	NOUN
ap-688	203	5	of	of	ADP
ap-688	203	6	eq	eq	PROPN
ap-688	203	7	.	.	PROPN
ap-688	203	8	6	6	NUM
ap-688	203	9	,	,	PUNCT
ap-688	203	10	the	the	DET
ap-688	203	11	search	search	NOUN
ap-688	203	12	space	space	NOUN
ap-688	203	13	is	be	AUX
ap-688	203	14	well	well	ADV
ap-688	203	15	connected	connect	VERB
ap-688	203	16	.	.	PUNCT
ap-688	204	1	the	the	DET
ap-688	204	2	infeasible	infeasible	ADJ
ap-688	204	3	individuals	individual	NOUN
ap-688	204	4	were	be	AUX
ap-688	204	5	not	not	PART
ap-688	204	6	needed	need	VERB
ap-688	204	7	to	to	PART
ap-688	204	8	contribute	contribute	VERB
ap-688	204	9	to	to	ADP
ap-688	204	10	the	the	DET
ap-688	204	11	connectedness	connectedness	NOUN
ap-688	204	12	,	,	PUNCT
ap-688	204	13	and	and	CCONJ
ap-688	204	14	therefore	therefore	ADV
ap-688	204	15	the	the	DET
ap-688	204	16	value	value	NOUN
ap-688	204	17	of	of	ADP
ap-688	204	18	the	the	DET
ap-688	204	19	penalty	penalty	NOUN
ap-688	204	20	was	be	AUX
ap-688	204	21	chosen	choose	VERB
ap-688	204	22	well	well	ADV
ap-688	204	23	above	above	ADP
ap-688	204	24	any	any	DET
ap-688	204	25	possible	possible	ADJ
ap-688	204	26	value	value	NOUN
ap-688	204	27	of	of	ADP
ap-688	204	28	q.	q.	PROPN
ap-688	204	29	the	the	DET
ap-688	204	30	rest	rest	NOUN
ap-688	204	31	of	of	ADP
ap-688	204	32	the	the	DET
ap-688	204	33	genetic	genetic	ADJ
ap-688	204	34	algorithm	algorithm	NOUN
ap-688	204	35	was	be	AUX
ap-688	204	36	quite	quite	ADV
ap-688	204	37	classical	classical	ADJ
ap-688	204	38	,	,	PUNCT
ap-688	204	39	with	with	ADP
ap-688	204	40	single	single	ADJ
ap-688	204	41	-	-	PUNCT
ap-688	204	42	point	point	NOUN
ap-688	204	43	crossover	crossover	NOUN
ap-688	204	44	and	and	CCONJ
ap-688	204	45	linear	linear	VERB
ap-688	204	46	scaling	scaling	NOUN
ap-688	204	47	of	of	ADP
ap-688	204	48	fitness	fitness	NOUN
ap-688	204	49	values	value	NOUN
ap-688	204	50	.	.	PUNCT
ap-688	205	1	the	the	DET
ap-688	205	2	adaptive	adaptive	ADJ
ap-688	205	3	nature	nature	NOUN
ap-688	205	4	of	of	ADP
ap-688	205	5	linear	linear	PROPN
ap-688	205	6	scaling	scaling	NOUN
ap-688	205	7	caused	cause	VERB
ap-688	205	8	the	the	DET
ap-688	205	9	convergence	convergence	NOUN
ap-688	205	10	to	to	PART
ap-688	205	11	remain	remain	VERB
ap-688	205	12	unchanged	unchanged	ADJ
ap-688	205	13	even	even	ADV
ap-688	205	14	in	in	ADP
ap-688	205	15	the	the	DET
ap-688	205	16	presence	presence	NOUN
ap-688	205	17	of	of	ADP
ap-688	205	18	large	large	ADJ
ap-688	205	19	a0	a0	NOUN
ap-688	205	20	and	and	CCONJ
ap-688	205	21	t0	t0	PROPN
ap-688	205	22	,	,	PUNCT
ap-688	205	23	where	where	SCONJ
ap-688	205	24	the	the	DET
ap-688	205	25	differences	difference	NOUN
ap-688	205	26	in	in	ADP
ap-688	205	27	evaluations	evaluation	NOUN
ap-688	205	28	are	be	AUX
ap-688	205	29	relatively	relatively	ADV
ap-688	205	30	small	small	ADJ
ap-688	205	31	.	.	PUNCT
ap-688	206	1	it	it	PRON
ap-688	206	2	seems	seem	VERB
ap-688	206	3	that	that	SCONJ
ap-688	206	4	the	the	DET
ap-688	206	5	number	number	NOUN
ap-688	206	6	of	of	ADP
ap-688	206	7	clock	clock	NOUN
ap-688	206	8	cycles	cycle	NOUN
ap-688	206	9	spent	spend	VERB
ap-688	206	10	in	in	ADP
ap-688	206	11	iterative	iterative	ADJ
ap-688	206	12	squarings	squaring	NOUN
ap-688	206	13	is	be	AUX
ap-688	206	14	approx	approx	NOUN
ap-688	206	15	.	.	PUNCT
ap-688	207	1	�	�	PROPN
ap-688	207	2	o	o	PROPN
ap-688	207	3	k	k	PROPN
ap-688	207	4	mk	mk	PROPN
ap-688	207	5	�	�	PROPN
ap-688	207	6	1	1	NUM
ap-688	207	7	,	,	PUNCT
ap-688	207	8	where	where	SCONJ
ap-688	207	9	k	k	PROPN
ap-688	207	10	is	be	AUX
ap-688	207	11	the	the	DET
ap-688	207	12	number	number	NOUN
ap-688	207	13	of	of	ADP
ap-688	207	14	rotation	rotation	NOUN
ap-688	207	15	blocks	block	NOUN
ap-688	207	16	.	.	PUNCT
ap-688	208	1	the	the	DET
ap-688	208	2	total	total	ADJ
ap-688	208	3	time	time	NOUN
ap-688	208	4	necessary	necessary	ADJ
ap-688	208	5	for	for	SCONJ
ap-688	208	6	the	the	DET
ap-688	208	7	point	point	NOUN
ap-688	208	8	addition	addition	NOUN
ap-688	208	9	is	be	AUX
ap-688	208	10	then	then	ADV
ap-688	208	11	t	t	NOUN
ap-688	208	12	o	o	NOUN
ap-688	208	13	m	m	VERB
ap-688	208	14	d	d	NOUN
ap-688	208	15	m	m	VERB
ap-688	208	16	k	k	NOUN
ap-688	208	17	m	m	VERB
ap-688	208	18	dk	dk	PROPN
ap-688	208	19	padd	padd	PROPN
ap-688	208	20	�	�	PROPN
ap-688	208	21	�	�	PROPN
ap-688	208	22	�	�	PROPN
ap-688	208	23	�	�	PROPN
ap-688	208	24	�	�	PROPN
ap-688	208	25	�	�	PROPN
ap-688	208	26	�	�	PROPN
ap-688	208	27	�	�	PROPN
ap-688	208	28	�	�	PROPN
ap-688	208	29	�	�	PROPN
ap-688	208	30	�	�	PROPN
ap-688	208	31	�	�	PROPN
ap-688	208	32	�	�	PROPN
ap-688	208	33	�	�	PROPN
ap-688	208	34	�	�	PROPN
ap-688	208	35	�	�	PROPN
ap-688	208	36	log	log	PROPN
ap-688	208	37	log1	log1	NOUN
ap-688	208	38	.	.	PUNCT
ap-688	209	1	(	(	PUNCT
ap-688	209	2	7	7	X
ap-688	209	3	)	)	PUNCT
ap-688	209	4	6	6	NUM
ap-688	209	5	implementation	implementation	NOUN
ap-688	209	6	the	the	DET
ap-688	209	7	proposed	propose	VERB
ap-688	209	8	multiplier	multipli	ADJ
ap-688	209	9	/	/	SYM
ap-688	209	10	inverter	inverter	NOUN
ap-688	209	11	has	have	AUX
ap-688	209	12	been	be	AUX
ap-688	209	13	implemented	implement	VERB
ap-688	209	14	in	in	ADP
ap-688	209	15	the	the	DET
ap-688	209	16	xilinx	xilinx	PROPN
ap-688	209	17	virtex300	virtex300	PROPN
ap-688	209	18	fpga	fpga	PROPN
ap-688	209	19	using	use	VERB
ap-688	209	20	the	the	DET
ap-688	209	21	synopsys	synopsys	PROPN
ap-688	209	22	fpga	fpga	PROPN
ap-688	209	23	express	express	ADJ
ap-688	209	24	synthesis	synthesis	NOUN
ap-688	209	25	tool	tool	NOUN
ap-688	209	26	and	and	CCONJ
ap-688	209	27	the	the	DET
ap-688	209	28	foundation	foundation	NOUN
ap-688	209	29	3.3i	3.3i	NUM
ap-688	209	30	implementation	implementation	NOUN
ap-688	209	31	tool	tool	NOUN
ap-688	209	32	.	.	PUNCT
ap-688	210	1	the	the	DET
ap-688	210	2	functionality	functionality	NOUN
ap-688	210	3	has	have	AUX
ap-688	210	4	been	be	AUX
ap-688	210	5	verified	verify	VERB
ap-688	210	6	in	in	ADP
ap-688	210	7	the	the	DET
ap-688	210	8	modelsim	modelsim	NOUN
ap-688	210	9	simulator	simulator	NOUN
ap-688	210	10	.	.	PUNCT
ap-688	211	1	note	note	VERB
ap-688	211	2	that	that	PRON
ap-688	211	3	point	point	VERB
ap-688	211	4	addition	addition	NOUN
ap-688	211	5	and	and	CCONJ
ap-688	211	6	doubling	doubling	NOUN
ap-688	211	7	are	be	AUX
ap-688	211	8	completely	completely	ADV
ap-688	211	9	oblivious	oblivious	ADJ
ap-688	211	10	,	,	PUNCT
ap-688	211	11	i.e.	i.e.	X
ap-688	211	12	the	the	DET
ap-688	211	13	sequence	sequence	NOUN
ap-688	211	14	of	of	ADP
ap-688	211	15	steps	step	NOUN
ap-688	211	16	depends	depend	VERB
ap-688	211	17	on	on	ADP
ap-688	211	18	m	m	ADJ
ap-688	211	19	only	only	ADV
ap-688	211	20	,	,	PUNCT
ap-688	211	21	not	not	PART
ap-688	211	22	on	on	ADP
ap-688	211	23	the	the	DET
ap-688	211	24	processed	process	VERB
ap-688	211	25	data	datum	NOUN
ap-688	211	26	.	.	PUNCT
ap-688	212	1	therefore	therefore	ADV
ap-688	212	2	the	the	DET
ap-688	212	3	simulation	simulation	NOUN
ap-688	212	4	was	be	AUX
ap-688	212	5	also	also	ADV
ap-688	212	6	able	able	ADJ
ap-688	212	7	to	to	PART
ap-688	212	8	show	show	VERB
ap-688	212	9	that	that	SCONJ
ap-688	212	10	the	the	DET
ap-688	212	11	numbers	number	NOUN
ap-688	212	12	of	of	ADP
ap-688	212	13	clock	clock	NOUN
ap-688	212	14	cycles	cycle	NOUN
ap-688	212	15	used	use	VERB
ap-688	212	16	in	in	ADP
ap-688	212	17	equations	equation	NOUN
ap-688	212	18	3	3	NUM
ap-688	212	19	,	,	PUNCT
ap-688	212	20	4	4	NUM
ap-688	212	21	,	,	PUNCT
ap-688	212	22	and	and	CCONJ
ap-688	212	23	7	7	NUM
ap-688	212	24	were	be	AUX
ap-688	212	25	correct	correct	ADJ
ap-688	212	26	.	.	PUNCT
ap-688	213	1	6.1	6.1	NUM
ap-688	213	2	digit	digit	NOUN
ap-688	213	3	-	-	PUNCT
ap-688	213	4	serial	serial	ADJ
ap-688	213	5	multiplier	multipli	ADJ
ap-688	213	6	/	/	SYM
ap-688	213	7	inverter	inverter	NOUN
ap-688	213	8	because	because	SCONJ
ap-688	213	9	of	of	ADP
ap-688	213	10	limited	limited	ADJ
ap-688	213	11	space	space	NOUN
ap-688	213	12	,	,	PUNCT
ap-688	213	13	table	table	NOUN
ap-688	213	14	1	1	NUM
ap-688	213	15	presents	present	NOUN
ap-688	213	16	results	result	NOUN
ap-688	213	17	for	for	ADP
ap-688	213	18	m	m	PROPN
ap-688	213	19	�	�	PROPN
ap-688	213	20	180	180	NUM
ap-688	213	21	and	and	CCONJ
ap-688	213	22	for	for	ADP
ap-688	213	23	several	several	ADJ
ap-688	213	24	digit	digit	NOUN
ap-688	213	25	widths	width	NOUN
ap-688	213	26	d	d	X
ap-688	213	27	only	only	ADV
ap-688	213	28	.	.	PUNCT
ap-688	214	1	no	no	DET
ap-688	214	2	additional	additional	ADJ
ap-688	214	3	blocks	block	NOUN
ap-688	214	4	performing	perform	VERB
ap-688	214	5	“	"	PUNCT
ap-688	214	6	long	long	ADJ
ap-688	214	7	distance	distance	NOUN
ap-688	214	8	”	"	PUNCT
ap-688	214	9	rotations	rotation	NOUN
ap-688	214	10	have	have	AUX
ap-688	214	11	been	be	AUX
ap-688	214	12	used	use	VERB
ap-688	214	13	in	in	ADP
ap-688	214	14	these	these	DET
ap-688	214	15	cases	case	NOUN
ap-688	214	16	.	.	PUNCT
ap-688	215	1	as	as	SCONJ
ap-688	215	2	expected	expect	VERB
ap-688	215	3	,	,	PUNCT
ap-688	215	4	the	the	DET
ap-688	215	5	area	area	NOUN
ap-688	215	6	of	of	ADP
ap-688	215	7	the	the	DET
ap-688	215	8	multiplier	multipli	ADJ
ap-688	215	9	/	/	SYM
ap-688	215	10	inverter	inverter	NOUN
ap-688	215	11	grows	grow	VERB
ap-688	215	12	with	with	ADP
ap-688	215	13	growing	grow	VERB
ap-688	215	14	d	d	NOUN
ap-688	215	15	,	,	PUNCT
ap-688	215	16	and	and	CCONJ
ap-688	215	17	can	can	AUX
ap-688	215	18	be	be	AUX
ap-688	215	19	expressed	express	VERB
ap-688	215	20	as	as	ADP
ap-688	215	21	approx	approx	PROPN
ap-688	215	22	.	.	PUNCT
ap-688	216	1	(	(	PUNCT
ap-688	216	2	2	2	NUM
ap-688	216	3	�	�	PROPN
ap-688	216	4	0.5	0.5	NUM
ap-688	216	5	d)×	d)×	NOUN
ap-688	216	6	m	m	NOUN
ap-688	216	7	slices	slice	NOUN
ap-688	216	8	or	or	CCONJ
ap-688	216	9	(	(	PUNCT
ap-688	216	10	2	2	NUM
ap-688	216	11	�	�	PROPN
ap-688	216	12	0.5	0.5	NUM
ap-688	216	13	d	d	NOUN
ap-688	216	14	)	)	PUNCT
ap-688	216	15	slices	slice	NOUN
ap-688	216	16	per	per	ADP
ap-688	216	17	1	1	NUM
ap-688	216	18	bit	bit	NOUN
ap-688	216	19	.	.	PUNCT
ap-688	217	1	the	the	DET
ap-688	217	2	computation	computation	NOUN
ap-688	217	3	time	time	NOUN
ap-688	217	4	does	do	AUX
ap-688	217	5	not	not	PART
ap-688	217	6	depend	depend	VERB
ap-688	217	7	on	on	ADP
ap-688	217	8	the	the	DET
ap-688	217	9	digit	digit	NOUN
ap-688	217	10	width	width	ADJ
ap-688	217	11	d	d	NOUN
ap-688	217	12	in	in	ADP
ap-688	217	13	such	such	DET
ap-688	217	14	a	a	DET
ap-688	217	15	straightforward	straightforward	ADJ
ap-688	217	16	manner	manner	NOUN
ap-688	217	17	.	.	PUNCT
ap-688	218	1	the	the	DET
ap-688	218	2	results	result	NOUN
ap-688	218	3	in	in	ADP
ap-688	218	4	the	the	DET
ap-688	218	5	last	last	ADJ
ap-688	218	6	column	column	NOUN
ap-688	218	7	of	of	ADP
ap-688	218	8	table	table	NOUN
ap-688	218	9	1	1	NUM
ap-688	218	10	and	and	CCONJ
ap-688	218	11	in	in	ADP
ap-688	218	12	fig	fig	NOUN
ap-688	218	13	.	.	PUNCT
ap-688	219	1	5	5	NUM
ap-688	219	2	correspond	correspond	NOUN
ap-688	219	3	to	to	ADP
ap-688	219	4	eq	eq	NOUN
ap-688	219	5	.	.	PROPN
ap-688	219	6	4	4	X
ap-688	219	7	.	.	PUNCT
ap-688	220	1	the	the	DET
ap-688	220	2	minimum	minimum	ADJ
ap-688	220	3	time	time	NOUN
ap-688	220	4	is	be	AUX
ap-688	220	5	obtained	obtain	VERB
ap-688	220	6	for	for	ADP
ap-688	220	7	d	d	PROPN
ap-688	220	8	�	�	PROPN
ap-688	220	9	6	6	NUM
ap-688	220	10	.	.	PUNCT
ap-688	221	1	the	the	DET
ap-688	221	2	other	other	ADJ
ap-688	221	3	local	local	ADJ
ap-688	221	4	minima	minima	NOUN
ap-688	221	5	are	be	AUX
ap-688	221	6	caused	cause	VERB
ap-688	221	7	by	by	ADP
ap-688	221	8	the	the	DET
ap-688	221	9	granularity	granularity	NOUN
ap-688	221	10	of	of	ADP
ap-688	221	11	the	the	DET
ap-688	221	12	fpga	fpga	PROPN
ap-688	221	13	.	.	PUNCT
ap-688	222	1	whenever	whenever	SCONJ
ap-688	222	2	the	the	DET
ap-688	222	3	capacity	capacity	NOUN
ap-688	222	4	of	of	ADP
ap-688	222	5	a	a	DET
ap-688	222	6	look	look	VERB
ap-688	222	7	-	-	PUNCT
ap-688	222	8	up	up	ADP
ap-688	222	9	table	table	NOUN
ap-688	222	10	is	be	AUX
ap-688	222	11	exhausted	exhaust	VERB
ap-688	222	12	,	,	PUNCT
ap-688	222	13	the	the	DET
ap-688	222	14	length	length	NOUN
ap-688	222	15	of	of	ADP
ap-688	222	16	the	the	DET
ap-688	222	17	critical	critical	ADJ
ap-688	222	18	path	path	NOUN
ap-688	222	19	increases	increase	NOUN
ap-688	222	20	.	.	PUNCT
ap-688	223	1	6.2	6.2	NUM
ap-688	223	2	improving	improve	VERB
ap-688	223	3	the	the	DET
ap-688	223	4	iterative	iterative	NOUN
ap-688	223	5	squarings	squaring	NOUN
ap-688	223	6	the	the	DET
ap-688	223	7	optimizer	optimizer	NOUN
ap-688	223	8	was	be	AUX
ap-688	223	9	implemented	implement	VERB
ap-688	223	10	using	use	VERB
ap-688	223	11	the	the	DET
ap-688	223	12	galib	galib	PROPN
ap-688	223	13	c	c	PROPN
ap-688	223	14	�	�	PROPN
ap-688	223	15	�	�	PROPN
ap-688	223	16	library	library	NOUN
ap-688	223	17	[	[	X
ap-688	223	18	8	8	NUM
ap-688	223	19	]	]	PUNCT
ap-688	223	20	.	.	PUNCT
ap-688	224	1	a	a	DET
ap-688	224	2	number	number	NOUN
ap-688	224	3	of	of	ADP
ap-688	224	4	experiments	experiment	NOUN
ap-688	224	5	have	have	AUX
ap-688	224	6	been	be	AUX
ap-688	224	7	performed	perform	VERB
ap-688	224	8	,	,	PUNCT
ap-688	224	9	with	with	ADP
ap-688	224	10	m	m	PROPN
ap-688	224	11	in	in	ADP
ap-688	224	12	the	the	DET
ap-688	224	13	range	range	NOUN
ap-688	224	14	interesting	interesting	ADJ
ap-688	224	15	for	for	ADP
ap-688	224	16	elliptic	elliptic	ADJ
ap-688	224	17	curve	curve	NOUN
ap-688	224	18	cryptography	cryptography	NOUN
ap-688	224	19	,	,	PUNCT
ap-688	224	20	that	that	ADV
ap-688	224	21	is	is	ADV
ap-688	224	22	,	,	PUNCT
ap-688	224	23	from	from	ADP
ap-688	224	24	160	160	NUM
ap-688	224	25	to	to	ADP
ap-688	224	26	250	250	NUM
ap-688	224	27	.	.	PUNCT
ap-688	225	1	the	the	DET
ap-688	225	2	following	follow	VERB
ap-688	225	3	facts	fact	NOUN
ap-688	225	4	were	be	AUX
ap-688	225	5	observed	observe	VERB
ap-688	225	6	:	:	PUNCT
ap-688	225	7	�	�	PROPN
ap-688	225	8	where	where	SCONJ
ap-688	225	9	a	a	DET
ap-688	225	10	brute	brute	ADJ
ap-688	225	11	force	force	NOUN
ap-688	225	12	optimum	optimum	ADJ
ap-688	225	13	solution	solution	NOUN
ap-688	225	14	was	be	AUX
ap-688	225	15	available	available	ADJ
ap-688	225	16	,	,	PUNCT
ap-688	225	17	the	the	DET
ap-688	225	18	algorithm	algorithm	NOUN
ap-688	225	19	gave	give	VERB
ap-688	225	20	an	an	DET
ap-688	225	21	identical	identical	ADJ
ap-688	225	22	answer	answer	NOUN
ap-688	225	23	.	.	PUNCT
ap-688	226	1	©	©	PROPN
ap-688	226	2	czech	czech	PROPN
ap-688	226	3	technical	technical	PROPN
ap-688	226	4	university	university	PROPN
ap-688	226	5	publishing	publishing	NOUN
ap-688	226	6	house	house	NOUN
ap-688	226	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	226	8	59	59	NUM
ap-688	226	9	czech	czech	PROPN
ap-688	226	10	technical	technical	PROPN
ap-688	226	11	university	university	PROPN
ap-688	226	12	in	in	ADP
ap-688	226	13	prague	prague	PROPN
ap-688	226	14	acta	acta	PROPN
ap-688	226	15	polytechnica	polytechnica	PROPN
ap-688	226	16	vol	vol	NOUN
ap-688	226	17	.	.	PROPN
ap-688	227	1	45	45	NUM
ap-688	227	2	no	no	NOUN
ap-688	227	3	.	.	PUNCT
ap-688	228	1	2/2005	2/2005	NUM
ap-688	228	2	d	d	NOUN
ap-688	228	3	freq	freq	NOUN
ap-688	228	4	(	(	PUNCT
ap-688	228	5	mhz	mhz	NOUN
ap-688	228	6	)	)	PUNCT
ap-688	228	7	#	#	SYM
ap-688	228	8	slices	slice	NOUN
ap-688	228	9	#	#	NOUN
ap-688	228	10	slices	slice	NOUN
ap-688	228	11	per	per	ADP
ap-688	228	12	1	1	NUM
ap-688	228	13	bit	bit	NOUN
ap-688	228	14	point	point	NOUN
ap-688	228	15	addition	addition	NOUN
ap-688	228	16	(	(	PUNCT
ap-688	228	17	clocks	clock	NOUN
ap-688	228	18	)	)	PUNCT
ap-688	228	19	(	(	PUNCT
ap-688	228	20	�	�	NOUN
ap-688	228	21	s	s	PART
ap-688	228	22	)	)	PUNCT
ap-688	228	23	1	1	NUM
ap-688	228	24	122.489	122.489	NUM
ap-688	228	25	451	451	NUM
ap-688	228	26	2.51	2.51	NUM
ap-688	228	27	2582	2582	NUM
ap-688	228	28	21.08	21.08	NUM
ap-688	228	29	2	2	NUM
ap-688	228	30	102.533	102.533	NUM
ap-688	228	31	544	544	NUM
ap-688	228	32	3.02	3.02	NUM
ap-688	228	33	1412	1412	NUM
ap-688	228	34	13.77	13.77	NUM
ap-688	228	35	3	3	NUM
ap-688	228	36	101.502	101.502	NUM
ap-688	228	37	632	632	NUM
ap-688	228	38	3.51	3.51	NUM
ap-688	228	39	1022	1022	NUM
ap-688	228	40	10.07	10.07	NUM
ap-688	228	41	4	4	NUM
ap-688	228	42	100.492	100.492	NUM
ap-688	228	43	724	724	NUM
ap-688	228	44	4.02	4.02	NUM
ap-688	228	45	827	827	NUM
ap-688	228	46	8.23	8.23	NUM
ap-688	228	47	5	5	NUM
ap-688	228	48	97.069	97.069	NUM
ap-688	228	49	815	815	NUM
ap-688	228	50	4.53	4.53	NUM
ap-688	228	51	710	710	NUM
ap-688	228	52	7.31	7.31	NUM
ap-688	228	53	6	6	NUM
ap-688	228	54	94.153	94.153	NUM
ap-688	228	55	903	903	NUM
ap-688	228	56	5.02	5.02	NUM
ap-688	228	57	632	632	NUM
ap-688	228	58	6.71	6.71	NUM
ap-688	228	59	9	9	NUM
ap-688	228	60	64.008	64.008	NUM
ap-688	228	61	1174	1174	NUM
ap-688	228	62	6.52	6.52	NUM
ap-688	228	63	502	502	NUM
ap-688	228	64	7.84	7.84	NUM
ap-688	228	65	10	10	NUM
ap-688	228	66	61.054	61.054	NUM
ap-688	228	67	1265	1265	NUM
ap-688	228	68	7.03	7.03	NUM
ap-688	228	69	476	476	NUM
ap-688	228	70	7.80	7.80	NUM
ap-688	228	71	12	12	NUM
ap-688	228	72	54.174	54.174	NUM
ap-688	228	73	1480	1480	NUM
ap-688	228	74	8.22	8.22	NUM
ap-688	228	75	437	437	NUM
ap-688	228	76	8.07	8.07	NUM
ap-688	228	77	15	15	NUM
ap-688	228	78	58.042	58.042	NUM
ap-688	228	79	1798	1798	NUM
ap-688	228	80	9.99	9.99	NUM
ap-688	228	81	398	398	NUM
ap-688	228	82	6.86	6.86	NUM
ap-688	228	83	18	18	NUM
ap-688	228	84	44.607	44.607	NUM
ap-688	228	85	2026	2026	NUM
ap-688	228	86	11.26	11.26	NUM
ap-688	228	87	372	372	NUM
ap-688	228	88	8.34	8.34	NUM
ap-688	228	89	20	20	NUM
ap-688	228	90	40.955	40.955	NUM
ap-688	228	91	2248	2248	NUM
ap-688	228	92	12.49	12.49	NUM
ap-688	228	93	359	359	NUM
ap-688	228	94	8.77	8.77	NUM
ap-688	228	95	table	table	NOUN
ap-688	228	96	1	1	NUM
ap-688	228	97	:	:	PUNCT
ap-688	228	98	implementation	implementation	NOUN
ap-688	228	99	of	of	ADP
ap-688	228	100	a	a	DET
ap-688	228	101	modified	modify	VERB
ap-688	228	102	multiplier	multipli	ADJ
ap-688	228	103	/	/	SYM
ap-688	228	104	inverter	inverter	NOUN
ap-688	228	105	in	in	ADP
ap-688	228	106	xilinx	xilinx	PROPN
ap-688	228	107	virtex300	virtex300	PROPN
ap-688	228	108	�	�	PROPN
ap-688	228	109	any	any	DET
ap-688	228	110	realized	realize	VERB
ap-688	228	111	rotation	rotation	NOUN
ap-688	228	112	si	si	X
ap-688	228	113	in	in	ADP
ap-688	228	114	an	an	DET
ap-688	228	115	optimum	optimum	ADJ
ap-688	228	116	solution	solution	NOUN
ap-688	228	117	was	be	AUX
ap-688	228	118	identical	identical	ADJ
ap-688	228	119	to	to	ADP
ap-688	228	120	some	some	DET
ap-688	228	121	given	give	VERB
ap-688	228	122	rotation	rotation	NOUN
ap-688	228	123	ki	ki	PROPN
ap-688	228	124	,	,	PUNCT
ap-688	228	125	although	although	SCONJ
ap-688	228	126	even	even	ADV
ap-688	228	127	slightly	slightly	ADV
ap-688	228	128	sub	sub	ADJ
ap-688	228	129	-	-	ADJ
ap-688	228	130	optimum	optimum	ADJ
ap-688	228	131	solutions	solution	NOUN
ap-688	228	132	did	do	AUX
ap-688	228	133	not	not	PART
ap-688	228	134	have	have	VERB
ap-688	228	135	this	this	DET
ap-688	228	136	property	property	NOUN
ap-688	228	137	.	.	PUNCT
ap-688	229	1	�	�	PROPN
ap-688	229	2	the	the	DET
ap-688	229	3	left	left	ADJ
ap-688	229	4	side	side	NOUN
ap-688	229	5	of	of	ADP
ap-688	229	6	equation	equation	NOUN
ap-688	229	7	6	6	NUM
ap-688	229	8	was	be	AUX
ap-688	229	9	less	less	ADJ
ap-688	229	10	than	than	ADP
ap-688	229	11	m	m	VERB
ap-688	229	12	in	in	ADP
ap-688	229	13	all	all	ADV
ap-688	229	14	optimum	optimum	ADJ
ap-688	229	15	and	and	CCONJ
ap-688	229	16	some	some	DET
ap-688	229	17	sub	sub	ADJ
ap-688	229	18	-	-	ADJ
ap-688	229	19	optimum	optimum	ADJ
ap-688	229	20	solutions	solution	NOUN
ap-688	229	21	.	.	PUNCT
ap-688	230	1	�	�	PROPN
ap-688	230	2	when	when	SCONJ
ap-688	230	3	the	the	DET
ap-688	230	4	above	above	ADJ
ap-688	230	5	observation	observation	NOUN
ap-688	230	6	was	be	AUX
ap-688	230	7	exploited	exploit	VERB
ap-688	230	8	to	to	PART
ap-688	230	9	simplify	simplify	VERB
ap-688	230	10	the	the	DET
ap-688	230	11	evaluation	evaluation	NOUN
ap-688	230	12	procedure	procedure	NOUN
ap-688	230	13	,	,	PUNCT
ap-688	230	14	the	the	DET
ap-688	230	15	search	search	NOUN
ap-688	230	16	space	space	NOUN
ap-688	230	17	became	become	VERB
ap-688	230	18	disconnected	disconnected	ADJ
ap-688	230	19	,	,	PUNCT
ap-688	230	20	and	and	CCONJ
ap-688	230	21	more	more	ADJ
ap-688	230	22	time	time	NOUN
ap-688	230	23	was	be	AUX
ap-688	230	24	needed	need	VERB
ap-688	230	25	to	to	PART
ap-688	230	26	achieve	achieve	VERB
ap-688	230	27	equivalent	equivalent	ADJ
ap-688	230	28	results	result	NOUN
ap-688	230	29	.	.	PUNCT
ap-688	231	1	�	�	NOUN
ap-688	231	2	neither	neither	CCONJ
ap-688	231	3	brute	brute	ADJ
ap-688	231	4	force	force	NOUN
ap-688	231	5	nor	nor	CCONJ
ap-688	231	6	the	the	DET
ap-688	231	7	described	describe	VERB
ap-688	231	8	algorithm	algorithm	NOUN
ap-688	231	9	gave	give	VERB
ap-688	231	10	any	any	DET
ap-688	231	11	optimum	optimum	ADJ
ap-688	231	12	or	or	CCONJ
ap-688	231	13	sub	sub	ADJ
ap-688	231	14	-	-	ADJ
ap-688	231	15	optimum	optimum	ADJ
ap-688	231	16	solution	solution	NOUN
ap-688	231	17	violating	violate	VERB
ap-688	231	18	the	the	DET
ap-688	231	19	tentative	tentative	ADJ
ap-688	231	20	assumption	assumption	NOUN
ap-688	231	21	in	in	ADP
ap-688	231	22	subsection	subsection	NOUN
ap-688	231	23	5.2	5.2	NUM
ap-688	231	24	.	.	PUNCT
ap-688	232	1	�	�	PROPN
ap-688	232	2	with	with	ADP
ap-688	232	3	a	a	DET
ap-688	232	4	population	population	NOUN
ap-688	232	5	size	size	NOUN
ap-688	232	6	of	of	ADP
ap-688	232	7	100	100	NUM
ap-688	232	8	,	,	PUNCT
ap-688	232	9	the	the	DET
ap-688	232	10	algorithm	algorithm	NOUN
ap-688	232	11	required	require	VERB
ap-688	232	12	circa	circa	NOUN
ap-688	232	13	3000	3000	NUM
ap-688	232	14	generations	generation	NOUN
ap-688	232	15	to	to	PART
ap-688	232	16	converge	converge	VERB
ap-688	232	17	at	at	ADP
ap-688	232	18	m	m	PROPN
ap-688	232	19	�	�	PROPN
ap-688	232	20	160	160	NUM
ap-688	232	21	,	,	PUNCT
ap-688	232	22	rising	rise	VERB
ap-688	232	23	to	to	ADP
ap-688	232	24	4000	4000	NUM
ap-688	232	25	at	at	ADP
ap-688	232	26	m	m	PROPN
ap-688	232	27	�	�	PROPN
ap-688	232	28	250	250	NUM
ap-688	232	29	.	.	PUNCT
ap-688	233	1	�	�	PROPN
ap-688	233	2	infeasible	infeasible	ADJ
ap-688	233	3	individuals	individual	NOUN
ap-688	233	4	were	be	AUX
ap-688	233	5	rare	rare	ADJ
ap-688	233	6	.	.	PUNCT
ap-688	234	1	�	�	PROPN
ap-688	235	1	the	the	DET
ap-688	235	2	running	running	ADJ
ap-688	235	3	time	time	NOUN
ap-688	235	4	was	be	AUX
ap-688	235	5	below	below	ADP
ap-688	235	6	20	20	NUM
ap-688	235	7	minutes	minute	NOUN
ap-688	235	8	on	on	ADP
ap-688	235	9	an	an	DET
ap-688	235	10	office	office	NOUN
ap-688	235	11	-	-	PUNCT
ap-688	235	12	grade	grade	NOUN
ap-688	235	13	pc	pc	NOUN
ap-688	235	14	.	.	PUNCT
ap-688	236	1	table	table	NOUN
ap-688	236	2	2	2	NUM
ap-688	236	3	illustrates	illustrate	VERB
ap-688	236	4	the	the	DET
ap-688	236	5	influence	influence	NOUN
ap-688	236	6	of	of	ADP
ap-688	236	7	the	the	DET
ap-688	236	8	multiplier	multipli	ADJ
ap-688	236	9	size	size	NOUN
ap-688	236	10	on	on	ADP
ap-688	236	11	the	the	DET
ap-688	236	12	shifter	shifter	NOUN
ap-688	236	13	.	.	PUNCT
ap-688	237	1	the	the	DET
ap-688	237	2	results	result	NOUN
ap-688	237	3	were	be	AUX
ap-688	237	4	obtained	obtain	VERB
ap-688	237	5	for	for	ADP
ap-688	237	6	m	m	PROPN
ap-688	237	7	�	�	PROPN
ap-688	237	8	163	163	NUM
ap-688	237	9	,	,	PUNCT
ap-688	237	10	where	where	SCONJ
ap-688	237	11	the	the	DET
ap-688	237	12	required	require	VERB
ap-688	237	13	set	set	NOUN
ap-688	237	14	of	of	ADP
ap-688	237	15	rotations	rotation	NOUN
ap-688	237	16	is	be	AUX
ap-688	237	17	{	{	PUNCT
ap-688	237	18	1	1	NUM
ap-688	237	19	,	,	PUNCT
ap-688	237	20	2	2	NUM
ap-688	237	21	,	,	PUNCT
ap-688	237	22	5	5	NUM
ap-688	237	23	,	,	PUNCT
ap-688	237	24	10	10	NUM
ap-688	237	25	,	,	PUNCT
ap-688	237	26	20	20	NUM
ap-688	237	27	,	,	PUNCT
ap-688	237	28	40	40	NUM
ap-688	237	29	,	,	PUNCT
ap-688	237	30	81	81	NUM
ap-688	237	31	}	}	PUNCT
ap-688	237	32	.	.	PUNCT
ap-688	238	1	the	the	DET
ap-688	238	2	area	area	NOUN
ap-688	238	3	of	of	ADP
ap-688	238	4	the	the	DET
ap-688	238	5	multiplier	multipli	ADJ
ap-688	238	6	was	be	AUX
ap-688	238	7	amux(n	amux(n	NOUN
ap-688	238	8	)	)	PUNCT
ap-688	238	9	�	�	PROPN
ap-688	238	10	1.5	1.5	NUM
ap-688	238	11	n	n	NOUN
ap-688	238	12	and	and	CCONJ
ap-688	238	13	the	the	DET
ap-688	238	14	critical	critical	ADJ
ap-688	238	15	path	path	NOUN
ap-688	238	16	of	of	ADP
ap-688	238	17	the	the	DET
ap-688	238	18	unit	unit	NOUN
ap-688	238	19	was	be	AUX
ap-688	238	20	outside	outside	ADP
ap-688	238	21	the	the	DET
ap-688	238	22	shifter	shifter	NOUN
ap-688	238	23	.	.	PUNCT
ap-688	239	1	the	the	DET
ap-688	239	2	effect	effect	NOUN
ap-688	239	3	of	of	ADP
ap-688	239	4	adding	add	VERB
ap-688	239	5	one	one	NUM
ap-688	239	6	rotation	rotation	NOUN
ap-688	239	7	block	block	NOUN
ap-688	239	8	(	(	PUNCT
ap-688	239	9	i.e.	i.e.	X
ap-688	239	10	k	k	X
ap-688	239	11	�	�	PROPN
ap-688	239	12	2	2	NUM
ap-688	239	13	)	)	PUNCT
ap-688	239	14	is	be	AUX
ap-688	239	15	illustrated	illustrate	VERB
ap-688	239	16	in	in	ADP
ap-688	239	17	fig	fig	NOUN
ap-688	239	18	.	.	PUNCT
ap-688	240	1	5	5	X
ap-688	240	2	.	.	X
ap-688	240	3	the	the	DET
ap-688	240	4	expansion	expansion	NOUN
ap-688	240	5	of	of	ADP
ap-688	240	6	multiplexers	multiplexer	NOUN
ap-688	240	7	did	do	AUX
ap-688	240	8	not	not	PART
ap-688	240	9	influence	influence	VERB
ap-688	240	10	the	the	DET
ap-688	240	11	clock	clock	NOUN
ap-688	240	12	period	period	NOUN
ap-688	240	13	,	,	PUNCT
ap-688	240	14	as	as	SCONJ
ap-688	240	15	they	they	PRON
ap-688	240	16	did	do	AUX
ap-688	240	17	not	not	PART
ap-688	240	18	lie	lie	VERB
ap-688	240	19	on	on	ADP
ap-688	240	20	the	the	DET
ap-688	240	21	critical	critical	ADJ
ap-688	240	22	path	path	NOUN
ap-688	240	23	.	.	PUNCT
ap-688	241	1	the	the	DET
ap-688	241	2	new	new	ADJ
ap-688	241	3	design	design	NOUN
ap-688	241	4	is	be	AUX
ap-688	241	5	systematically	systematically	ADV
ap-688	241	6	faster	fast	ADJ
ap-688	241	7	.	.	PUNCT
ap-688	242	1	for	for	ADP
ap-688	242	2	d	d	PROPN
ap-688	242	3	�	�	PROPN
ap-688	242	4	6	6	NUM
ap-688	242	5	,	,	PUNCT
ap-688	242	6	the	the	DET
ap-688	242	7	speedup	speedup	NOUN
ap-688	242	8	is	be	AUX
ap-688	242	9	over	over	ADP
ap-688	242	10	20	20	NUM
ap-688	242	11	%	%	NOUN
ap-688	242	12	,	,	PUNCT
ap-688	242	13	while	while	SCONJ
ap-688	242	14	the	the	DET
ap-688	242	15	area	area	NOUN
ap-688	242	16	increased	increase	VERB
ap-688	242	17	by	by	ADP
ap-688	242	18	10	10	NUM
ap-688	242	19	%	%	NOUN
ap-688	242	20	.	.	PUNCT
ap-688	243	1	recall	recall	VERB
ap-688	243	2	that	that	SCONJ
ap-688	243	3	the	the	DET
ap-688	243	4	speedup	speedup	NOUN
ap-688	243	5	is	be	AUX
ap-688	243	6	based	base	VERB
ap-688	243	7	on	on	ADP
ap-688	243	8	minimization	minimization	NOUN
ap-688	243	9	of	of	ADP
ap-688	243	10	the	the	DET
ap-688	243	11	last	last	ADJ
ap-688	243	12	term	term	NOUN
ap-688	243	13	in	in	ADP
ap-688	243	14	eq	eq	ADP
ap-688	243	15	.	.	PROPN
ap-688	244	1	7	7	X
ap-688	244	2	.	.	X
ap-688	244	3	in	in	ADP
ap-688	244	4	our	our	PRON
ap-688	244	5	case	case	NOUN
ap-688	244	6	,	,	PUNCT
ap-688	244	7	this	this	DET
ap-688	244	8	mechanism	mechanism	NOUN
ap-688	244	9	caused	cause	VERB
ap-688	244	10	the	the	DET
ap-688	244	11	second	second	ADJ
ap-688	244	12	local	local	ADJ
ap-688	244	13	minimum	minimum	NOUN
ap-688	244	14	on	on	ADP
ap-688	244	15	the	the	DET
ap-688	244	16	original	original	ADJ
ap-688	244	17	curve	curve	NOUN
ap-688	244	18	to	to	PART
ap-688	244	19	prevail	prevail	VERB
ap-688	244	20	,	,	PUNCT
ap-688	244	21	where	where	SCONJ
ap-688	244	22	the	the	DET
ap-688	244	23	optimum	optimum	ADJ
ap-688	244	24	digit	digit	NOUN
ap-688	244	25	width	width	NOUN
ap-688	244	26	is	be	AUX
ap-688	244	27	d	d	PROPN
ap-688	244	28	�	�	PROPN
ap-688	244	29	15	15	NUM
ap-688	244	30	for	for	ADP
ap-688	244	31	m	m	PROPN
ap-688	244	32	�	�	PROPN
ap-688	244	33	180	180	NUM
ap-688	244	34	.	.	PUNCT
ap-688	245	1	in	in	ADP
ap-688	245	2	this	this	DET
ap-688	245	3	case	case	NOUN
ap-688	245	4	the	the	DET
ap-688	245	5	actual	actual	ADJ
ap-688	245	6	speedup	speedup	NOUN
ap-688	245	7	is	be	AUX
ap-688	245	8	37	37	NUM
ap-688	245	9	%	%	NOUN
ap-688	245	10	.	.	PUNCT
ap-688	246	1	7	7	NUM
ap-688	246	2	conclusions	conclusion	NOUN
ap-688	246	3	a	a	DET
ap-688	246	4	pipelined	pipelined	ADJ
ap-688	246	5	version	version	NOUN
ap-688	246	6	of	of	ADP
ap-688	246	7	the	the	DET
ap-688	246	8	massey	massey	NOUN
ap-688	246	9	-	-	PUNCT
ap-688	246	10	omura	omura	NOUN
ap-688	246	11	multiplier	multiplier	ADV
ap-688	246	12	modified	modify	VERB
ap-688	246	13	for	for	ADP
ap-688	246	14	easy	easy	ADJ
ap-688	246	15	implementation	implementation	NOUN
ap-688	246	16	of	of	ADP
ap-688	246	17	itt	itt	ADJ
ap-688	246	18	inversion	inversion	NOUN
ap-688	246	19	algorithm	algorithm	NOUN
ap-688	246	20	has	have	AUX
ap-688	246	21	been	be	AUX
ap-688	246	22	presented	present	VERB
ap-688	246	23	.	.	PUNCT
ap-688	247	1	the	the	DET
ap-688	247	2	performance	performance	NOUN
ap-688	247	3	of	of	ADP
ap-688	247	4	this	this	DET
ap-688	247	5	multiplier	multipli	ADJ
ap-688	247	6	/	/	SYM
ap-688	247	7	inverter	inverter	NOUN
ap-688	247	8	can	can	AUX
ap-688	247	9	be	be	AUX
ap-688	247	10	improved	improve	VERB
ap-688	247	11	by	by	ADP
ap-688	247	12	employing	employ	VERB
ap-688	247	13	digit	digit	NOUN
ap-688	247	14	-	-	PUNCT
ap-688	247	15	serialization	serialization	NOUN
ap-688	247	16	and	and	CCONJ
ap-688	247	17	by	by	ADP
ap-688	247	18	speeding	speed	VERB
ap-688	247	19	up	up	ADP
ap-688	247	20	the	the	DET
ap-688	247	21	iterative	iterative	NOUN
ap-688	247	22	squarings	squaring	NOUN
ap-688	247	23	.	.	PUNCT
ap-688	248	1	the	the	DET
ap-688	248	2	multiplier	multipli	ADJ
ap-688	248	3	/	/	SYM
ap-688	248	4	inverter	inverter	NOUN
ap-688	248	5	has	have	AUX
ap-688	248	6	been	be	AUX
ap-688	248	7	implemented	implement	VERB
ap-688	248	8	in	in	ADP
ap-688	248	9	xilinx	xilinx	PROPN
ap-688	248	10	virtex	virtex	PROPN
ap-688	248	11	300	300	NUM
ap-688	248	12	.	.	PUNCT
ap-688	249	1	without	without	ADP
ap-688	249	2	speeding	speed	VERB
ap-688	249	3	up	up	ADP
ap-688	249	4	the	the	DET
ap-688	249	5	iterative	iterative	NOUN
ap-688	249	6	squarings	squaring	NOUN
ap-688	249	7	,	,	PUNCT
ap-688	249	8	the	the	DET
ap-688	249	9	shortest	short	ADJ
ap-688	249	10	computation	computation	NOUN
ap-688	249	11	time	time	NOUN
ap-688	249	12	has	have	AUX
ap-688	249	13	been	be	AUX
ap-688	249	14	obtained	obtain	VERB
ap-688	249	15	for	for	ADP
ap-688	249	16	digit	digit	NOUN
ap-688	249	17	width	width	PROPN
ap-688	249	18	d	d	X
ap-688	249	19	�	�	PROPN
ap-688	249	20	6	6	NUM
ap-688	249	21	.	.	PUNCT
ap-688	250	1	the	the	DET
ap-688	250	2	use	use	NOUN
ap-688	250	3	of	of	ADP
ap-688	250	4	“	"	PUNCT
ap-688	250	5	long	long	ADJ
ap-688	250	6	distance	distance	NOUN
ap-688	250	7	”	"	PUNCT
ap-688	250	8	rotation	rotation	NOUN
ap-688	250	9	blocks	block	NOUN
ap-688	250	10	further	far	ADV
ap-688	250	11	speeded	speed	VERB
ap-688	250	12	up	up	ADP
ap-688	250	13	the	the	DET
ap-688	250	14	design	design	NOUN
ap-688	250	15	and	and	CCONJ
ap-688	250	16	benefited	benefit	VERB
ap-688	250	17	higher	high	ADJ
ap-688	250	18	digit	digit	NOUN
ap-688	250	19	widths	width	NOUN
ap-688	250	20	.	.	PUNCT
ap-688	251	1	references	reference	NOUN
ap-688	251	2	[	[	X
ap-688	251	3	1	1	NUM
ap-688	251	4	]	]	X
ap-688	251	5	agnew	agnew	PROPN
ap-688	251	6	,	,	PUNCT
ap-688	251	7	g.	g.	PROPN
ap-688	251	8	b.	b.	PROPN
ap-688	251	9	,	,	PUNCT
ap-688	251	10	mullin	mullin	PROPN
ap-688	251	11	,	,	PUNCT
ap-688	251	12	r.	r.	PROPN
ap-688	251	13	c.	c.	PROPN
ap-688	251	14	,	,	PUNCT
ap-688	251	15	onyszchuk	onyszchuk	PROPN
ap-688	251	16	,	,	PUNCT
ap-688	251	17	i.	i.	NOUN
ap-688	251	18	m.	m.	NOUN
ap-688	251	19	,	,	PUNCT
ap-688	251	20	vanstone	vanstone	NOUN
ap-688	251	21	,	,	PUNCT
ap-688	251	22	s.	s.	PROPN
ap-688	251	23	a.	a.	PROPN
ap-688	251	24	:	:	PUNCT
ap-688	251	25	“	"	PUNCT
ap-688	251	26	an	an	DET
ap-688	251	27	implementation	implementation	NOUN
ap-688	251	28	for	for	ADP
ap-688	251	29	a	a	DET
ap-688	251	30	fast	fast	ADJ
ap-688	251	31	public	public	ADJ
ap-688	251	32	-	-	PUNCT
ap-688	251	33	key	key	NOUN
ap-688	251	34	cryptosystem	cryptosystem	NOUN
ap-688	251	35	,	,	PUNCT
ap-688	251	36	”	"	PUNCT
ap-688	251	37	journal	journal	NOUN
ap-688	251	38	of	of	ADP
ap-688	251	39	cryptology	cryptology	NOUN
ap-688	251	40	,	,	PUNCT
ap-688	251	41	vol	vol	NOUN
ap-688	251	42	.	.	NOUN
ap-688	251	43	3	3	NUM
ap-688	251	44	(	(	PUNCT
ap-688	251	45	1999	1999	NUM
ap-688	251	46	)	)	PUNCT
ap-688	251	47	,	,	PUNCT
ap-688	252	1	p.	p.	NOUN
ap-688	252	2	63–79	63–79	NUM
ap-688	252	3	.	.	PUNCT
ap-688	253	1	[	[	X
ap-688	253	2	2	2	NUM
ap-688	253	3	]	]	PUNCT
ap-688	253	4	ieee	ieee	NOUN
ap-688	253	5	1363	1363	NUM
ap-688	253	6	.	.	PUNCT
ap-688	254	1	standard	standard	NOUN
ap-688	254	2	for	for	ADP
ap-688	254	3	public	public	ADJ
ap-688	254	4	-	-	PUNCT
ap-688	254	5	key	key	NOUN
ap-688	254	6	cryptography	cryptography	NOUN
ap-688	254	7	,	,	PUNCT
ap-688	254	8	ieee	ieee	NOUN
ap-688	254	9	2000	2000	NUM
ap-688	254	10	.	.	PUNCT
ap-688	255	1	[	[	X
ap-688	255	2	3	3	NUM
ap-688	255	3	]	]	X
ap-688	255	4	itoh	itoh	NOUN
ap-688	255	5	,	,	PUNCT
ap-688	255	6	t.	t.	PROPN
ap-688	255	7	,	,	PUNCT
ap-688	255	8	teechai	teechai	PROPN
ap-688	255	9	,	,	PUNCT
ap-688	255	10	o.	o.	INTJ
ap-688	255	11	,	,	PUNCT
ap-688	255	12	tsujii	tsujii	NOUN
ap-688	255	13	,	,	PUNCT
ap-688	255	14	s.	s.	PROPN
ap-688	255	15	:	:	PUNCT
ap-688	255	16	“	"	PUNCT
ap-688	255	17	a	a	DET
ap-688	255	18	fast	fast	ADJ
ap-688	255	19	algorithm	algorithm	NOUN
ap-688	255	20	for	for	ADP
ap-688	255	21	computing	compute	VERB
ap-688	255	22	multiplicative	multiplicative	ADJ
ap-688	255	23	inverses	inverse	NOUN
ap-688	255	24	in	in	ADP
ap-688	255	25	gf(2	gf(2	PROPN
ap-688	255	26	t	t	PROPN
ap-688	255	27	)	)	PUNCT
ap-688	255	28	using	use	VERB
ap-688	255	29	normal	normal	ADJ
ap-688	255	30	bases	basis	NOUN
ap-688	255	31	,	,	PUNCT
ap-688	255	32	”	"	PUNCT
ap-688	255	33	j.	j.	PROPN
ap-688	255	34	society	society	PROPN
ap-688	255	35	for	for	ADP
ap-688	255	36	electronic	electronic	ADJ
ap-688	255	37	communications	communication	NOUN
ap-688	255	38	(	(	PUNCT
ap-688	255	39	japan	japan	PROPN
ap-688	255	40	)	)	PUNCT
ap-688	255	41	,	,	PUNCT
ap-688	255	42	vol	vol	NOUN
ap-688	255	43	.	.	PROPN
ap-688	255	44	44	44	NUM
ap-688	255	45	(	(	PUNCT
ap-688	255	46	1986	1986	NUM
ap-688	255	47	)	)	PUNCT
ap-688	255	48	,	,	PUNCT
ap-688	255	49	p.	p.	NOUN
ap-688	255	50	31–36	31–36	NUM
ap-688	255	51	.	.	PUNCT
ap-688	256	1	[	[	X
ap-688	256	2	4	4	NUM
ap-688	256	3	]	]	PUNCT
ap-688	257	1	leong	leong	PROPN
ap-688	257	2	p.	p.	PROPN
ap-688	257	3	h.	h.	PROPN
ap-688	257	4	w.	w.	PROPN
ap-688	257	5	,	,	PUNCT
ap-688	257	6	leung	leung	PROPN
ap-688	257	7	,	,	PUNCT
ap-688	257	8	k.	k.	PROPN
ap-688	257	9	h.	h.	PROPN
ap-688	257	10	:	:	PUNCT
ap-688	257	11	“	"	PUNCT
ap-688	257	12	a	a	DET
ap-688	257	13	microcoded	microcode	VERB
ap-688	257	14	elliptic	elliptic	ADJ
ap-688	257	15	curve	curve	NOUN
ap-688	257	16	processor	processor	NOUN
ap-688	257	17	using	use	VERB
ap-688	257	18	fpga	fpga	PROPN
ap-688	257	19	technology	technology	NOUN
ap-688	257	20	,	,	PUNCT
ap-688	257	21	”	"	PUNCT
ap-688	257	22	ieee	ieee	NOUN
ap-688	257	23	transactions	transaction	NOUN
ap-688	257	24	on	on	ADP
ap-688	257	25	vlsi	vlsi	PROPN
ap-688	257	26	systems	system	NOUN
ap-688	257	27	,	,	PUNCT
ap-688	257	28	vol	vol	NOUN
ap-688	257	29	.	.	PROPN
ap-688	257	30	10	10	NUM
ap-688	257	31	,	,	PUNCT
ap-688	257	32	no	no	INTJ
ap-688	257	33	.	.	NOUN
ap-688	257	34	5	5	NUM
ap-688	257	35	,	,	PUNCT
ap-688	257	36	oct	oct	PROPN
ap-688	257	37	.	.	PROPN
ap-688	257	38	2002	2002	NUM
ap-688	257	39	,	,	PUNCT
ap-688	257	40	p.	p.	NOUN
ap-688	257	41	550–559	550–559	NUM
ap-688	257	42	.	.	PUNCT
ap-688	258	1	[	[	X
ap-688	258	2	5	5	NUM
ap-688	258	3	]	]	SYM
ap-688	258	4	savas	savas	PROPN
ap-688	258	5	,	,	PUNCT
ap-688	258	6	e.	e.	PROPN
ap-688	258	7	,	,	PUNCT
ap-688	258	8	koc	koc	PROPN
ap-688	258	9	,	,	PUNCT
ap-688	258	10	c.	c.	PROPN
ap-688	258	11	k.	k.	PROPN
ap-688	258	12	:	:	PUNCT
ap-688	258	13	“	"	PUNCT
ap-688	258	14	architectures	architecture	NOUN
ap-688	258	15	for	for	ADP
ap-688	258	16	unified	unified	ADJ
ap-688	258	17	field	field	NOUN
ap-688	258	18	inversion	inversion	NOUN
ap-688	258	19	with	with	ADP
ap-688	258	20	applications	application	NOUN
ap-688	258	21	“	"	PUNCT
ap-688	258	22	.	.	PUNCT
ap-688	259	1	in	in	ADP
ap-688	259	2	:	:	PUNCT
ap-688	259	3	elliptic	elliptic	ADJ
ap-688	259	4	curve	curve	NOUN
ap-688	259	5	cryptography	cryptography	NOUN
ap-688	259	6	.	.	PUNCT
ap-688	260	1	the	the	DET
ap-688	260	2	9th	9th	ADJ
ap-688	260	3	ieee	ieee	NOUN
ap-688	260	4	international	international	ADJ
ap-688	260	5	conference	conference	NOUN
ap-688	260	6	on	on	ADP
ap-688	260	7	electronics	electronic	NOUN
ap-688	260	8	,	,	PUNCT
ap-688	260	9	circuits	circuit	NOUN
ap-688	260	10	and	and	CCONJ
ap-688	260	11	systems	system	NOUN
ap-688	260	12	–	–	PUNCT
ap-688	260	13	icecs	icec	NOUN
ap-688	260	14	2002	2002	NUM
ap-688	260	15	,	,	PUNCT
ap-688	260	16	dubrovnik	dubrovnik	PROPN
ap-688	260	17	,	,	PUNCT
ap-688	260	18	croatia	croatia	PROPN
ap-688	260	19	,	,	PUNCT
ap-688	260	20	september	september	PROPN
ap-688	260	21	15–18	15–18	NUM
ap-688	260	22	,	,	PUNCT
ap-688	260	23	2002	2002	NUM
ap-688	260	24	,	,	PUNCT
ap-688	260	25	vol	vol	NOUN
ap-688	260	26	.	.	PROPN
ap-688	260	27	3	3	NUM
ap-688	260	28	,	,	PUNCT
ap-688	260	29	p.	p.	NOUN
ap-688	260	30	1155–1158	1155–1158	NUM
ap-688	260	31	.	.	PUNCT
ap-688	261	1	[	[	X
ap-688	261	2	6	6	NUM
ap-688	261	3	]	]	X
ap-688	261	4	massey	massey	PROPN
ap-688	261	5	,	,	PUNCT
ap-688	261	6	j.	j.	PROPN
ap-688	261	7	,	,	PUNCT
ap-688	261	8	omura	omura	PROPN
ap-688	261	9	,	,	PUNCT
ap-688	261	10	j.	j.	PROPN
ap-688	261	11	:	:	PUNCT
ap-688	261	12	“	"	PUNCT
ap-688	261	13	computational	computational	ADJ
ap-688	261	14	method	method	NOUN
ap-688	261	15	and	and	CCONJ
ap-688	261	16	apparatus	apparatus	NOUN
ap-688	261	17	for	for	ADP
ap-688	261	18	finite	finite	ADJ
ap-688	261	19	field	field	NOUN
ap-688	261	20	arithmetic	arithmetic	ADJ
ap-688	261	21	,	,	PUNCT
ap-688	261	22	”	"	PUNCT
ap-688	261	23	u.s	u.s	PROPN
ap-688	261	24	.	.	PROPN
ap-688	261	25	patent	patent	NOUN
ap-688	261	26	number	number	NOUN
ap-688	261	27	4,587,627	4,587,627	NUM
ap-688	261	28	,	,	PUNCT
ap-688	261	29	1986	1986	NUM
ap-688	261	30	.	.	PUNCT
ap-688	262	1	[	[	X
ap-688	262	2	7	7	NUM
ap-688	262	3	]	]	X
ap-688	262	4	blake	blake	PROPN
ap-688	262	5	,	,	PUNCT
ap-688	262	6	i.	i.	PROPN
ap-688	262	7	,	,	PUNCT
ap-688	262	8	seroussi	seroussi	PROPN
ap-688	262	9	,	,	PUNCT
ap-688	262	10	g.	g.	PROPN
ap-688	262	11	,	,	PUNCT
ap-688	262	12	smart	smart	ADJ
ap-688	262	13	,	,	PUNCT
ap-688	262	14	n.	n.	NOUN
ap-688	262	15	:	:	PUNCT
ap-688	262	16	“	"	PUNCT
ap-688	262	17	elliptic	elliptic	ADJ
ap-688	262	18	curves	curve	NOUN
ap-688	262	19	in	in	ADP
ap-688	262	20	cryptography	cryptography	NOUN
ap-688	262	21	”	"	PUNCT
ap-688	262	22	,	,	PUNCT
ap-688	262	23	chapter	chapter	NOUN
ap-688	262	24	1	1	NUM
ap-688	262	25	.	.	PUNCT
ap-688	263	1	cambridge	cambridge	PROPN
ap-688	263	2	university	university	PROPN
ap-688	263	3	press	press	PROPN
ap-688	263	4	,	,	PUNCT
ap-688	263	5	cambridge	cambridge	PROPN
ap-688	263	6	(	(	PUNCT
ap-688	263	7	uk	uk	PROPN
ap-688	263	8	)	)	PUNCT
ap-688	263	9	,	,	PUNCT
ap-688	263	10	1999	1999	NUM
ap-688	263	11	.	.	PUNCT
ap-688	264	1	[	[	X
ap-688	264	2	8	8	NUM
ap-688	264	3	]	]	X
ap-688	264	4	wall	wall	NOUN
ap-688	264	5	,	,	PUNCT
ap-688	264	6	m.	m.	NOUN
ap-688	264	7	:	:	PUNCT
ap-688	264	8	“	"	PUNCT
ap-688	264	9	galib	galib	PROPN
ap-688	264	10	,	,	PUNCT
ap-688	264	11	a	a	DET
ap-688	264	12	c	c	PROPN
ap-688	264	13	�	�	NOUN
ap-688	264	14	�	�	PROPN
ap-688	264	15	library	library	NOUN
ap-688	264	16	of	of	ADP
ap-688	264	17	genetic	genetic	ADJ
ap-688	264	18	algorithm	algorithm	NOUN
ap-688	264	19	components	component	NOUN
ap-688	264	20	”	"	PUNCT
ap-688	265	1	[	[	X
ap-688	265	2	online	online	X
ap-688	265	3	]	]	X
ap-688	265	4	available	available	ADJ
ap-688	265	5	from	from	ADP
ap-688	265	6	http://sourceforge.net/projects/galib/	http://sourceforge.net/projects/galib/	PROPN
ap-688	265	7	ing	ing	PROPN
ap-688	265	8	.	.	PUNCT
ap-688	266	1	jan	jan	PROPN
ap-688	266	2	schmidt	schmidt	PROPN
ap-688	266	3	,	,	PUNCT
ap-688	266	4	ph.d	ph.d	PROPN
ap-688	266	5	.	.	PUNCT
ap-688	266	6	phone	phone	NOUN
ap-688	266	7	:	:	PUNCT
ap-688	266	8	+420	+420	PROPN
ap-688	266	9	224	224	NUM
ap-688	266	10	357	357	NUM
ap-688	266	11	473	473	NUM
ap-688	266	12	e	e	NOUN
ap-688	266	13	-	-	NOUN
ap-688	266	14	mail	mail	NOUN
ap-688	266	15	:	:	PUNCT
ap-688	266	16	schmidt@fel.cvut.cz	schmidt@fel.cvut.cz	VERB
ap-688	266	17	ing	ing	ADJ
ap-688	266	18	.	.	PUNCT
ap-688	267	1	martin	martin	PROPN
ap-688	267	2	novotný	novotný	PROPN
ap-688	267	3	phone	phone	NOUN
ap-688	267	4	:	:	PUNCT
ap-688	267	5	+420	+420	PROPN
ap-688	267	6	224	224	NUM
ap-688	267	7	357	357	NUM
ap-688	267	8	261	261	NUM
ap-688	267	9	e	e	NOUN
ap-688	267	10	-	-	NOUN
ap-688	267	11	mail	mail	NOUN
ap-688	267	12	:	:	PUNCT
ap-688	267	13	novotnym@fel.cvut.cz	novotnym@fel.cvut.cz	PROPN
ap-688	267	14	department	department	PROPN
ap-688	267	15	of	of	ADP
ap-688	267	16	computer	computer	NOUN
ap-688	267	17	science	science	NOUN
ap-688	267	18	and	and	CCONJ
ap-688	267	19	engineering	engineering	NOUN
ap-688	267	20	czech	czech	PROPN
ap-688	267	21	technical	technical	PROPN
ap-688	267	22	university	university	PROPN
ap-688	267	23	in	in	ADP
ap-688	267	24	prague	prague	PROPN
ap-688	267	25	faculty	faculty	NOUN
ap-688	267	26	of	of	ADP
ap-688	267	27	eletrical	eletrical	ADJ
ap-688	267	28	engineering	engineering	PROPN
ap-688	267	29	karlovo	karlovo	PROPN
ap-688	267	30	nám	nám	PROPN
ap-688	267	31	.	.	PUNCT
ap-688	268	1	13	13	NUM
ap-688	268	2	121	121	NUM
ap-688	268	3	35	35	NUM
ap-688	268	4	praha	praha	NOUN
ap-688	268	5	2	2	NUM
ap-688	268	6	,	,	PUNCT
ap-688	268	7	czech	czech	PROPN
ap-688	268	8	republic	republic	NOUN
ap-688	268	9	60	60	NUM
ap-688	268	10	©	©	PROPN
ap-688	268	11	czech	czech	PROPN
ap-688	268	12	technical	technical	PROPN
ap-688	268	13	university	university	PROPN
ap-688	268	14	publishing	publishing	NOUN
ap-688	268	15	house	house	NOUN
ap-688	268	16	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-688	268	17	acta	acta	PROPN
ap-688	268	18	polytechnica	polytechnica	PROPN
ap-688	268	19	vol	vol	NOUN
ap-688	268	20	.	.	PROPN
ap-688	269	1	45	45	NUM
ap-688	269	2	no	no	NOUN
ap-688	269	3	.	.	PUNCT
ap-688	270	1	2/2005	2/2005	NUM
ap-688	270	2	czech	czech	PROPN
ap-688	270	3	technical	technical	PROPN
ap-688	270	4	university	university	PROPN
ap-688	270	5	in	in	ADP
ap-688	270	6	prague	prague	PROPN
ap-688	270	7	multiplier	multiplier	ADV
ap-688	270	8	shifter	shifter	NOUN
ap-688	270	9	digit	digit	NOUN
ap-688	270	10	width	width	PROPN
ap-688	270	11	a0	a0	PROPN
ap-688	270	12	t0	t0	PROPN
ap-688	270	13	a	a	DET
ap-688	270	14	t	t	NOUN
ap-688	270	15	rotations	rotation	NOUN
ap-688	270	16	si	si	X
ap-688	270	17	–	–	PUNCT
ap-688	270	18	0	0	NUM
ap-688	270	19	0	0	NUM
ap-688	270	20	976	976	NUM
ap-688	270	21	10	10	NUM
ap-688	270	22	1	1	NUM
ap-688	270	23	,	,	PUNCT
ap-688	270	24	5	5	NUM
ap-688	270	25	,	,	PUNCT
ap-688	270	26	20	20	NUM
ap-688	270	27	,	,	PUNCT
ap-688	270	28	81	81	NUM
ap-688	270	29	1	1	NUM
ap-688	270	30	489	489	NUM
ap-688	270	31	1956	1956	NUM
ap-688	270	32	244	244	NUM
ap-688	270	33	159	159	NUM
ap-688	270	34	1	1	NUM
ap-688	270	35	6	6	NUM
ap-688	270	36	2934	2934	NUM
ap-688	270	37	326	326	NUM
ap-688	270	38	488	488	NUM
ap-688	270	39	24	24	NUM
ap-688	270	40	1	1	NUM
ap-688	270	41	,	,	PUNCT
ap-688	270	42	10	10	NUM
ap-688	270	43	table	table	NOUN
ap-688	270	44	2	2	NUM
ap-688	270	45	:	:	PUNCT
ap-688	270	46	shifters	shifter	NOUN
ap-688	270	47	adjusted	adjust	VERB
ap-688	270	48	to	to	ADP
ap-688	270	49	different	different	ADJ
ap-688	270	50	multipliers	multiplier	NOUN
ap-688	270	51	time	time	NOUN
ap-688	270	52	of	of	ADP
ap-688	270	53	point	point	NOUN
ap-688	270	54	addition	addition	NOUN
ap-688	270	55	m	m	VERB
ap-688	270	56	=	=	NOUN
ap-688	270	57	180	180	NUM
ap-688	270	58	0	0	NUM
ap-688	270	59	5	5	NUM
ap-688	270	60	10	10	NUM
ap-688	270	61	15	15	NUM
ap-688	270	62	20	20	NUM
ap-688	270	63	25	25	NUM
ap-688	270	64	0	0	NUM
ap-688	270	65	5	5	NUM
ap-688	270	66	10	10	NUM
ap-688	270	67	15	15	NUM
ap-688	270	68	20	20	NUM
ap-688	270	69	25	25	NUM
ap-688	270	70	digit	digit	NOUN
ap-688	270	71	width	width	NOUN
ap-688	270	72	d	d	X
ap-688	270	73	u	u	NOUN
ap-688	270	74	s	s	X
ap-688	270	75	k=1	k=1	NOUN
ap-688	270	76	fig	fig	NOUN
ap-688	270	77	.	.	PUNCT
ap-688	271	1	5	5	NUM
ap-688	271	2	:	:	PUNCT
ap-688	271	3	time	time	NOUN
ap-688	271	4	of	of	ADP
ap-688	271	5	point	point	NOUN
ap-688	271	6	addition	addition	NOUN
ap-688	271	7	for	for	ADP
ap-688	271	8	different	different	ADJ
ap-688	271	9	digit	digit	NOUN
ap-688	271	10	widths	width	NOUN
ap-688	271	11	.	.	PUNCT
ap-688	272	1	one	one	NUM
ap-688	272	2	rotation	rotation	NOUN
ap-688	272	3	block	block	NOUN
ap-688	272	4	(	(	PUNCT
ap-688	272	5	k	k	X
ap-688	272	6	�	�	PROPN
ap-688	272	7	1	1	NUM
ap-688	272	8	)	)	PUNCT
ap-688	272	9	and	and	CCONJ
ap-688	272	10	two	two	NUM
ap-688	272	11	rotation	rotation	NOUN
ap-688	272	12	blocks	block	NOUN
ap-688	272	13	(	(	PUNCT
ap-688	272	14	k	k	X
ap-688	272	15	�	�	PROPN
ap-688	272	16	2	2	NUM
ap-688	272	17	)	)	PUNCT
ap-688	272	18	used	use	VERB