List of Algorithms

1.1	RSA key pair generation . . . . . . . . . . . . . . . . . . . . . . . . . .	7
1.2	Basic RSA encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . .	7
1.3	Basic RSA decryption . . . . . . . . . . . . . . . . . . . . . . . . . . . .	7
1.4	Basic RSA signature generation . . . . . . . . . . . . . . . . . . . . . .	8
1.5	Basic RSA signature veriﬁcation . . . . . . . . . . . . . . . . . . . . . .	8
1.6	DL domain parameter generation . . . . . . . . . . . . . . . . . . . . . .	9
1.7	DL key pair generation . . . . . . . . . . . . . . . . . . . . . . . . . . .	9
1.8	Basic ElGamal encryption . . . . . . . . . . . . . . . . . . . . . . . . .	10
1.9	Basic ElGamal decryption . . . . . . . . . . . . . . . . . . . . . . . . .	10
1.10	DSA signature generation . . . . . . . . . . . . . . . . . . . . . . . . . .	11
1.11	DSA signature veriﬁcation . . . . . . . . . . . . . . . . . . . . . . . . .	11
1.12	Elliptic curve key pair generation . . . . . . . . . . . . . . . . . . . . . .	14
1.13	Basic ElGamal elliptic curve encryption . . . . . . . . . . . . . . . . . .	14
1.14	Basic ElGamal elliptic curve decryption . . . . . . . . . . . . . . . . . .	14
2.5	Multiprecision addition . . . . . . . . . . . . . . . . . . . . . . . . . . .	30
2.6	Multiprecision subtraction . . . . . . . . . . . . . . . . . . . . . . . . .	30
2.7	Addition in F p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	31
2.8	Subtraction in F p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	31
2.9	Integer multiplication (operand scanning form) . . . . . . . . . . . . . .	31
2.10	Integer multiplication (product scanning form) . . . . . . . . . . . . . . .	32
2.13	Integer squaring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	35
2.14	Barrett reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	36
2.17	Montgomery exponentiation (basic) . . . . . . . . . . . . . . . . . . . .	38
2.19	Extended Euclidean algorithm for integers . . . . . . . . . . . . . . . . .	40
2.20	Inversion in F p using the extended Euclidean algorithm . . . . . . . . . .	40
2.21	Binary gcd algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .	41
2.22	Binary algorithm for inversion in F p . . . . . . . . . . . . . . . . . . . .	41
2.23	Partial Montgomery inversion in F p . . . . . . . . . . . . . . . . . . . .	42

x List of Algorithms

2.25	Montgomery inversion in F p . . . . . . . . . . . . . . . . . . . . . . . .																																			43
2.26	Simultaneous inversion . . . . . . . . . . . . . . . . . . . . . . . . . . .																																			44
																			192						64		− 1 . . . . . . . . . . . . . . . .
2.27	Fast reduction modulo p192 = 2224																					− 296														45
2.28	Fast reduction modulo p224 = 2256																												. . . . . . . . . . . . . . .							45
																						− 2224+ 1 .192										296		−	1 . . . . . . . .	46
2.29	Fast reduction modulo p256 = 2384																					− 2128 + 296									+ 32
2.30	Fast reduction modulo p384 = 2521																					− 2					− 2			+ 2			− 1 . . . . . . . . .			46
2.31	Fast reduction modulo p521 = 2																					− 1 . . . . . . . . . . . . . . . . . . .														46
2.32	Addition in F2m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .																																			47
2.33	Right-to-left shift-and-add ﬁeld multiplication in F2m . . . . . . . . . . .																																			48
2.34	Right-to-left comb method for polynomial multiplication . . . . . . . . .																																			49
2.35	Left-to-right comb method for polynomial multiplication . . . . . . . . .																																			50
2.36	Left-to-right comb method with windows of width w . . . . . . . . . . .																																			50
2.39	Polynomial squaring . . . . . . . . . . . . . . . . . . . . . . . . . . . .																																			53
2.40	Modular reduction (one bit at a time) . . . . . . . . . . . . . . . . . . . .																																			53
											f (z) = z									163		+ z			7			6	+ z		3	+ 1 . . . . . . . . . . .
2.41	Fast reduction modulo																			233					74+ z											55
2.42	Fast reduction modulo										f (z) = z									283		+ z			12		+ 17. . .5 . . . . . . . . . . . . .									55
2.43	Fast reduction modulo										f (z) = z									409		+ z			87		+ z		+ z			+ 1 . . . . . . . . . .				56
2.44	Fast reduction modulo										f (z) = z									571		+ z			10		+ 15. . .2 . . . . . . . . . . . . .									56
2.45	Fast reduction modulo										f (z) = z											+ z					+ z		+ z			+ 1 . . . . . . . . . .				56
2.47	Extended Euclidean algorithm for binary polynomials . . . . . . . . . . .																																			58
2.48	Inversion in F2m using the extended Euclidean algorithm . . . . . . . . .																																			58
2.49	Binary algorithm for inversion in F2m . . . . . . . . . . . . . . . . . . .																																			59
2.50	Almost Inverse Algorithm for inversion in F2m . . . . . . . . . . . . . . .																																			60
2.54	Reduction modulo M = Bn − c . . . . . . . . . . . . . . . . . . . . . . .																																			64
2.59	OEF inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .																																			69
3.21	Point doubling (		y2				=		x3			−			3x		+			b, Jacobian coordinates) . . . . . . . . .																91
				2						3					x																					91
3.22	Point addition (y						= x												b, afﬁne-Jacobian coordinates) . . . . . .
											− 32					+			3			3x				b, Jacobian coordinates) . . . . .										93
3.23	Repeated point	doubling (y														=		x		2−				+
			y		2			x y					x		3												0, 1 , LD coordinates) . . . . .									94
3.24	Point doubling (						+				=						ax				+		b, a
				2										3 +					2							{			}
3.25	Point addition (y					+x y=x									+ax						+b, a {0, 1}, LD-afﬁne coordinates) . .															95
3.26	Right-to-left binary method for point multiplication . . . . . . . . . . . .																																			96
3.27	Left-to-right binary method for point multiplication . . . . . . . . . . . .																																			97
3.30	Computing the NAF of a positive integer . . . . . . . . . . . . . . . . . .																																			98
3.31	Binary NAF method for point multiplication . . . . . . . . . . . . . . . .																																			99

3.35Computing the width-w NAF of a positive integer . . . . . . . . . . . . . 100

3.36Window NAF method for point multiplication . . . . . . . . . . . . . . . 100

3.38Sliding window method for point multiplication . . . . . . . . . . . . . . 101

3.40Montgomery point multiplication (for elliptic curves over F2m ) . . . . . . 103

3.41	Fixed-base windowing method for point multiplication . . . . . . . . . .	104
3.42	Fixed-base NAF windowing method for point multiplication . . . . . . .	105
3.44	Fixed-base comb method for point multiplication . . . . . . . . . . . . .	106

				List of Algorithms	xi
3.45	Fixed-base comb method (with two tables) for point multiplication . . . .				106
3.48	Simultaneous multiple point multiplication . . . . . . . . . . . . . . . . .				109
3.50	Joint sparse form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .				111
3.51	Interleaving with NAFs . . . . . . . . . . . . . . . . . . . . . . . . . . .				112
3.61	Computing the TNAF of an element in Z[τ ] . . . . . . . . . . . . . . . .				117
3.62	Division in Z[τ ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .				118
3.63	Rounding off in Z[τ ] . . . . .		. . . . . . . . . . . . . . . . . . . . . . .		118
			m	− 1)/(τ − 1) . . . . . . . . . . . . . .
3.65	Partial reduction modulo δ = (τ				119
3.66	TNAF method for point multiplication on Koblitz curves . . . . . . . . .				119
3.69	Computing a width-w TNAF of an element in Z[τ ] . . . . . . . . . . . .				123
3.70	Window TNAF point multiplication method for Koblitz curves . . . . . .				123
3.74	Balanced length-two representation of a multiplier . . . . . . . . . . . . .				127
3.77	Point multiplication with efﬁciently computable endomorphisms . . . . .				129
3.81	Point halving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .				131
	2	+ x = c (basic version) . . . . . . . . . . . . . . . . . . . . . .			133
3.85	Solve x2
3.86	Solve x	+ x = c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .			134

3.91Halve-and-add w-NAF (right-to-left) point multiplication . . . . . . . . . 138

3.92Halve-and-add w-NAF (left-to-right) point multiplication . . . . . . . . . 139

4.3Pollard’s rho algorithm for the ECDLP (single processor) . . . . . . . . . 159

4.5 Parallelized Pollard’s rho algorithm for the ECDLP . . . . . . . . . . . . 161

4.14Domain parameter generation . . . . . . . . . . . . . . . . . . . . . . . . 174

4.15Explicit domain parameter validation . . . . . . . . . . . . . . . . . . . . 175

4.17	Generating a random elliptic curve over a prime ﬁeld F p . . . . . . . . .	176
4.18	Verifying that an elliptic curve over F p was randomly generated . . . . .	176
4.19	Generating a random elliptic curve over a binary ﬁeld F2m . . . . . . . .	177
4.21	Verifying that an elliptic curve over F2m was randomly generated . . . . .	177
4.22	Generating a random elliptic curve over an OEF F pm . . . . . . . . . . .	178

4.23Verifying that an elliptic curve over F pm was randomly generated . . . . . 178

4.24Key pair generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

4.25	Public key validation . . . . . . . . . . . . . . . . . . . . . . . . . . . .	181
4.26	Embedded public key validation . . . . . . . . . . . . . . . . . . . . . .	181
4.29	ECDSA signature generation . . . . . . . . . . . . . . . . . . . . . . . .	184
4.30	ECDSA signature veriﬁcation . . . . . . . . . . . . . . . . . . . . . . .	184
4.36	EC-KCDSA signature generation . . . . . . . . . . . . . . . . . . . . . .	187
4.37	EC-KCDSA signature veriﬁcation . . . . . . . . . . . . . . . . . . . . .	187

4.42ECIES encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

4.43ECIES decryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

4.47	PSEC encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	191
4.48	PSEC decryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	191
4.50	Station-to-station key agreement . . . . . . . . . . . . . . . . . . . . . .	194
4.51	ECMQV key agreement . . . . . . . . . . . . . . . . . . . . . . . . . . .	195

xii List of Algorithms

5.3Most signiﬁcant bit ﬁrst (MSB) multiplier for F2m . . . . . . . . . . . . . 230

5.4	Least signiﬁcant bit ﬁrst (LSB) multiplier for F2m . . . . . . . . . . . . .	231
5.5	Digit-serial multiplier for F2m . . . . . . . . . . . . . . . . . . . . . . .	234
5.6	Inversion in F2m (m odd) . . . . . . . . . . . . . . . . . . . . . . . . . .	237
5.7	SPA-resistant left-to-right binary point multiplication . . . . . . . . . . .	242

5.8RSA-OAEP encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.9RSA-OAEP decryption . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

A.1 Testing a polynomial for irreducibility . . . . . . . . . . . . . . . . . . . 258

<<< < Предыдущая 1 23 / 463 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 > Следующая >>>

Соседние файлы в предмете Профессионально-ориентированный английский язык

#
15.03.20151.37 Mб56Google Secrets - How To Get A Top 10 Ranking.pdf
#
15.03.2015114.88 Кб28Google Spamguide.pdf
#
15.03.2015135.12 Кб17GRC.com Denial Of Service Attack.pdf
#
15.03.2015830.4 Кб27Groupware & Security.pdf
#
15.03.2015590.68 Кб47GSM and GPRS.pdf
#
15.03.20154.58 Mб64Guide to Elliptic Curve Cryptography.pdf
#
15.03.201512.39 Mб75Hack Proofing Linux.pdf
#
15.03.20155.14 Mб58Hackers Beware.pdf
#
15.03.2015534.15 Кб44Hackers Desk Reference.pdf
#
15.03.201510.83 Mб146Hacking GPS.pdf
#
15.03.201512.74 Mб82Hacking Windows XP.pdf