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Koblitz N., Menezes A.J. (Contributor), Wu Y.-H. (Contributor) — Algebraic Aspects of Cryptography
Koblitz N., Menezes A.J. (Contributor), Wu  Y.-H. (Contributor) — Algebraic Aspects of Cryptography

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Название: Algebraic Aspects of Cryptography

Авторы: Koblitz N., Menezes A.J. (Contributor), Wu Y.-H. (Contributor)

Аннотация:

This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyperelliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. It is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 206

Добавлена в каталог: 05.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\wp$-function      122
3-Coloring      106
3-Coloring, problem      34 35
Abelian group      56
Addition on elliptic curve      118
Addition on hyperelliptic jacobian      145
Addition time estimate      25
Affine, plane      121
Affine, space      85
Algebraic, arithmetic      16
Algebraic, closure      55
Algebraic, element      54
Algebraic, geometry      69
Algebraically closed      55
Algorithm      27
Algorithm, deterministic      37
Algorithm, probabilistic      45
Algorithm, randomized      45
Arithmetic algebraic geometry      16
Arthur — Merlin Protocol      51
Asymptotically equal      19
Attack, chosen-ciphertext      5 110 136
Attack, linear algebra      113
Authentication      4
Automorphism      54
Average — Case Complexity      50 116
Baby — Step — Giant-Step      134
Basis of ideal      70
Basis of vector space      53
Basis, normal      136
Big-o      18
Bilinear map      92
Binary, digit      22
Binary, quadratic form      145
Binary, search      36
Birch — Swinnerton — Dyer conjecture      140
Bit      22
Bit, commitment      4 10
Bit, operation      25
Boolean circuit      11
bpp      47
Brassard’s Theorem      103 104
Breaking a Cryptosystem      13
Buchberger’s Theorem      75
Canonical Suijection      68
Catherine, hours on homework      12
Catherine, the cryptanalyst      6 8 80 87 109
Catherine, the Great      3
Cellular automaton      104
Certificate      38
Certificate for Ideal Membership      111
Certificate of primality      38
Certificate, unique      49
Characteristic of field      55
Chinese remainder theorem      33
Chinese remainder theorem for polynomials      64 170 183
Chosen — Ciphertext Attack      5 110 136
Ciphertext      1
CLIQUE      113
CM — Field      123
co — NP      38 41 104 180
Coin Flip      4 10
Collision Resistant      6
Combinatorial Cryptosystem      103
Combinatorial-Algebraic Cryptosystem      105
Complex multiplication      123
complexity      18
Complexity, average-case      50 116
Complexity, computational      18
Complexity, probabilistic      45 46
Complexity, randomized      45 46
Compositeness Problem      46
Computational complexity      18
Concealing Information      11
Congruent Number Problem      139
conjugate      54
Conjugate of polynomial function on C      159
Coordinate ring      159
Cracking Problem      13 44 104
Cracking Problem for Polly Cracker      106
Cryptanalysis      13
Cryptanalysis of Little Dragon      92
Cryptography      1
Cryptography, impractical      16
Cryptography, practical      13
Cryptosystem, combinatorial-algebraic      103
Cryptosystem, elliptic curve      131
Cryptosystem, hyperelliptic      148
Cryptosystem, Imai — Matsumoto      80
Curve, elliptic      117
Curve, hyperelliptic      144 156
Cyclic group      56
Decision problem      35
Degree of divisor      144 167
Degree of field extension      53
Degree of polynomial      53
Degree of polynomial on C      160
Degree of total      65
Degree-lexicographical Order      71
Derivative      54
Deterministic, algorithm      37
Deterministic, encryption      5
Diffie-Hellman, key exchange      8 132
Diffie-Hellman, one-way function      104
Diffie-Hellman, problem      8 43 132 133
Digital Signature Algorithm      9
Digital Signature Algorithm, elliptic curve variant      134
Dimension of ring      70
Dimension of vector space      53
Discrete Log Problem in arbitrary group      132
Discrete Log Problem in finite field      8 9 43 103
Discrete Log Problem on elliptic curve      131 132 142
Discrete Log Problem on hyperelliptic jacobian      148 153
Discriminant      118 140
Division points      123
Divisor of a rational function      145 167
Divisor on a curve      120 144 167
Divisor, equivalence of      168
Divisor, norm of      171
Divisor, principal      145 168
Divisor, reduced      145 171
Divisor, semi-reduced      168
Divisor, support of      168
Dominant Term      18
DSA      9
DSA, elliptic curve variant      134
ECDSA      134
Efficiency      14
ElGamal, cryptosystem      132 136
ElGamal, signature      9
Elliptic, curve      16 38 117
Elliptic, curve complex multiplication      123
Elliptic, curve cryptosystem      131
Elliptic, curve digital signature algorithm      134
Elliptic, curve endomorphism      123
Elliptic, curve in characteristics      2
Elliptic, curve nonsupersingular      118 125 127 131
Elliptic, curve over $\mathbb{C}$      121
Elliptic, curve over $\mathbb{Q}$      124 130
Elliptic, curve over $\mathbb{R}$      118
Elliptic, curve over finite field      125
Elliptic, curve, rank      124
Elliptic, curve, supersingular      118 125 127 131
Elliptic, function      123
Endomorphism of elliptic curve      123
Envelope      11
Equivalent divisors      168
Error — Correcting Code      107 155
Euclidean algorithm      28
Euclidean algorithm for Gaussian integers      63 183
Euclidean algorithm for polynomials      63
Euler $\varphi$ — Function      56
Exponential time      14 31
EXPSPACE      51
EXPSPACE-hard      51 111
Extension field      53
Extraterrestrial Being      15 38 48 51
Fermat, Last Theorem      140 150 183
Fermat, little theorem      45
Fermat, prime      30
Fermat, strong primality test      45
Fibonacci number      23 32
Field      53
Field, algebraically closed      55
Field, automorphism      54
Field, extension      53
Field, finite      55
Field, isomorphism      54
Field, prime      55
Field, splitting      55
Finite, field      55
Finite, point      157
Frequency analysis      2
Function, defined at $P \in G$      160
Function, doubly periodic      120
Function, elliptic      123
Function, field      160
Function, hash      4 6 13 100
Function, one-way      2 3 12 104
Function, one-way Diffie — Hellman      104
Function, one-way RSA      104
Function, rational on C      160
Function, rational pole      161
Function, rational value at $\infty$      161
Function, trapdoor      3 12
Function, value at $P \in C$      160
Function, zero      161
Fundamental parallelogram      122
Gaussian integers      59 63 65 122
Generator of finite field      56
Generator of ideal      66
Genus      144 156
Germain, Sophie      137 183
Graph      34
Graph, coloring      34 106
Graph, Perfect Code      107 114
Graph, planar      180
Graph, r-regular      110
Greatest Common Divisor of divisors      144 167
Greatest common divisor of Gaussian integers      63 183
Greatest common divisor of integers      28
Greatest common divisor of polynomials      55 63
Grobner basis      74
Grobner basis, minimal      77
Grobner Basis, reduced      78
Ground field      126
Group, abelian      56
Group, cyclic      56
Hard-on — Average      50 116
Hash function      4 6 13 100
Hasse’s Theorem J      127
Height of a Point      142
Hidden Monomial      87
Hilbert, Basis Theorem      66
Hilbert, Nullstellensatz      69
Hilbert, Nullstellensatz, strong      69
Hilbert, Nullstellensatz, weak      69
Homogeneous, coordinates      188
Homogeneous, equation      118 121
Homomorphism      67
Hyperelliptic, cryptosystem      148
Hyperelliptic, curve      144 156
Hyperelliptic, curve supersingular      153
Ideal      65
Ideal, finitely generated      66
Ideal, maximal      66
Ideal, membership      111 112 187
Ideal, Membership, Phantom      112
Ideal, nontrivial      65
Ideal, prime      66
Ideal, principal      66
Ideal, proper      65
Ideal, radical of      69 111
Ideal, unit      65
Ideal, zero set of      68 69 107
Identification      4
Imai — Matsumoto Cryptosystem      80
Inclusion — Exclusion      185
Information, concealing of      11
Information, theory      2
Input      30 34
Input, length      15 30 34
Instance of Problem      34
Integer Factorization Problem      14 16 31 34—36 40 103
Integral domain      65
Interaction      50
Interactive proof system      50 51
IP      50 51
Isomorphism      54
Jacobi sum      150
Jacobian      145 168
Key, exchange      3 4 8 132
Key, generation      14 16
Key, private      2
Key, public      1 3
Kid Krypto      17 110
Knapsack      103
Lattice      122
Leading term      72
Length of input      15 30 34
Length of number      20 22
Lexicographical order      71
Line at infinity      121
Little Dragon      87
Little Dragon with weak exponent      90
Little Dragon, cryptanalysis of      92
Little-o      19
Map coloring      34 42
Massively Parallel      51
Maximal ideal      66
Menezes-Okamoto-Vanstone Reduction      131 136
Merkle — Hellman Knapsack      103
Mersenne prime      138 139 152 182
Message unit      1
Miller’s Test      45
Minimal, Grobner basis      77
Minimal, polynomial      54
Modular exponentiation      29 188
Monic polynomial      54
Mordell theorem      124
Multiplication, time estimate      26
NC      51
Neighborhood in Graph      107
Noetherian ring      66
non-repudiation      4 7
Non-uniformity      51
Nonsupersingular      118 125 127 131
Norm of algebraic number      54 151
Norm of divisor      171
Norm of polynomial function on C      159
Normal basis      136
NP      38
NP and co—NP      38 41 103 105 111 180
NP-hard      41 103 112
NP—complete      40
NP—equivalent      41
Nullstellensatz      69
Nullstellensatz, effective      111
Nullstellensatz, strong      69
Nullstellensatz, weak      69
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