Авторизация
Поиск по указателям
Koblitz N., Menezes A.J. (Contributor), Wu Y.-H. (Contributor) — Algebraic Aspects of Cryptography
Обсудите книгу на научном форуме Нашли опечатку?
Название: Algebraic Aspects of CryptographyАвторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 206Добавлена в каталог: 05.12.2010Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
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 121 Elliptic, curve over 124 130 Elliptic, curve over 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 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 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 161 Function, trapdoor 3 12 Function, value at 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
Реклама
-function 
— Function 
|
|
О проекте