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Koblitz N., Menezes A.J. (Contributor), Wu Y.-H. (Contributor) — Algebraic Aspects of Cryptography
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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 |
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Предметный указатель
Number field sieve 31 133 One — Time Pad 2 One — Way Function 2 3 12 104 One — Way Function, Diffie — Hellman 104 One — Way Function, RSA 104 Opposite Point 144 157 Oracle 40 Order in an imaginary quadratic field 123 Order of an element 56 Order of divisor at a point 167 Order of function at a point 165 167 Order of point on elliptic curve 123 Order of terms 71 Order, degree-lexicographical 71 Order, lexicographical 71 Ordinary point 157 P 37 P 39 40 49 103 180 Paper tiger 92 parallel 51 Password 2 4 12 Perfect code 107 Perfect Code, Graph 107 114 Perfect Code, Subset 107 Ph 48 Phantom, Ideal Membership 112 Phantom, input 112 PID 66 Plaintext 1 Point at infinity 117 121 144 157 Point finite 157 Point of finite order 124 Point opposite 144 157 Point ordinary 157 Point singular 156 Point special 157 Pole of rational function 161 Polly Cracker 105 Polly Cracker, generalization 108 Polly Cracker, linear algebra attack 113 Polynomial time 15 30 31 37 Polynomial Time on average 50 Polynomial Time probabilistic 46 Polynomial Time randomized 46 Polynomial Time, certificate 38 Polynomial Time, equivalent 41 43 Polynomial, function on C 159 Polynomial, hierarchy 48 Polynomial, monic 54 Polynomial, primitive 60 Polynomial, ring 53 65 Polynomial, sparse 46 113 116 187 Power product 71 Preimage Resistant 6 Primality probabilistic 45 Primality problem 37 48 Primality test 31 Prime field 55 Prime ideal 66 Prime Mersenne 182 Prime number theorem 19 187 Primitive in cryptography 5 Primitive, polynomial 60 Principal, divisor 145 168 Principal, ideal 66 Private key 2 Probabilistic, algorithm 45 Probabilistic, complexity class 45 46 Probabilistic, encryption 5 106 Probabilistic, polynomial time 46 Probabilistic, primality test 45 Problem, cracking 13 44 Problem, decision 35 Problem, instance 34 Problem, NP-complete 40 Problem, promise 44 Problem, reducing one to another 39 Problem, search 35 Product Polynomial Inequivalence 46 Projective, coordinates 121 188 Projective, equation of elliptic curve 121 Projective, geometry 120 Projective, plane 121 157 Projective, point 121 Promise Problem 44 Promise Problem, phantum input 112 Protocol 4 PSPACE 51 Public key 1 3 Quadratic Enciphering 97 Quotient ring 68 r-Regular Graph 110 Rabin’s Probabilistic Primality Test 45 Radical 69 111 Random algorithm 45 Random, complexity class 45—47 Random, polynomial time 46 Random, self-reducibility 116 Rank of elliptic curve 124 Rational Function on C 160 Rational Function pole 161 Rational Function value at 160 Rational Function value at 161 Rational Function zero 161 Reduced, divisor 145 171 Reduced, Groebner basis 78 Reduction of 72 Reduction of one problem to another 39 Relatively prime 28 Repeated squaring 29 93 Rewrite System 105 Riemann hypothesis 37 129 Ring 65 Ring, coordinate 159 Ring, homomorphism 67 Ring, Noetherian 66 Ring, polynomial 53 Ring, quotient 68 RP 46 RSA 3 16 43 104 S — Polynomial 75 Satisfiability 110 Sato — Tate Distribution 141 Search problem 35 Secret sharing 4 Self-Reducibility, random 116 Semi — Reduced Divisor 168 Series 51 Signature 4 7 12 100 Silver — Pohlig — Hellman algorithm 133 138 Singular point 156 Smart card 14 Smooth, curve 117 Smooth, integer 133 Sparse Polynomial 46 113 116 187 Special point 157 Spider 116 Spider, circling prey 116 Splitting field 55 Square and Multiply 29 Square Roots in 98 128 Standards 16 134 Stirling’s formula 23 30 Strong Fermat Primality Test 45 Subexponential Time 31 Subset, Perfect Code 107 Subset, Sum 103 Supersingular 118 125 127 131 153 Support of a divisor 168 Taniyama Conjecture 140 Term 71 Term, leading 72 Term, order 70 71 Three Coloring 106 Three Coloring, problem 34 35 Time exponential 31 Time polynomial 30 31 37 Time subexponential 31 Torsion subgroup 124 137 Torus 122 Total degree 65 Tour 35 Toy Example 82 Trace 62 183 Transcendental element 68 Trapdoor 104 Trapdoor, function 3 12 Trapdoor, problem 45 104 Traveling Salesrep Problem 34 38 Twists 151 Uniformizing parameter 163 Unique, factorization 54 Unique, P 49 Unreasonable Effectiveness 15 UP 49 Value of Rational Function at 160 Value of Rational Function at 161 Vector space 53 Vigenere cipher 1 Weak Exponent 90 Weierstrass, 122 Weil, pairing 131 Weil, theorem 146 Word problem 105 XOR 11 Zariski — Open Set 114 Zero of rational function 161 Zero, knowledge 4 Zero, set of ideal 68 69 107 Zeta-Function of elliptic curve 126 Zeta-Function of hyperelliptic curve 146 ZPP 48
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conjecture 
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modulo g 
-function 
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