| Cryptography: Theory and Practice by Douglas Stinson CRC Press, CRC Press LLC ISBN: 0849385210 Pub Date: 03/17/95 |
Index
- abelian group, 4, 116, 184
- accept, 385
- access structure, 331
- threshold, 332, 333
- active adversary, 258
- additive identity, 3
- additive inverse, 3
- adjoint matrix, 16
- adversary
- active, 258
- passive, 258
- Affine Cipher, 8, 8-12
- cryptanalysis of, 26-27
- affine function, 8
- Affine-Hill Cipher, 41
- algorithm
- deterministic, 129
- Las Vegas, 139, 171, 234
- Monte Carlo, 129, 129
- probabilistic, 129
- associative property, 3
- of cryptosystems, 66
- authentication code, 304, 304-323
- combinatorial bounds, 311-313
- deception probability, 305, 306-313, 319-323
- entropy bounds, 321-323
- impersonation attack, 305, 306-308
- orthogonal array characterization, 319-320
- substitution attack, 305, 307-309
- authentication matrix, 306
- authentication rule, 305
- authentication tag, 305
- authorized subset, 331
- minimal, 332
- Autokey Cipher, 23, 23
- basis, 332
- Bayes Theorem, 45, 60, 135, 340, 341
- binding, 399
- binomial coefficient, 31
- birthday paradox, 236
- bit commitment scheme, 399, 398-401, 405-407
- blob, 399
- block cipher, 20
- Blom Key Predistribution Scheme, 261, 260-263
- Blum-Blum-Shub Generator, 371, 370-377, 379
- Blum-Goldwasser Cryptosystem, 380, 379-382
- boolean circuit, 333
- fan-in, 333
- fan-out, 333
- monotone, 333
- boolean formula, 333
- conjunctive normal form, 337
- disjunctive normal form, 334
- Bos-Chaum Signature Scheme, 216, 215-217
- Brickell Secret Sharing Scheme, 344, 343-348
- Caesar Cipher, 4
- certificate, 264
- challenge, 385
- challenge-and-response protocol, 217, 283, 385
- Chaum-van Antwerpen Signature Scheme, 218, 217-223
- Chaum-van Heijst-Pfitzmann hash function, 238, 238-241
- Chinese remainder theorem, 122, 119-122, 142, 166, 380
- Chor-Rivest Cryptosystem, 115
- chosen ciphertext cryptanalysis, 25
- chosen plaintext cryptanalysis, 25
- cipher
- block, 20
- stream, 20, 20-24, 360
- cipher block chaining mode, 83, 83, 267
- cipher feedback mode, 83, 85
- ciphertext, 1, 20, 378
- ciphertext-only cryptanalysis, 25
- closure, 332
- closure property, 3
- code, 194
- distance of, 194
- dual code, 194
- generating matrix, 194
- Goppa code, 195
- Hamming code, 196
- nearest neighbor decoding, 194
- parity-check matrix, 194
- syndrome, 194
- syndrome decoding, 195
- coin-flipping by telephone, 400
- commutative cryptosystems, 66
- commutative property, 3
- complete graph, 346
- complete multipartite graph, 346, 352, 353
- completeness, 286, 386
- Composites, 129, 130
- computational security, 44
- concave function, 56
- strictly, 56
- concealing, 399
- conditional entropy, 59
- conditional probability, 45
- congruence, 3
- conjunctive normal form boolean formula, 337
- cryptanalysis, 6
- chosen ciphertext, 25
- chosen plaintext, 25
- ciphertext-only, 25
- known-plaintext, 25
- cryptogram, 7
- cryptosystem, 1
- endomorphic, 64
- idempotent, 66
- iterated, 66
- monoalphabetic, 12
- polyalphabetic, 13
- private-key, 114
- probabilistic public-key, 378
- product, 64, 64-67
- public-key, 114
- cyclic group, 123, 183, 187
- Data Encryption Standard, 51, 70
- description of, 70-78
- differential cryptanalysis of, 89, 89-104
- dual keys, 110
- exhaustive key search, 82
- expansion function, 71, 73
- initial permutation, 70, 73
- key schedule, 71, 75-78
- modes of operation, 83, 83-86
- S-boxes, 72, 73-75, 82
- time-memory tradeoff, 86, 86-89
- dealer, 326
- deception probability, 305
- decision problem, 129, 190
- decomposition construction, 354, 355, 353-357
- decryption rule, 1, 21, 378
- determinant, 16
- deterministic algorithm, 129
- differential cryptanalysis, 89
- characteristic, 98
- filtering operation, 101
- input x-or, 89
- output x-or, 89
- right pair, 100
- wrong pair, 100
- Diffie-Hellman Key Exchange, 270, 270-271
- Diffie-Hellman Key Predistribution Scheme, 265, 263-267
- Diffie-Hellman problem, 266, 265-267, 275
- Digital Signature Standard, 205, 211, 209-213
- digram, 25
- disavowal protocol, 217
- Discrete Logarithm Generator, 383
- Discrete Logarithm problem, 162, 163, 164-177, 206, 207, 210, 238, 263, 266, 276, 287, 290, 362, 397, 400, 406
- bit security of, 172-177, 400
- elliptic curve, 187
- generalized, 177, 177-180
- in Galois fields, 183
- index calculus method, 170-172
- ith Bit problem, 173
- Pohlig-Hellman algorithm, 169, 166-170
- Shanks algorithm, 165, 165-166
- disjunctive normal form boolean formula, 334
- distinguishable probability distributions, 364
- distinguisher, 364
- distribution rule, 338
- distributive property, 4
- electronic codebook mode, 83, 83
- ElGamal Cryptosystem, 115, 163, 162-164, 266-267
- elliptic curve, 187-190
- generalized, 178, 177-178
- ElGamal Signature Scheme, 205, 205-209
- elliptic curve, 183, 183-187
- point at infinity, 183
- Elliptic Curve Cryptosystem, 115, 187-190
- encryption matrix, 47
- encryption rule, 1, 21, 378
- endomorphic cryptosystem, 64
- entropy, 52, 51-52
- conditional, 59
- of a natural language, 61
- of a secret sharing scheme, 349-352
- of authentication code, 321-323
- properties of, 56-59, 349
- Euclidean algorithm, 116-120, 140, 179, 181
- extended, 117, 119
- running time of, 128
- Euler phi-function, 9
- Euler pseudo-prime, 132
- Eulers criterion, 130, 131, 173
- exclusive-or, 21
- exhaustive key search, 6, 13
- of DES, 82
- factor base, 171
- factoring, 150-156
- factor base, 153
- number field sieve, 155
- p - 1 algorithm, 151, 151-152
- quadratic sieve, 154
- trial division, 150
- fan-in, 333
- fan-out, 333
- Fermats theorem, 122, 137
- Fibonacci number, 128
- field, 10, 181
- forging algorithm, 390
- for Graph 3-colorability, 405
- for Graph Isomorphism, 391, 394
- Galois field, 180-183
- Girault Key Agreement Scheme, 278, 276-279
- Goldwasser-Micali Cryptosystem, 379, 378-379, 399
- graph, 346
- complete, 346
- complete multipartite, 346, 352, 353
- induced subgraph, 352
- isomorphic, 386
- proper 3-coloring, 401
- Graph 3-colorability, 401
- Graph 3-colorability Interactive Proof System, 402, 400-404, 406-407
- Graph Isomorphism, 386
- Graph Isomorphism Interactive Proof System, 389, 388-395
- Graph Non-isomorphism, 386
- Graph Non-isomorphism Interactive Proof System, 387, 386-388, 395-396
- group, 4
- abelian, 4, 116, 184
- cyclic, 123, 183, 187
- order of element in, 122
- Guillou-Quisquater Identification Scheme, 296, 295-299
- identity-based, 300
- Hamming distance, 194
- hash function, 203, 232, 232-254
- birthday attack, 236-237
- collision-free, 233-236
- constructed from a cryptosystem, 246
- extending, 241-246
- one-way, 234
- strongly collision-free, 233
- weakly collision-free, 233
- Hill Cipher, 13-17, 18
- cryptanalysis of, 36-37
- Huffman encoding, 53-56
- Huffmans algorithm, 55
- ideal decomposition, 353
- ideal secret sharing scheme, 343, 344, 346-348
- idempotent cryptosystem, 66
- identification scheme, 282-300
- converted to signature scheme, 300
- identity-based, 299, 299
- identity matrix, 14
- impersonation, 305
- implicit key authentication, 276, 278
- independent random variables, 45
- index of coincidence, 31
- mutual, 33
- indistinguishable probability distributions, 363-370, 378, 404
- induced subgraph, 352
- information rate, 342
- monotone circuit construction, 343
- injective function, 2
- interactive argument
- perfect zero-knowledge, 407
- zero-knowledge, 406, 405-407
- interactive proof, 385, 385-397
- computational zero-knowledge, 398, 404, 400-404
- perfect zero-knowledge, 393, 388-397
- perfect zero-knowledge for Vic, 391
- zero-knowledge, 385
- intruder-in-the-middle attack, 271, 305
- inverse matrix, 15
- inverse permutation, 7
- isomorphic graphs, 386
- iterated cryptosystem, 66
- Jacobi symbol, 132, 132-134, 370, 379
- Jensens Inequality, 56, 63, 316
- joint probability, 45
- Kasiski test, 31
- Kerberos, 268, 267-270
- key lifetime, 268
- session key, 267
- timestamp, 268
- Kerckhoffs principle, 24
- key, 1, 20, 203, 305, 326, 378
- key agreement, 258
- authenticated, 271
- key confirmation, 269
- key distribution, 258
- on-line, 259
- key equivocation, 59
- key freshness, 267
- key predistribution, 259, 260-267
- key server, 259
- keystream, 20
- keystream alphabet, 21
- keystream generator, 21
- keyword, 12
- known-plaintext cryptanalysis, 25
- Lagrange interpolation formula, 329, 329-330
- Lagranges theorem, 122
- Lamés theorem, 128
- Lamport Signature Scheme, 213, 213-215
- Las Vegas algorithm, 139, 171, 234
- Legendre symbol, 131, 131-132
- Linear Congruential Generator, 360, 360
- linear feedback shift register, 22, 360, 362
- linear recurrence, 21
- linear transformation, 14
- m-gram Substitution Cipher, 68
- matrix product, 14
- McEliece Cryptosystem, 115, 196, 193-198
- MD4 Hash Function, 248, 247-250
- MD5 Hash Function, 247, 250
- memoryless source, 53
- Menezes-Vanstone Cryptosystem, 189, 188-190
- Merkle-Hellman Cryptosystem, 115, 193, 190-193
- message, 203, 305
- message authentication code, 86, 304
- message digest, 232
- Miller-Rabin algorithm, 129, 130, 137, 136-138
- error probability of, 138
- mod operator, 3
- modular exponentiation, 127
- square-and-multiply algorithm, 127, 127, 131
- modular multiplication, 126
- modular reduction, 3
- modulus, 3
- monoalphabetic cryptosystem, 12
- monotone circuit, 333
- monotone circuit construction, 333, 335
- information rate, 343
- monotone property, 332
- Monte Carlo algorithm, 129, 129, 374
- error probability of, 129
- no-biased, 129
- unbiased, 374, 374-377
- yes-biased, 129
- MTI Key Agreement Protocol, 274, 273-276
- Multiplicative Cipher, 65, 65
- multiplicative identity, 4
- multiplicative inverse, 10
- mutual index of coincidence, 33
- next bit predictor, 365-370
- NP-complete problem, 44, 191, 193, 400, 404
- Okamoto Identification Scheme, 291, 290-295
- One-time Pad, 50, 50
- one-way function, 116, 213, 234
- trapdoor, 116
- oracle, 139
- orthogonal array, 314, 313-320
- bounds, 315-318
- constructions, 318-319
- output feedback mode, 83, 85, 362
- passive adversary, 258
- perfect secrecy, 48, 44-51
- perfect secret sharing scheme, 332, 339, 349
- periodic stream cipher, 21
- permutation, 2
- Permutation Cipher, 18, 17-20
- permutation matrix, 19
- plaintext, 1, 20, 378
- polyalphabetic cryptosystem, 13
- polynomial
- congruence of, 180
- degree of, 180
- division, 180
- irreducible, 181
- modular reduction of, 181
- polynomial equivalence, 126
- prefix-free encoding, 54
- previous bit predictor, 373
- primality testing, 129-138
- prime, 9
- Prime number theorem, 129, 135
- primitive element, 123
- principal square root, 373, 379
- private-key cryptosystem, 114
- probabilistic algorithm, 129
- probabilistic encryption, 377-382
- probabilistic public-key cryptosystem, 378
- probability, 45
- conditional, 45
- joint, 45
- product cryptosystem, 64, 64-67
- proof of forgery algorithm, 224
- proof of knowledge, 285
- proper 3-coloring, 401
- protocol failure, 156, 158, 208
- prover, 385
- pseudo-random bit generator, 359, 359-377
- pseudo-square, 370
- public-key cryptosystem, 114
- probabilistic, 378
- quadratic non-residue, 130
- Quadratic Non-residues Interactive Proof System, 408
- quadratic reciprocity, 132
- quadratic residue, 130
- Quadratic Residues, 130, 130, 371, 370-371, 374, 375, 377, 396, 399, 406
- Quadratic Residues Interactive Proof System, 396, 396-397
- Rabin Cryptosystem, 147, 145-150
- security of, 149-150
- rank, 226
- redundancy of a natural language, 61
- reject, 385
- relative shift, 33
- relatively prime, 9
- replay attack, 269
- response, 385
- ring, 4, 180
- round, 385
- RSA Cryptosystem, 114, 124, 124
- attacks on, 138-145
- bit security of, 144-145
- implementation of, 125-128
- RSA Generator, 362, 362-363
- RSA Signature Scheme, 203, 204
- Schnorr Identification Scheme, 286, 284-289, 295
- Schnorr Signature Scheme, 301
- search problem, 190
- secret sharing scheme, 326-357
- decomposition construction, 353-357
- ideal, 343, 344, 346-348
- information rate, 342, 341-343, 349-355
- monotone circuit construction, 333-338
- threshold scheme, 326-331
- Secure Hash Standard, 247, 250-252
- security parameter, 284, 378
- seed, 359
- self-certifying public key, 276
- session key, 259
- Shamir Threshold Scheme, 327, 327-330, 343, 346
- share, 326
- Shift Cipher, 4, 3-7
- Shrinking Generator, 362
- signature, 203
- signature scheme, 203, 202-229
- constructed from identification
- scheme, 300
- fail-stop, 224-229
- one-time, 213-217, 228
- undeniable, 217-223
- signing algorithm, 203
- simulator, 390
- Solovay-Strassen algorithm, 133, 129-136
- error probability, 136, 134-136
- soundness, 288, 386
- source state, 304
- Sperner property, 215
- spurious keys, 61, 59-64
- expected number of, 63
- square-and-multiply algorithm, 127, 127, 131
- Station-to-station Protocol, 272, 271-273
- Stirlings formula, 68, 216
- stream cipher, 20, 20-24, 360
- cryptanalysis of, 37
- synchronous, 21, 85
- Subgroup Membership, 397
- Subgroup Membership Interactive Proof System, 398
- Subset Sum problem, 190, 190-191
- modular transformation, 192
- superincreasing, 191
- substitution, 305
- Substitution Cipher, 7, 7, 7-8
- cryptanalysis of, 27-31
- m-gram, 68
- synchronous stream cipher, 21, 85
- threshold scheme, 326, 326-331
- timestamping, 252-254
- transcript, 390
- Transposition Cipher, 17
- trapdoor, 116
- trigram, 25
- trusted authority, 258
- unconditional security, 45
- unicity distance, 63, 59-64
- van Heyst-Pedersen Signature Scheme, 225, 224-229
- Vandermonde matrix, 329
- determinant of, 329
- verification algorithm, 203
- verifier, 385
- Vernam One-time Pad, 50, 50
- Vigenere Cipher, 12, 12-13, 40
- cryptanalysis of, 31-36
- zero-knowledge interactive argument, 406, 405-407
- perfect, 407
- zero-knowledge interactive proof, 385
- computational, 398, 404, 400-404
- perfect, 393, 388-397
- perfect, for Vic, 391
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