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Copyrighted Material INDEX 3DES see Triple DES Encoding algorithm, 6 3G, 223, 276 Identifier, 197 4G, 276 Alphabet, 7, 9, 67, 69, 70, 73, 100, 102, 103, 107, 7-Zip, 126 114, 141, 211 Code alphabet, 7, 27, 100 A posteriori probability see APP Source alphabet, 7, 18, 27, 69, 71, 100, 104 A5/0, 26 Amount of information, 19, 20, 74, 101, 102, 215 A5/1, 26 Annihilator, 86, 87 A5/3, 143 APP, 244–249, 275, 334 Abelian see Group Arithmetic coding, 109, 110, 112, 116, 123, 131 Access control, 133 Arity, 70 Acrypta, 62 ARQ, 211, 218 Active byte, 160 ASCII, 27, 114, 119, 124, 170, 205, 310 AddRoundKey, 153, 154, 157, 160, 307, 309 7 bits, 124 ADFVGX code, 26 ASN.1, 197 Adleman see RSA Asymmetric cryptosystem, 138 ADSL, 210, 276 Asymmetric Digital Subscriber Line see ADSL Advanced Encryption Standard see AES Attack, 10, 26, 68, 77, 140, 144, 149, 166, 174, AES, 139, 144, 149, 151–160, 175, 179, 180, 185, 193, 322 200, 206, 307–309 Active attack, 139 Agrawal–Kayal–SaxenaCOPYRIGHTEDsee AKS Birthday MATERIAL attack see Yuval AKS, 45, 46 Brute force attack, 15, 140 Algorithm, 6 By repetition, 166 Complexity, 13 By signature, 173 Cryptographic algorithm, 26, 137, 141 Chosen ciphertext attack, 140 Decoding algorithm, 10 Chosen plaintext attack, 140 Foundations of Coding: Compression, Encryption, Error Correction, First Edition. Jean-Guillaume Dumas, Jean-Louis Roch, Éric Tannier and Sébastien Varrette. © 2015 John Wiley & Sons, Inc. Published 2015 by John Wiley & Sons, Inc. http://foundationsofcoding.imag.fr 345 346 INDEX Attack (Continued) Flip, 246 Ciphertext only attack, 140 Operation, 13 Common exponent attack, 173 Blahut, 258 Common modulus attack, 173 blake, 180 Differential analysis attack, 140 Block Factorial attack, 173 Cipher, 26, 144 Forced sequence attack, 140 Coding, 211 Known plaintext attack, 140 Blu-ray, 209, 210 Known sequence attack, 140 Bluetooth, 65, 143 Man-in-the-middle see Man-in-the-middle Blum-Blum-Shub, 192 Meet-in-the-middle see Meet-in-the-middle Blum-Micali, 66 On LCGs,85 Bose–Chaudhuri–Hocquenghem see BCH Passive attack, 139 Bound Yuval’s attack see Yuval Of Shannon, 217 Audio, 79, 134 Singleton bound, 233 Audio CD, 266, 268 BPA, 244–250, 334 Authentic, 187 Breaking, 68, 85, 150, 185, 315 Authentication, 75, 133, 175, 185–187, 198–200, BSC, 216, 217, 226, 242, 245, 248, 250, 324, 328, 206, 207, 318 329, 333 Unique authentication, 163 Burrows–Wheeler Transform see BWT Authenticator, 164 Burst of errors, 222 Auto-dual (code), 237 BWT, 120–122, 126 Automatic Repeat reQuest see ARQ bzip2, 122, 126 Aztec, 220 CA, 193, 195–198, 201–203, 321 Baby step, giant step, 95, 175 Caesar encryption, 9–11, 16, 26, 141 Basic Bank Account Number see BBAN CAIN, 138 Bayes Camellia, 152 Formula, 17, 18, 215, 283 Cantor–Zassenhaus, 252 BBAN, 219, 220 Capacity, 215–217, 225, 239, 256, 279, 324, 341 BCH, 249, 254–257 Caracteristic, 32 Primitive code, 256 Card Verification Key, 221 BEC, 250 Card Verification Value see CVV Belief Propagation Algorithm see BPA Cardinal number, 7, 30, 31, 38, 48, 49, 51, 52, Ben-Or, 50 100, 229, 232, 287, 289 Berlekamp–Massey, 254, 259 CBC, 27–30, 144, 159, 185, 188, 206, 284 Berlekamp-Massey, 65, 85, 88, 259 CBC-MAC, 185 Bézout, 32, 33, 35, 37, 38, 47, 48 CBC-MAC-AES, 185 Bézout, 157, 303, 316 CD ROM, 134, 210 BI-AWGNC, 250 Certificate, 193–201, 320, 321 Big-O,14 Chain of certificates, 193 Binary Check, 197 Channel, 211, 216, 217 Directory, 198 Exponentiation, 41, 57, 58, 61, 287 Extraction, 197 Weight see Hamming Issuing, 194 Binary Erasure Channel see BEC Repository, 195, 198 Binary Symmetric Channel see BSC User certificate, 201 Binary-input Additive White Gaussian Verification, 197, 199 Noise Channel see BI-AWGNC Certification Authority see CA Birthday Certification Revocation List see CRL Attack see Yuval CFB, 28, 30, 144, 185, 188, 206, 284 Paradox, 88 Channel coding, 209, 210 Bit, 13 Character, 7 Extraction, 144 Characteristic, 52–54, 149 INDEX 347 Checksum see Parity Constant, 14 Chinese remainder, 39, 40, 169, 286, 288, 315 Exponential, 14 Chroma, 129, 131, 132 Linear, 14 Chrominance see Chroma Logarithmic, 14 Cipher Block Chaining see CBC Polynomial, 14 Cipher FeedBack see CFB Quasilinear, 14 Ciphering, 137 Space complexity, 13 Ciphertext, 9, 12 Time complexity, 13 CIRC, 218, 261, 266, 268 compress, 125, 126 Cleartext, 137 Compression CML, 249 Dynamic compression, 114 Code Dynamic Huffman, 114 Arity of a code, 100 Lossless compression, 99, 128, 132 Auto-dual code, 237 Lossy compression, 23, 68, 74, 100, 128, 129, Bar code, 219, 220, 261 134, 135, 295 Cyclic code, 85, 250, 251, 253, 254, 258, 335 Confidentiality, 133, 138–140, 149, 186, 187, Depth of a code, 72 204 Dual code, 237 Confidentiality, Authentication, Integrity, Equivalent code, 227 Nonrepudiation see CAIN Error-correcting code, 210, 222, 269 Content Scrambling System see CSS Error-detecting code, 210, 218, 222 Control matrix, 235, 237, 257, 258 Extended code, 227, 228 Convolutional Golay code, 237 Non-systematic see NSC Hamming code, 230–232 Recursive see RSC Huffman code, 72, 73, 105, 106, 292 Systematic, 272 Instantaneous code, 70, 71, 73, 107, 118, 291 Coppersmith (Index Calculus), 96 Interleaved code, 263 Coprime, 39, 47, 48, 50, 156, 169, 173, 287 Irreducible code, 70 Correction Linear code, 160, 232–235, 238, 250, 269, By retransmission see ARQ 335 Direct correction, 211 Message Authentication see MAC Rate, 250, 271 Minitel code, 232 Counter Mode Encryption see CTR Non-ambiguous code, 69 Covertext, 23 Perfect code, 229, 230, 234 CRC, 205, 210, 218, 221–223 Punctured code, 228, 229, 234, 272, 330, 331, Credit card, 220 336 One-time credit card, 193 QR-code see QR-code One-time credit card, 193 Rate, 211, 212, 214, 215, 217, 224, 226–228, CRL, 195, 197, 198, 203 230, 231, 239, 272, 279, 326, 330, 341 Issuer, 195, 198 Recursive code see RSC Cross-Interleaved Reed–Solomon Code see CIRC Shortened code, 227–229, 234, 261, 262, 266, Cryptanalysis, 10, 11, 16, 84, 88, 90, 136, 139, 331, 332, 337, 338 149, 150, 159, 170, 177 Systematic code, 218, 224, 234, 235, 272 Frequency Analysis, 12, 171 Turbo code see Turbo Cryptographically secure see Generator Uniquely decodable code, 69 Cryptography Codebreaking, 10 Functionalities see CAIN Coded Modulation Library see CML Fundamental relation, 137 Codeword, 27, 54, 68–73, 211, 251, 291, 292 Services see CAIN Coding theory, 209 CSS,26 Collision, 74, 78, 88–90, 96, 159, 177, 182, 292, CTR, 27, 29, 30, 144, 185, 186, 283 318 Curve point, 58, 92, 95, 175, 191 Complexity, 12–14, 38, 41, 42, 45, 55, 63, 81, 82, CVV, 221 84, 86, 88, 95, 96, 128, 140, 149, 168, 176, Cyclic Redundancy Checks see CRC 181, 259, 282 Cyclic shift, 155, 250 348 INDEX DAT, 210 DVB-S2, 239, 249, 276 Data Encryption Standard see DES DVD, 26, 134, 209 Datamatrix, 220 Dating service, 166 E-mail DCT, 80, 129–133, 135, 301 Address, 192, 321 DDF, 252, 335 Client, 149 Decoding Securization, 201 Iterative decoding, 275 EAN-13, 218–220, 325 Nearest neighbor, 213 ECB, 27–30, 144, 159, 283 Decryption, 85 ECC, 175, 237, 332 Degree ECDSA, 190 Distribution polynomials, 241 Edwards curve, 61, 62 Of a polynomial, 46 EFM, 266 Of liberty, 67 El Gamal, 174, 175 Demultiplexor, 275 Electronic Code Book see ECB Depth Elliptic curve, 59 Of a code, 72 Elliptic curve, 58–61, 91–95, 175, 190, 191, 290 Of a tree, 72 Addition, 60 Of interleaving, 263 Doubling, 60 DES, 144–152, 159, 203, 206, 308 Elliptic Curve Cryptography see ECC DFT, 79–84, 129, 135, 221, 258–260 Elliptic Curve Digital Signature Algorithm Fast DFT,82 see ECDSA Dictionary, 123 Encoding Diffie-Hellman, 163, 194, 207 Adaptive encoding, 116 Key exchange protocol, 161, 162 Channel coding, 214 Public key, 168 Lattice, 270 Digest, 73 Lossless encoding see Compression Digital Right Management see DRM Lossy encoding see Compression Digital Signature Standard see DSS Noiseless encoding, 102 Digital Video Broadcasting see DVB With data loss, 11 dim, 34 Encryption, 133, 137 Dimension, 34 Almost secure encryption, 26, 145 Discrete Cosine Transform see DCT Asymmetric encryption, 168 Discrete Fourier Transform see DFT Mode, 27, 28, 144, 159 Discrete Logarithm Problem see DLP CBC,28 Disorder, 19 CFB,28 Distance, 222 CTR,29 Binary distance see Hamming ECB,27 Free distance, 271 OFB,29 Of a code, 225, 227 Perfect Encryption, 144 Distinct Degree Factorization see DDF Perfect encryption, 24, 141, 144, 149, 282, 304 Distortion, 209 Public key encryption, 168 Distribution Symmetric encryption, 141, 144, 145, 167, 168, Probability, 17 179, 185, 203 Uniform distribution, 19, 67, 216, 291 Unconditionally secure, 144 div, 32 Vernam encryption, 65 DivX, 134 Entropy, 19, 20, 22, 23, 25, 71, 101, 103, 120, DLP, 42, 58, 59, 174, 175 135, 140, 215, 283, 299 Double DES, 150 Conditional entropy, 19, 20, 215 Double-and-add, 61, 92, 191, 290 Induced entropy, 19 DRM, 23, 133 Joint entropy, 19, 20 DSS, 189, 190 Maximum entropy, 19 Dual (code), 237 Pool of entropy, 200 DVB, 239, 249, 276 Equivalence RSA-Factoring, 172 INDEX 349 Equivalence RSA-Factoring, 172 Characteristic of a field, 33 Equivalent (code), 227 Commutative field, 33, 34 Erased, 339 Finite field, 34, 43, 46, 48, 49, 51–57, 151, 232 Erasure, 260, 261, 266–268, 336, 338 Galois field, 48 Error Number field, 93 Correction, 211 Prime field, 33, 43, 46, 48, 49, 55, 56 Correction rate, 217, 226, 227, 250, 271 Splitting field, 84, 257 Detection, 211 Final entity, 193, 198 Detection rate, 226, 227 FinalRound, 154, 308 Rate, 8, 11, 209, 210, 215, 232, 239 Fingerprint, 73, 74, 89, 178, 179, 181, 182, 322 Syndrome, 236, 240, 242, 254, 257, 259, 268, Flash, 210 333, 338 Floyd, 90 estream,
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