Coding Theory and Cryptography 9780824704650

9780824704650-Coding-Theory-and-Cryptography
Auteur: D.R. Hankerson & D.G. HoffmanD.R. Hankerson & D.G. Hoffman
ISBN: 9780824704650
Druk: 2
Uitvoering: Hardcover
Uitgever: Taylor & Francis Inc

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Preface v
Part I: Coding Theory




Introduction to Coding Theory

1(26)




Introduction

1(1)




Basic assumptions

2(2)




Correcting and detecting error patterns

4(2)




Information rate

6(1)




The effects of error correction and detection

7(1)




Finding the most likely codeword transmitted

8(2)




Some basic algebra

10(1)




Weight and distance

11(1)




Maximum likelihood decoding

12(4)




Reliability of MLD

16(2)




Error-detecting codes

18(4)




Error-correcting codes

22(5)




Linear Codes

27(38)




Linear Codes

27(1)




Two important subspaces

28(2)




Independence, basis, dimension

30(5)




Matrices

35(2)




Bases for C = <S> and C⊥

37(4)




Generating matrices and encoding

41(4)




Parity-check matrices

45(3)




Equivalent codes

48(4)




Distance of a linear code

52(1)




Cosets

53(4)




MLD for linear codes

57(5)




Reliability of IMLD for linear codes

62(3)




Perfect and Related Codes

65(26)




Some bounds for codes

65(5)




Perfect codes

70(2)




Hamming codes

72(3)




Extended codes

75(2)




The extended Golay code

77(2)




Decoding the extended Golay code

79(3)




The Golay code

82(2)




Reed-Muller codes

84(4)




Fast decoding for RM (l, m)

88(3)




Cyclic Linear Codes

91(20)




Polynomials and words

91(5)




Introduction to cyclic codes

96(5)




Generating and parity check matrices for cyclic codes

101(3)




Finding cyclic codes

104(5)




Dual cyclic codes

109(2)




BCH Codes

111(16)




Finite fields

111(4)




Minimal polynomials

115(3)




Cyclic Hamming codes

118(2)




BCH codes

120(2)




Decoding 2 error-correcting BCH code

122(5)




Reed-Solomon Codes

127(32)




Codes over GF(2r)

127(2)




Reed-Solomon codes

129(6)




Decoding Reed-Solomon codes

135(6)




Transform approach to Reed-Solomon codes

141(7)




Berlekamp-Massey algorithm

148(5)




Erasures

153(6)




Burst Error-Correcting Codes

159(14)




Introduction

159(4)




Interleaving

163(7)




Application to compact discs

170(3)




Convolutional Codes

173(32)




Shift registers and polynomials

173(6)




Encoding convolutional codes

179(7)




Decoding convolutional codes

186(7)




Truncated Viterbi decoding

193(12)




Reed-Muller and Preparata Codes

205(22)




Reed-Muller codes

205(3)




Decoding Reed-Muller codes

208(5)




Extended Preparata codes

213(6)




Encoding extended Preparata codes

219(3)




Decoding extended Preparata codes

222(5)
Part II: Cryptography




Classical Cryptography

227(26)




Encryption schemes

228(2)




Symmetric-key encryption

230(8)




Feistel ciphers and DES

238(11)




The New Data Seal

240(3)




The Data Encryption Standard

243(6)




Notes

249(4)




Topics in Algebra and Number Theory

253(26)




Algorithms, complexity, and modular arithmetic

253(7)




Quadratic residues

260(4)




Primality testing

264(3)




Factoring and square roots

267(7)




Pollard's rho

267(2)




Random squares

269(2)




Square roots

271(3)




Discrete logarithms

274(3)




Baby-step giant-step

274(1)




Index calculus

275(2)




Notes

277(2)




Public-key Cryptography

279(28)




One-way and hash functions

280(4)




RSA

284(6)




Provable security

290(3)




ElGamal

293(4)




Cryptographic protocols

297(8)




Diffie-Hellman key agreement

298(1)




Zero-knowledge proofs

299(2)




Coin-tossing and mental poker

301(4)




Notes

305(2)
A The Euclidean Algorithm 307(4)
B Factorization of 1 + xn 311(2)
C Example of Compact Disc Encoding 313(4)
D Solutions to Selected Exercises 317(18)
Bibliography 335(8)
Index 343