Coding Theory and Cryptography The Essentials

ISBN-10: 0824704657
ISBN-13: 9780824704650
Edition: 2nd 2000 (Revised)
List price: $115.95 Buy it from $42.39
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Book details

List price: $115.95
Edition: 2nd
Copyright year: 2000
Publisher: CRC Press LLC
Publication date: 8/4/2000
Binding: Hardcover
Pages: 368
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 1.848

Preface
Coding Theory
Introduction to Coding Theory
Introduction
Basic assumptions
Correcting and detecting error patterns
Information rate
The effects of error correction and detection
Finding the most likely codeword transmitted
Some basic algebra
Weight and distance
Maximum likelihood decoding
Reliability of MLD
Error-detecting codes
Error-correcting codes
Linear Codes
Linear codes
Two important subspaces
Independence, basis, dimension
Matrices
Bases for C = [S] and C[superscript perpendicular, bottom]
Generating matrices and encoding
Parity-check matrices
Equivalent codes
Distance of a linear code
Cosets
MLD for linear codes
Reliability of IMLD for linear codes
Perfect and Related Codes
Some bounds for codes
Perfect codes
Hamming codes
Extended codes
The extended Golay code
Decoding the extended Golay code
The Golay code
Reed-Muller codes
Fast decoding for RM(1, m)
Cyclic Linear Codes
Polynomials and words
Introduction to cyclic codes
Generating and parity check matrices for cyclic codes
Finding cyclic codes
Dual cyclic codes
BCH Codes
Finite fields
Minimal polynomials
Cyclic Hamming codes
BCH codes
Decoding 2 error-correcting BCH code
Reed-Solomon Codes
Codes over GF(2[superscript r])
Reed-Solomon codes
Decoding Reed-Solomon codes
Transform approach to Reed-Solomon codes
Berlekamp-Massey algorithm
Erasures
Burst Error-Correcting Codes
Introduction
Interleaving
Application to compact discs
Convolutional Codes
Shift registers and polynomials
Encoding convolutional codes
Decoding convolutional codes
Truncated Viterbi decoding
Reed-Muller and Preparata Codes
Reed-Muller codes
Decoding Reed-Muller codes
Extended Preparata codes
Encoding extended Preparata codes
Decoding extended Preparata codes
Cryptography
Classical Cryptography
Encryption schemes
Symmetric-key encryption
Feistel ciphers and DES
The New Data Seal
The Data Encryption Standard
Notes
Topics in Algebra and Number Theory
Algorithms, complexity, and modular arithmetic
Quadratic residues
Primality testing
Factoring and square roots
Pollard's rho
Random squares
Square roots
Discrete logarithms
Baby-step giant-step
Index calculus
Notes
Public-key Cryptography
One-way and hash functions
RSA
Provable security
ElGamal
Cryptographic protocols
Diffie-Hellman key agreement
Zero-knowledge proofs
Coin-tossing and mental poker
Notes
The Euclidean Algorithm
Factorization of 1 + x[superscript n]
Example of Compact Disc Encoding
Solutions to Selected Exercises
Bibliography
Index

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