Primality Testing and Integer Factorization in Public-Key Cryptography

By: Song Y. Yan

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Hardcover | 1 December 2008 | Edition Number 2

At a Glance

Hardcover
392 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 15.88 x 2.54

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Preface to the Second Edition.- Preface to the First Edition.- Number-Theoretic Preliminaries.- Problems in Number Theory. Divisibility Properties. Euclid's Algorithm and Continued Fractions. Arithmetic Functions. Linear Congruences. Quadratic Congruences. Primitive Roots and Power Residues. Arithmetic of Elliptic Curves. Chapter Notes and Further Reading.- Primality Testing and Prime Generation.- Computing with Numbers and Curves. Riemann Zeta and Dirichlet L Functions. Rigorous Primality Tests. Compositeness and Pseudoprimality Tests. Lucas Pseudoprimality Test. Elliptic Curve Primality Tests. Superpolynomial-Time Tests. Polynomial-Time Tests. Primality Tests for Special Numbers. Prime Number Generation. Chapter Notes and Further Reading.- Integer Factorization and Discrete Logarithms.- Introduction. Simple Factoring Methods. Elliptic Curve Method (ECM). General Factoring Congruence. Continued FRACtion Method (CFRAC). Quadratic Sieve (QS). Number Field Sieve (NFS). Quantum Factoring Algorithm. Discrete Logarithms. kth Roots. Elliptic Curve Discrete Logarithms. Chapter Notes and Further Reading.- Number-Theoretic Cryptography.- Public-Key Cryptography. RSA Cryptosystem. Rabin Cryptography. Quadratic Residuosity Cryptography. Discrete Logarithm Cryptography. Elliptic Curve Cryptography. Zero-Knowledge Techniques. Deniable Authentication. Non-Factoring Based Cryptography. Chapter Notes and Further Reading.- Bibliography.- Index.- About the Author.

Industry Reviews

From the reviews of the second edition:

"The well-written and self-contained second edition 'is designed for a professional audience composed of researchers practitioners in industry.' In addition, 'this book is also suitable as a secondary text for graduate-level students in computer science, mathematics, and engineering,' as it contains about 300 problems. ... Overall ... 'this monograph provides a survey of recent progress in Primality Testing and Integer Factorization, with implications in factoring-based Public Key Cryptography.'" (Hao Wang, ACM Computing Reviews, April, 2009)

"This is the second edition of a book originally published in 2004. ... I used it as a reference in preparing lectures for an advanced cryptography course for undergraduates, and it proved to be a wonderful source for a general description of the algorithms. ... the book will be a valuable addition to any good reference library on cryptography and number theory ... . It contains descriptions of all the main algorithms, together with explanations of the key ideas behind them." (S. C. Coutinho, SIGACT News, April, 2012)

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Paperback

Published: 29th November 2010

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Preface to the Second Edition	p. ix
Preface to the First Edition	p. xi
Number-Theoretic Preliminaries	p. 1
Problems in Number Theory	p. 1
Groups, Rings and Fields	p. 13
Divisibility Properties	p. 23
Euclid's Algorithm and Continued Fractions	p. 34
Arithmetic Functions ¿(n), ¿(n), ¿(n), ¿(n), ¿(n)	p. 50
Linear Congruences	p. 63
Quadratic Congruences	p. 85
Primitive Roots and Power Residues	p. 103
Arithmetic of Elliptic Curves	p. 113
Chapter Notes and Further Reading	p. 124
Primality Testing and Prime Generation	p. 127
Computing with Numbers and Curves	p. 127
Riemann ¿ and Dirichlet L Functions	p. 139
Rigorous Primality Tests	p. 149
Compositeness and Pseudoprimality Tests	p. 157
Lucas Pseudoprimality Test	p. 168
Elliptic Curve Primality Tests	p. 172
Superpolynomial-Time Tests	p. 177
Polynomial-Time Tests	p. 182
Comparison of General Purpose Primality Tests	p. 188
Primality Tests for Special Numbers	p. 192
Prime Number Generation	p. 201
Chapter Notes and Further Reading	p. 207
Integer Factorization and Discrete Logarithms	p. 209
Introduction	p. 209
Simple Factoring Methods	p. 212
Elliptic Curve Method (ECM)	p. 221
General Factoring Congruence	p. 226
Continued FRACtion Method (CFRAC)	p. 230
Quadratic Sieve (QS)	p. 234
Number Field Sieve (NFS)	p. 239
Quantum Factoring Algorithm	p. 251
Discrete Logarithms	p. 257
kth Roots	p. 270
Elliptic Curve Discrete Logarithms	p. 278
Chapter Notes and Further Reading	p. 285
Number-Theoretic Cryptography	p. 287
Public-Key Cryptography	p. 287
RSA Cryptosystem	p. 292
Security and Cryptanalysis of RSA	p. 301
Rabin Cryptography	p. 314
Quadratic Residuosity Cryptography	p. 320
Discrete Logarithm Cryptography	p. 326
Elliptic Curve Cryptography	p. 331
Zero-Knowledge Techniques	p. 338
Deniable Authentication	p. 341
Non-Factoring Based Cryptography	p. 346
Chapter Notes and Further Reading	p. 351
Bibliography	p. 353
Index	p. 367
About the Author	p. 373
Table of Contents provided by Ingram. All Rights Reserved.

Primality Testing and Integer Factorization in Public-Key Cryptography

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Hardcover

Industry Reviews

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