Description
Book SynopsisIntended for advanced level students in computer science and mathematics, this key text, now in a brand new edition, provides a survey of recent progress in primality testing and integer factorization, with implications for factoring based public key cryptography.
Trade ReviewFrom 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)
Table of ContentsPreface 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.
