Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Montgomery's work.

This book constitutes the refereed proceedings of the 10th International Conference on Information Security Conference, ISC 2007, held in Valparaiso, Chile, October 9-12, 2007.

The 28 revised full papers presented were carefully reviewed and selected from 116 submissions. The topics include Intrusion Detection, Digital Rights Management, Symmetric-Key Cryptography, Cryptographic Protocols and Schemes, Identity-Based Schemes, Cryptanalysis, DoS Protection, Software Obfuscation, Public-Key Cryptosystems, Elliptic Curves and Applications and Security Issues in Databases.

The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.