The development of the number field sieve

H. W. Lenstra Jr. (auth.), Arjen K. Lenstra, Hendrik W. Lenstra Jr. (eds.)3540570136, 9783540570134, 0387570136

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.

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Table of contents :
The number field sieve: An annotated bibliography….Pages 1-3
Factoring with cubic integers….Pages 4-10
The number field sieve….Pages 11-42
The lattice sieve….Pages 43-49
Factoring integers with the number field sieve….Pages 50-94
Computing a square root for the number field sieve….Pages 95-102
A general number field sieve implementation….Pages 103-126