The Development of the Number Field Sieve

by Arjen K. Lenstra (Editor), Hendrik W. Lenstra Jr. (Editor)

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.

Genres: Mathematics

148 pages, Paperback

First published August 30, 1993

Reviews

[Dan · Rating 3 out of 5]

This book is not the best place to learn about the general number field sieve for the first time. But it is a good way to see how the sieve was developed over time and when the various parts of the algorithm were introduced. It also helps illustrate the differences between the GNFS and the SNFS factoring algorithms.

I read this book because I was doing a project on the General Number Field Sieve for an algebraic number theory class.

UPDATE: I got this book from the library again and used it to implement the Lattice Sieve for a course project in a computational number theory course.