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The development of the number field sieve

โœ Scribed by H. W. Lenstra Jr. (auth.), Arjen K. Lenstra, Hendrik W. Lenstra Jr. (eds.)

Book ID
127453356
Publisher
Springer
Year
1993
Tongue
English
Weight
1 MB
Edition
1
Category
Library
City
Berlin; New York
ISBN
3540478922

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โœฆ Synopsis

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.

โœฆ Subjects

Combinatorics

๐Ÿ“œ SIMILAR VOLUMES

The Development of the Number Field Siev
The Development of the Number Field Sieve
โœ Arjen K. Lenstra, Hendrik W.Jr. Lenstra ๐Ÿ“‚ Library ๐Ÿ“… 1993 ๐Ÿ› Springer ๐ŸŒ English โš– 127 KB

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 fo

Development of the Number Field Sieve
Development of the Number Field Sieve
โœ Lenstra H. W. ๐Ÿ“‚ Library ๐Ÿ“… 1993 ๐ŸŒ English โš– 611 KB

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 fo

Modifications to the Number Field Sieve
Modifications to the Number Field Sieve
โœ Don Coppersmith ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Springer ๐ŸŒ English โš– 469 KB

I-LLMP'I and Buhler et al. I'BLP], is a new routine for factoring integers. We present here a modification of that sieve. We use the fact that certain smoothness computations can be reused, and thereby reduce the asymptotic running time of the Number Field Sieve. We also give a way to precompute tab