Mersenne factorization factory

Thorsten Kleinjung; Joppe W.  Bos; Arjen K.  Lenstra

Paper 2014/653 Original: eprint.iacr.org/2014/653 ↗

Mersenne factorization factory

Thorsten Kleinjung

Joppe W. Bos

Arjen K. Lenstra

Abstract

We present work in progress to fully factor seventeen Mersenne numbers using a variant of the special number field sieve where sieving on the algebraic side is shared among the numbers. It is expected that it reduces the overall factoring effort by more than 50\%. As far as we know this is the first practical application of Coppersmith's ``factorization factory'' idea. Most factorizations used a new double-product approach that led to additional savings in the matrix step.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
History: 2015-01-12: last updated; 2014-08-27: published
Short URL: https://ia.cr/2014/653
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2014/653,
      author = {Thorsten Kleinjung and Joppe W.  Bos and Arjen K.  Lenstra},
      title = {Mersenne factorization factory},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/653},
      year = {2014},
      url = {https://eprint.iacr.org/2014/653}
}