Cryptology ePrint Archive: Report 2014/653

Mersenne factorization factory

Thorsten Kleinjung and Joppe W. Bos and 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.

Category / Keywords: implementation / Mersenne numbers, factorization factory, special number field sieve, block Wiedemann algorithm

Original Publication (with minor differences): IACR-ASIACRYPT-2014

Date: received 22 Aug 2014, last revised 14 Sep 2014

Contact author: akl at epfl ch

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Version: 20140915:050234 (All versions of this report)

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