Cryptology ePrint Archive: Report 2007/205

A kilobit special number field sieve factorization

Kazumaro Aoki and Jens Franke and Thorsten Kleinjung and Arjen Lenstra and Dag Arne Osvik

Abstract: We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number $2^{1039}-1$. Although this factorization is orders of magnitude `easier' than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result shed new light on the feasibility of the latter computation.

Category / Keywords: implementation / factoring, number field sieve, block Wiedemann