Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment

F.  Boudot; P.  Gaudry; A.  Guillevic; N.  Heninger; E.  Thomé; P.  Zimmermann

Paper 2020/697 Original: eprint.iacr.org/2020/697 ↗

Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment

F. Boudot

P. Gaudry

A. Guillevic

N. Heninger

E. Thomé

P. Zimmermann

Abstract

We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorization of RSA-768 in 2009 and a 768-bit discrete logarithm computation in 2016. Our two computations at the 795-bit level were done using the same hardware and software, and show that computing a discrete logarithm is not much harder than a factorization of the same size. Moreover, thanks to algorithmic variants and well-chosen parameters, our computations were significantly less expensive than anticipated based on previous records. The last page of this paper also reports on the factorization of RSA-250.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2020-08-17: last updated; 2020-06-10: published
Short URL: https://ia.cr/2020/697
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2020/697,
      author = {F.  Boudot and P.  Gaudry and A.  Guillevic and N.  Heninger and E.  Thomé and P.  Zimmermann},
      title = {Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/697},
      year = {2020},
      url = {https://eprint.iacr.org/2020/697}
}