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

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

F. Boudot, P. Gaudry, A. Guillevic, N. Heninger, E. Thomé, and 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.

Note: Update DOI.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in CRYPTO 2020
DOI: 10.1007/978-3-030-56880-1_3
Keywords: cryptanalysis factoring discrete logarithm problem number field sieve implementation
Contact author(s): fabrice boudot @ orange fr
pierrick gaudry @ loria fr
aurore guillevic @ inria fr
nadiah @ cs ucsd edu
emmanuel thome @ inria fr
paul zimmermann @ inria fr
History: 2020-08-17: last of 2 revisions; 2020-06-10: received; See all versions
Short URL: https://ia.cr/2020/697
License: CC BY

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},
      doi = {10.1007/978-3-030-56880-1_3},
      note = {\url{https://eprint.iacr.org/2020/697}},
      url = {https://eprint.iacr.org/2020/697}
}