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


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.

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Available format(s)
Public-key cryptography
Publication info
Published by the IACR in CRYPTO 2020
cryptanalysisfactoringdiscrete logarithm problemnumber field sieveimplementation
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
2020-08-17: last of 2 revisions
2020-06-10: received
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      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{}},
      url = {}
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