Cryptology ePrint Archive: Report 2020/697

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

F. Boudot and P. Gaudry and A. Guillevic and N. Heninger and 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.

Category / Keywords: public-key cryptography / cryptanalysis, factoring, discrete logarithm problem, number field sieve, implementation

Original Publication (in the same form): IACR-CRYPTO-2020

Date: received 10 Jun 2020, last revised 10 Jun 2020

Contact author: fabrice boudot at orange fr,pierrick gaudry@loria fr,aurore guillevic@inria fr,nadiah@cs ucsd edu,emmanuel thome@inria fr,paul zimmermann@inria fr

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Version: 20200610:213303 (All versions of this report)

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