Faster discrete logarithms on FPGAs

D.J. Bernstein, S. Engels, T. Lange, R. Niederhagen, C. Paar, P. Schwabe, R. Zimmermann

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Abstract

This paper accelerates FPGA computations of discrete logarithms on elliptic curves over binary fields. As a toy example, this paper successfully attacks the SECG standard curve sect113r2, a binary elliptic curve that was not removed from the SECG standard until 2010 and was not disabled in OpenSSL until June 2015. This is a new size record for completed ECDL computations, using a prime order very slightly larger than the previous record holder. More importantly, this paper uses FPGAs much more efficiently, saving a factor close to 3/2 in the size of each high-speed ECDL core. This paper squeezes 3 cores into a low-cost Spartan-6 FPGA and many more cores into larger FPGAs. The paper also benchmarks many smaller-size attacks to demonstrate reliability of the estimates, and covers a much larger curve over a 127-bit field to demonstrate scalability.
Original languageEnglish
Place of Publications.l.
PublisherIACR
Number of pages16
Publication statusPublished - 2016

Publication series

NameCryptology ePrint Archive
Volume2016/382

Bibliographical note

IACR Cryptology ePrint Archive 2016/382

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