Paper 2016/382 Original: eprint.iacr.org/2016/382 ↗
Faster elliptic-curve discrete logarithms on FPGAs
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.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2016-12-28: last updated
- 2016-04-15: published
- Short URL
- https://ia.cr/2016/382
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2016/382,
author = {Daniel J. Bernstein and Susanne Engels and Tanja Lange and Ruben Niederhagen and Christof Paar and Peter Schwabe and Ralf Zimmermann},
title = {Faster elliptic-curve discrete logarithms on FPGAs},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/382},
year = {2016},
url = {https://eprint.iacr.org/2016/382}
}