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Harder, Better, Faster, Stronger - Elliptic Curve Discrete Logarithm Computations on FPGAs

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If you have a question about this talk, please contact Robert Mullins .

Computing discrete logarithms takes time. It takes time to develop new algorithms, choose the best algorithms, implement these algorithms correctly and efficiently, keep the system running for several months, and, finally, publish the results. In this paper, we present a highly performant architecture that can be used to compute discrete logarithms of Weierstrass curves defined over binary fields and Koblitz curves using FPG As. We used the architecture to compute for the first time a discrete logarithm of the elliptic curve “sect113r1”, a previously standardized binary curve, using 10 Kintex-7 FPG As. To achieve this result, we investigated different iteration functions, used a negation map, dealt with the fruitless cycle problem, built an efficient FPGA design that processes 900 million iterations per second, and we tended for several months the optimized implementations running on the FPG As.

This talk is part of the Computer Laboratory Computer Architecture Group Meeting series.

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