[Resource Topic] 2014/368: Solving the Discrete Logarithm of a 113-bit Koblitz Curve with an FPGA Cluster

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Title:
Solving the Discrete Logarithm of a 113-bit Koblitz Curve with an FPGA Cluster

Authors: Erich Wenger, Paul Wolfger

Abstract:

Using FPGAs to compute the discrete logarithms of elliptic curves is a well-known method. However, until to date only CPU clusters succeeded in computing new elliptic curve discrete logarithm records. This work presents a high-speed FPGA implementation that was used to compute the discrete logarithm of a 113-bit Koblitz curve. The core of the design is a fully unrolled, highly pipelined, self-sufficient Pollard’s rho iteration function. An 18-core Virtex-6 FPGA cluster computed the discrete logarithm of a 113-bit Koblitz curve in extrapolated 24 days. Until to date, no attack on such a large Koblitz curve succeeded using as little resources or in such a short time frame.

ePrint: https://eprint.iacr.org/2014/368

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