Solving the Discrete Logarithm of a 113-Bit Koblitz Curve with an FPGA Cluster
Solving the Discrete Logarithm of a 113-Bit Koblitz Curve with an FPGA Cluster
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使用 FPGA 集群求解 113 位 Koblitz 曲线的离散对数
DOI：
10.1007/978-3-319-13051-4_22
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Paul Wolfger
中科院分区：
文献类型：
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作者：
Erich Wenger;Paul Wolfger
用现场可编程门阵列计算椭圆曲线的离散对数是一种众所周知的方法。然而，到目前为止，只有CPU集群成功地计算了新的椭圆曲线离散对数记录。本文提出了一种用于计算113位Koblitz曲线离散对数的高速FPGA实现。设计的核心是一个完全展开的、高度流水线的、自给自足的Pollard的Rho迭代函数。一个18核的Virtex-6 FPGA集群在外推24天内计算了113位Koblitz曲线的离散对数。到目前为止，还没有一次在如此短的时间内使用如此少的资源对如此大的Koblitz曲线进行攻击成功。
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.