[Resource Topic] 2008/066: High Performance Architecture for Elliptic Curve Scalar Multiplication over GF(2^m)

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High Performance Architecture for Elliptic Curve Scalar Multiplication over GF(2^m)

Authors: Junjie Jiang, Jing Chen, Jian Wang, Duncan S. Wong, Xiaotie Deng


We propose a new architecture for performing Elliptic Curve Scalar Multiplication (ECSM) on elliptic curves over GF(2^m). This architecture maximizes the parallelism that the projective version of the Montgomery ECSM algorithm can achieve. It completes one ECSM operation in about 2(m-1)( \lceil m/D \rceil +4)+m cycles, and is at least three times the speed of the best known result currently available. When implemented on a Virtex-4 FPGA, it completes one ECSM operation over GF(2^163) in 12.5us with the maximum achievable frequency of 222MHz. Two other implementation variants for less resource consumption are also proposed. Our first variant reduces the resource consumption by almost 50% while still maintaining the utilization efficiency, which is measured by a performance to resource consumption ratio. Our second variant achieves the best utilization efficiency and in our actual implementation on an elliptic curve group over GF(2^163), it gives more than 30% reduction on resource consumption while maintaining almost the same speed of computation as that of our original design. For achieving this high performance, we also propose a modified finite field inversion algorithm which takes only m cycles to invert an element over GF(2^m), rather than 2m cycles as the traditional Extended Euclid algorithm does, and this new design yields much better utilization of the cycle time.

ePrint: https://eprint.iacr.org/2008/066

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