Flexible FPGA-Based Architectures for Curve Point Multiplication over GF(p)

Abstract

Elliptic curve cryptography (ECC) is widely used as an efficient mechanism to secure private data using public-key protocols. This paper focuses on ECC over prime fields (GF(p)). We present a novel hardware architecture that calculates the elliptic curve point multiplication (ECPM). Our processor supports arbitrary prime fields with sizes up to 1024 bits. Different standards, which use curves in short Weierstrass form are supported. A Xilinx Virtex-7 implementation of the proposed hardware architecture takes from 0.69 ms for a 192-bit point multiplication up to 9.7 ms for 512-bit. The implementation takes only 20 DSP slices and 6816 LUTs. To the authors knowledge, this is the best performance reported so far for ECC point multiplication for arbitrary prime field curves without the use of FPGA reconfiguration.