Fast Elliptic Curve Cryptography on FPGA

Abstract

This paper details the design of a new high-speed pipelined application-specific instruction set processor (ASIP) for elliptic curve cryptography (ECC) using field-programmable gate-array (FPGA) technology. Different levels of pipelining were applied to the data path to explore the resulting performances and find an optimal pipeline depth. Three complex instructions were used to reduce the latency by reducing the overall number of instructions, and a new combined algorithm was developed to perform point doubling and point addition using the application specific instructions. An implementation for the United States Government National Institute of Standards and Technology-recommended curve over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">163</sup> ) is shown, which achieves a point multiplication time of 33.05 s at 91 MHz on a Xilinx Virtex-E FPGA-the fastest figure reported in the literature to date. Using the more modern Xilinx Virtex-4 technology, a point multiplication time of 19.55 s was achieved, which translates to over 51120 point multiplications per second.