Bit-parallel coprocessor for standard ECC-GF(2m) on FPGA

This paper presents the design of a high-speed coprocessor for Elliptic Curve Cryptography over binary Galois Field (ECC- GF(2m)). The purpose of our coprocessor is to accelerate the scalar multiplication performed over elliptic curve points represented by affine coordinates in polynomial basis. Our method consists of using elliptic curve parameters over GF(2163) in accordance with international security requirements to implement a bit-parallel coprocessor on field-programmable gate-array (FPGA). Our coprocessor performs modular inversion by using a process based on the Stein's algorithm. Results are presented and compared to results of other related works. We conclude that our coprocessor is suitable for comparing with any other ECC-hardware proposal, since its speed is comparable to projective coordinate designs.