A compact finite field processor over GF(2m) for elliptic curve cryptography

This paper proposes a compact finite field processor over GF(2^m) using polynomial basis. The proposed processor uses the extended Euclidean algorithm for field division and the LSB-first procedure for field multiplication. Addition, multiplication, and division are implemented directly sharing a common datapath hardware. The presented processor accepts an external irreducible polynomial and allows several field sizes with small area overhead The proposed processor requires (6m²+16m+11m┌m/8┐-16┌m/8┐-17) cycles for elliptic curve scalar multiplication over GF(2^m) using double-addition method We were able to implement a finite field processor over GF(2¹⁹²) with 16,847 gate counts.