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

This paper proposes a compact finite field processor over GF(2/sup 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 (6m/sup 2/+16m+11m/spl lceil/m/8/spl rceil/-16/spl lceil/m/8/spl rceil/-17) cycles for elliptic curve scalar multiplication over GF(2/sup m/) using double-addition method We were able to implement a finite field processor over GF(2/sup 192/) with 16,847 gate counts.