A Fast Hardware Implementation of Elliptic Curve Cryptography

This paper describes an efficient hardware implementation of Elliptic Curve Cryptography (ECC) over GF(p). First it introduces an improved Montgomery modular multiplication method for efficient hardware implementation. The method velocity is faster compared to published implementations under equivalent cost. Then, the paper presents a fast mechanism of accelerating the elliptic curve point operation formulas by adopting modified Jacobian (Jm) coordinates. The modified formulas may reduce the number of multiplication in double procedure, so gain at total performance, because the double procedure appears often in point multiplication. The final result on VirtexII XC2V250 indicates the time of computing point multiplication of 256-bit ECC is 1.5 × 10^-3s.