International Arab Journal of Information Technology (IAJIT), vol. 4, no. 1, January, 2007.

Area Flexible GF(2^k) Elliptic Curve Cryptography Coprocessor

ADNAN ABDUL-AZIZ GUTUB

Computer Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, SAUDI ARABIA

gutub@kfupm.edu.sa

Abstract. Elliptic curve cryptography (ECC) is popularly defined either over GF(p) or GF(2^k). This research modifies a GF(p) multiplication algorithm to make it applicable for GF(2^k). Both algorithms, the GF(p) and GF(2^k) one, are designed in hardware to be compared. The GF(2^k) multiplier is found faster and small. This GF(2^k) multiplier is further improved to benefit in speed, it gained more than 40% faster speed with the cost of 5% more area. This multiplier hardware is furthermore adjusted to have area flexibility feature, which is used as the basic block in modeling a complete projective coordinate GF(2^k) ECC coprocessor.

Keywords. Elliptic curve cryptography, Modular multiplication, Area flexible multiplier, Projective coordinates arithmetic