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Area Flexible GF(2k) Elliptic Curve Cryptography Coprocessor

Adnan Abdul-Aziz

GutubComputer Engineering Department, King Fahd University of Petroleum and Minerals, SA 

Abstract: Elliptic Curve Cryptography (ECC) is popularly defined either over GF(p) or GF(2k). This research modifies a GF(p) multiplication algorithm to make it applicable for GF(2k). Both algorithms, the GF(p) and GF(2k), are designed in hardware to be compared. The GF(2k) multiplier is found to be faster and smaller. This GF(2k) 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(2k) ECC coprocessor.