Area Flexible GF(2k) Elliptic Curve Cryptography Coprocessor

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.