An Efficient Multiplier/Divider Design for Elliptic Curve Cryptosystem over GF(2m)

Using the concept of reciprocal polynomial, this paper shows that a field multiplication over GF(2 m ) can be implemented by extended Stein's algorithm, one of the algorithms used to accomplish division. In this way, a field multiplier can be efficiently embedded into a divider with very little hardware overhead for operand selection based on a fundamental change at the algorithmic level. When applying the developed combined multiplication and division (CMD) algorithm to Elliptic Curve Cryptography (ECC) using affine coordinates, we achieve about 13.8% reduction on the area requirement with almost no performance degradation compared to the one implemented with two distinct components. Experimental results also demonstrate that not only our CMD circuit has the area advantage (up to 12.7%) in comparison with other low-cost design but also the resulting area-efficient design of ECC system exhibits considerable improvement on the area-time (AT) complexity of previous work.