Over Fp vs. Over F2n and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems

Abstract

We consider the performance of hyperelliptic curve cryptosystems over the fields Fp vs. F2n. We analyze the complexity of the group law of the Jacobians JC(Fp) and JC(F2n) and compare their performance taking into consideration the effiectiveness of the word size (32- bit or 64-bit) of the applied CPU (Alpha and Pentium) on the arithmetic of the definition field. Our experimental results show that JC(F2n) is faster than JC(Fp) on an Alpha, whereas JC(Fp) is faster than JC(F2n) on a Pentium. Moreover, we investigate the algorithm of the Jacobian and the definition-field arithmetic to clarify our results from a practical point of view, with theoretical analysis.