On the practical performance of hyperelliptic curve cryptosystems in software implementation
We consider the performance of hyperelliptic curve cryptosystems over the fields F-p vs. F-2n. We analyze the complexity of the group law of the jacobians J(C)(F-p) and J(C)(F-2n) and compare their performance taking into consideration the effectiveness 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 J(C)(F-2n) is faster than J(C)(F-p) on an Alpha, whereas J(C)(F-p) is faster than J(C)(F-2n) 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.
hyperelliptic curve cryptosystem jacobian efficient implementation lagrange reduction