On the Practical Performance of Hyperelliptic Curve Cryptosystems in Software Implementation

Yasuyuki SAKAI  Kouichi SAKURAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.4   pp.692-703
Publication Date: 2000/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
hyperelliptic curve cryptosystem,  efficient implementation,  jacobian,  lagrange reduction,  

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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 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 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.