We investigate the discrete logarithm problem over jacobians of hyperelliptic curves suitable for public-key cryptosystems. We focus on the case when the definition field has small characteristic 2, 3, 5 and 7, then we present hyperelliptic cryptosystems that resist against all known attacks. We further implement our designed hyperelliptic cryptosystems over finite fields F2n in software on Alpha and Pentium-II computers. Our results indicate that if we choose curves carefully, hyperelliptic cryp-tosystems do have practical performance.
CITATION STYLE
Sakai, Y., & Sakurai, K. (1998). Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F2n. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1514, pp. 80–94). Springer Verlag. https://doi.org/10.1007/3-540-49649-1_8
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