Abstract
We investigate the discrete logarithm problem over jacobian varieties of hyperelliptic curves suitable for public-key cryptosystems, and clarify practical advantages of hyperelliptic cryptosystems compared to the elliptic cryptosystems and to RSA. We focus on the curves defined over the ground field of characteristic 2, and we present hyperelliptic cryptosystems from the jacobian associated with curves C : v 2 + v=u 2g+1 of genus g=3 and 11, which are secure against the known attacks. We further discuss the efficiency in implementation of such secure hyperelliptic cryptosystems.
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A part of this work was done while visiting in Columbia Univ. Computer Science Dept. from September 1997 for one year.
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Sakai, Y., Sakurai, K., Ishizuka, H. (1998). Secure hyperelliptic cryptosystems and their performance. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 1998. Lecture Notes in Computer Science, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054023
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DOI: https://doi.org/10.1007/BFb0054023
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