Abstract
Gaudry has described a new algorithm (Gaudry’s variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For hyperelliptic curves of small genus on finite field GF(q), Gaudry’s variant solves for the DLP in O(q 2 logγ(q)) time. This paper shows that C ab curves can be attacked with a modified form of Gaudry’s variant and presents the timing results of such attack. However, Gaudry’s variant cannot be effective in all of the C ab curve cryptosystems, this paper provides an example of a C ab curve that is unassailable by Gaudry’s variant.
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Arita, S. (2000). Gaudry’s Variant against C ab Curves. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 2000. Lecture Notes in Computer Science, vol 1751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46588-1_5
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DOI: https://doi.org/10.1007/978-3-540-46588-1_5
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