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Journal Articles Journal of Cryptology Year : 2011

An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves

Abstract

We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields $\FF_q$ are arbitrary, but their sizes should not grow too fast compared to the genus. For such families, the group structure and discrete logarithms can be computed in subexponential time of $L_{q^g}(1/3, O(1))$. The runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve.
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Dates and versions

inria-00383941 , version 1 (13-05-2009)
inria-00383941 , version 2 (20-12-2009)

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Cite

Andreas Enge, Pierrick Gaudry, Emmanuel Thomé. An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves. Journal of Cryptology, 2011, 24, pp.24-41. ⟨10.1007/s00145-010-9057-y⟩. ⟨inria-00383941v2⟩
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