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

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Executive Summary

The authors 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 Fq 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 Lqg (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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