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

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

2009-05-13

arxiv.org/abs/0905.2177v2

Computer Science

Cryptography and Security

Scientific paper

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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