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 $\mathbb{F}_{q}$ 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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