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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.
https://hal.inria.fr/inria-00383941
Contributor : Andreas Enge <>
Submitted on : Sunday, December 20, 2009 - 12:24:14 PM
Last modification on : Wednesday, October 14, 2020 - 3:54:03 PM
Long-term archiving on: : Thursday, September 23, 2010 - 10:58:09 AM
Contributor : Andreas Enge <>
Submitted on : Sunday, December 20, 2009 - 12:24:14 PM
Last modification on : Wednesday, October 14, 2020 - 3:54:03 PM
Long-term archiving on: : Thursday, September 23, 2010 - 10:58:09 AM
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