Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

Authors:
Andreas Enge
Affiliations:
-
Venue:
Mathematics of Computation
Year:
2002

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Abstract

We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for instances with genus g and underlying finite field Fq satisfying g ≥ ϑ log q for a positive constant ϑ is given by O(e(&frac5√6;(√1+3/2ϑ + √3/2ϑ) + o(1)) √(g log q) log (g log q)) The algorithm works over any finite field, and its running time does not rely on any unproven assumptions.