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

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 log q for a positive constant is given by O e 5 6 1+ 3 2 + 3 2 +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.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Andreas Enge
• Keywords: Discrete Logarithm Problem, Expected Running Time, Finite Field, MOC 2002