Smooth ideals in hyperelliptic function fields

Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over finite fields. Some of them have a provable subexponential running time and are using the fact that smooth reduced ideals are sufficiently dense. We explicitly show how these density results can be derived. All proofs are purely combinatorial and do not exploit analytic properties of generating functions.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Andreas Enge, Andreas Stein
• Keywords: Discrete Logarithm Problem, Finite Fields, MOC 2002, Provable Subexponential Running