An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2

We present an algorithm to compute the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for odd characteristic. Given a genus g hyperelliptic curve defined over F2n , the average-case time complexity is O(g4+ n3+ ) and the average-case space complexity is O(g3 n3 ), whereas the worst-case time and space complexities are O(g5+ n3+ ) and O(g4 n3 ) respectively.

• Type: Journal
• Year: 2006
• Where: JOC
• Authors: Jan Denef, Frederik Vercauteren
• Keywords: Arbitrary Hyperelliptic Curve, Finite Field Fq, Hyperelliptic Curve, JOC 2006