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Conference Papers Year : 2001

An extension of Kedlaya's algorithm to superelliptic curves

Abstract

We present an algorithm for counting points on superelliptic curves y^r=f(x) over a finite field F_q of small characteristic different from r. This is an extension of an algorithm for hyperelliptic curves due to Kedlaya. In this extension, the complexity, assuming r and the genus are fixed, is O(log^{3+epsilon}q) in time and space, just like for hyperelliptic curves. We give some numerical examples obtained with our first implementation, thus proving that cryptographic sizes are now reachable.
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Dates and versions

inria-00514826 , version 1 (03-09-2010)

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Pierrick Gaudry, Nicolas Gürel. An extension of Kedlaya's algorithm to superelliptic curves. Asiacrypt, 2001, Gold Coast, Australia. pp.480-494, ⟨10.1007/3-540-45682-1_28⟩. ⟨inria-00514826⟩
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