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ASIACRYPT
2001
Springer

An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves

14 years 3 months ago
An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves
We present an algorithm for counting points on superelliptic curves yr = f(x) over a finite field Fq 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(log3+ε 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.
Pierrick Gaudry, Nicolas Gürel
Added 28 Jul 2010
Updated 28 Jul 2010
Type Conference
Year 2001
Where ASIACRYPT
Authors Pierrick Gaudry, Nicolas Gürel
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