Lecture Notes in Computer Science vol:5011 pages:296-311
ANTS edition:VIII location:Banff (Canada) date:17-22 May 2008
We apply deformation theory to compute zeta functions in a family of Ca,b curves over a finite field of small characteristic. The method combines Denef and Vercauteren's extension of Kedlaya's algorithm to Ca,b curves with Hubrechts' recent work on point counting on hyper elliptic curves using deformation. As a result, it is now possible to generate Ca,b curves suitable for use in cryptography in a matter of minutes.