Computing Zeta Functions in Families of C{sub}(a,b) Curves Using Deformation

摘要

We apply deformation theory to compute zeta functions in a family of C{sub}(a,b) curves over a finite field of small characteristic. The method combines Denef and Vercauteren's extension of Kedlaya's algorithm to C{sub}(a,b) curves with Hubrechts' recent work on point counting on hyperelliptic curves using deformation. As a result, it is now possible to generate C{sub}(a,b) curves suitable for use in cryptography in a matter of minutes.