Abstract
We apply deformation theory to compute zeta functions in a family of C a,b curves over a finite field of small characteristic. The method combines Denef and Vercauteren’s extension of Kedlaya’s algorithm to C 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 a,b curves suitable for use in cryptography in a matter of minutes.
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Castryck, W., Hubrechts, H., Vercauteren, F. (2008). Computing Zeta Functions in Families of C a,b Curves Using Deformation. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_20
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DOI: https://doi.org/10.1007/978-3-540-79456-1_20
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