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Math 1 by syeda.m is a document available to read on EtoBox.
This document presents an algorithm for counting points on hyperelliptic curves over finite fields using Monsky-Washnitzer cohomology, achieving polynomial time complexity in the genus of the curve. The method involves computing a p-adic approximation of the characteristic polynomial of Frobenius, with a running time of O(g^4+ǫ n^3+ǫ) for curves with a rational Weierstrass point. The approach is shown to be broadly applicable to other algebraic varieties, potentially improving computational efficiency in al
- Author
- syeda.m
- Language
- EN