J. P. Sorenson, ANTS-8 Poster Session Organizer in both the genus 4 and genus 5 case. We represent C as a plane model and if this model is of low degree the expected running time to recover all the coe cients of the L-polynomial can be reduced to O(q 4/3 ). This is an improvement on the previous best running time of O(q 3/2 ) for genus 4 and 2 ) for genus 5 given by Elkies in [2]. O(q Let L(t) = 2g ai ti be the L-polynomial of the curve of genus g. From the Theorem of Weil i=0 given in [5] we know that a0 = 1, a2g = q g and we have bounds on the other coe cients. A proof of Weil s Theorem can be found in [3]. Let JC (Fqk ) denote the group of Fpk -rational points on the Jacobian Variety of C. The algorithm consists of 2 stages. The rst stage is based upon Diem s Index Calculus algorithm as described in [1]. We use an adapted version of the main algorithm in [1] to compute the #JC (Fq ). This stage is the most time intensive and in
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A statistical look at maps of the discrete logarithm (abstract only)
Holden, Joshua; Lindle, Nathan
Follow ACM Communications in Computer Algebra
, Volume 42 (1-2)
Association for Computing Machinery – Jul 25, 2008
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