Computing theta functions in quasi-linear time in genus 2 and aboveReport as inadecuate




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1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry 2 University of Calgary

Abstract : We outline an algorithm to compute θz, τ in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θz, τ in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus g.

Keywords : Quasi-linear time complexity Borchardt mean Number Theory Theta Functions





Author: Hugo Labrande - Emmanuel Thomé -

Source: https://hal.archives-ouvertes.fr/



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