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Computing theta functions in quasi-linear time in genus 2 and above
number theory hyperelliptic curves theta functions
2016/2/24
We outline an algorithm to compute θ(z, τ ) in genus 2 in quasi-optimal time, borrowing
ideas from the algorithm for theta constants and the one for θ(z, τ ) in genus 1. Our
implementation shows a l...
Side Channel Attacks against Pairing over Theta Functions
pairing based cryptography Theta function
2014/3/12
In \cite{LuRo2010}, Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the us...
Fast genus 2 arithmetic based on Theta functions
Fast genus 2 arithmetic Theta functions hardware configurations
2009/3/4
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming
from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea
and derive fast formulae fo...
Somos Sequence Near-Addition Formulas and Modular Theta Functions
Somos Sequence Near-Addition Formulas Modular Theta Functions
2008/9/9
We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.