Welcome to the resource topic for 2015/1104
Title:
Computing Jacobi’s \theta in quasi-linear time
Authors: Hugo Labrande
Abstract:Jacobi’s \theta function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of \theta(z, \tau), for z, \tau verifying certain conditions, with precision P in O(M(P) \sqrt{P}) bit operations, where M(P) denotes the number of operations needed to multiply two complex P-bit numbers. We generalize an algorithm which computes specific values of the \theta function (the theta-constants) in asymptotically faster time; this gives us an algorithm to compute \theta(z, \tau) with precision P in O(M(P) log P) bit operations, for any \tau \in F and z reduced using the quasi-periodicity of \theta.
ePrint: https://eprint.iacr.org/2015/1104
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