New factorization algorithm based on a continuous representation of truncated Gauss sums
Abstract
In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j>2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a single run without precalculating the ratio N/l, where l are all the possible trial factors. Continuous truncated exponential sums turn out to be a powerful tool for distinguishing factors from non-factors (we also suggest, with regard to this topic, to read an interesting paper by S. Woelk et al. also published in this issue [Woelk, Feiler, Schleich, J. Mod. Opt. in press]) and factorizing different numbers at the same time. We will also describe two possible M-path optical interferometers, which can be used to experimentally realize this algorithm: a liquid crystal grating and a generalized symmetric Michelson interferometer.
Cite
@article{arxiv.0811.1595,
title = {New factorization algorithm based on a continuous representation of truncated Gauss sums},
author = {Vincenzo Tamma and Heyi Zhang and Xuehua He and Augusto Garuccio and Yanhua Shih},
journal= {arXiv preprint arXiv:0811.1595},
year = {2015}
}
Comments
8 pages, 5 figures