Skip to content

New factorization algorithm based on a continuous representation of truncated Gauss sums

Research output: Contribution to journalArticlepeer-review

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. Wölk et al. also published in this issue [Wölk, 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.
Original languageEnglish
Pages (from-to)2125-2132
JournalJournal of Modern Optics
Volume56
Issue number18-19
DOIs
Publication statusPublished - 20 Oct 2009
Externally publishedYes

Related information

Relations Get citation (various referencing formats)

ID: 5174593