New factorization algorithm based on a continuous representation of truncated Gauss sums
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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 language | English |
|---|---|
| Pages (from-to) | 2125-2132 |
| Journal | Journal of Modern Optics |
| Volume | 56 |
| Issue number | 18-19 |
| DOIs | |
| Publication status | Published - 20 Oct 2009 |
| Externally published | Yes |
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