dorsal/arxiv
View SchemaPeriodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
| Authors | L. Barash, L. N. Shchur |
|---|---|
| Categories | |
| ArXiv ID | physics/0409069 |
| URL | https://arxiv.org/abs/physics/0409069 |
| DOI | 10.1103/PhysRevE.73.036701 |
| Journal | Phys. Rev. E 73, 036701 (2006) |
Abstract
We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.
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"abstract": "We propose methods for constructing high-quality pseudorandom number\ngenerators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit\ntwo-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the\ninformation hidden. The single cat map provides the random properties expected\nfrom a good RNG and is hence an appropriate building block for an RNG, although\nunnecessary correlations are always present in practice. We show that\nintroducing hidden variables and introducing rotation in the RNG output,\naccompanied with the proper initialization, dramatically suppress these\ncorrelations. We analyze the mechanisms of the single-cat-map correlations\nanalytically and show how to diminish them. We generalize the Percival-Vivaldi\ntheory in the case of the ensemble of maps, find the period of the proposed RNG\nanalytically, and also analyze its properties. We present efficient practical\nrealizations for the RNGs and check our predictions numerically. We also test\nour RNGs using the known stringent batteries of statistical tests and find that\nthe statistical properties of our best generators are not worse than those of\nother best modern generators.",
"arxiv_id": "physics/0409069",
"authors": [
"L. Barash",
"L. N. Shchur"
],
"categories": [
"physics.comp-ph",
"cond-mat.stat-mech",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.73.036701",
"journal_ref": "Phys. Rev. E 73, 036701 (2006)",
"title": "Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation",
"url": "https://arxiv.org/abs/physics/0409069"
},
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