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On a Non-periodic Shrinking Generator

Inese BerzinaJanis BulsEdmunds CersLiga KulesaRaivis Bets

subject

Discrete mathematicsPseudorandom number generatorSequenceRandom number generationSelf-shrinking generatorAutomata theoryTopologyElectronic mailStatistical hypothesis testingMathematicsShrinking generator

description

We present a new non-periodic random number generator based on the shrinking generator. The A-sequence is still generated using a LFSR, but the S-sequence is replaced by a finitely generated bi-ideal - a non-periodic sequence. The resulting pseudo-random sequence performs well in statistical tests. We show a method for the construction of an infinite number of finitely generated bi-ideals from a given A-sequence, such that the resulting sequence of the shrinking generator is nonperiodic. Further we prove the existence of what we call universal finitely generated bi-ideals that produce non-periodic words when used as the S-sequence of a shrinking generator for all non-trivial periodic A-sequences.

yearjournalcountryeditionlanguage
2011-09-012011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
https://doi.org/10.1109/synasc.2011.25