Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals (Q2759101)

The paper deals with aperiodic pseudorandom number generators (APRNGs), the novelty of which consists in using quasicrystals to combine several PRNGs. Unfortunately, it is known that this binary sequences has bad statistical properties. In the design suggested in this paper, the aperiodic sequence is used to combine two suitably chosen linear congruential generators (LCGs) and form an infinite aperiodic sequence with good statistical properties. Indeed, the aperiodic binary sequence is used to break the periodicity of LCGs while LCGs are used to eliminate the nonuniformity of the binary sequence. NEWLINENEWLINENEWLINEAn implementation and a statistical study of APRGNs are not treated in this paper. According to the authors, the prime motivation for this research was the use of quasicrystal generation in cryptographic systems. The design and study presented here is a first step in the building of such a cryptographic system.