A simple unpredictable pseudo random number generator
SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Random Permutations from Logarithmic Signatures
Proceedings of the The First Great Lakes Computer Science Conference on Computing in the 90's
A Public Key Cryptosystem Based on Non-abelian Finite Groups
Journal of Cryptology
Pseudorandom generators based on subcovers for finite groups
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
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Random covers for finite groups have been introduced in Magliveras et al. (J Cryptol 15:285---297, 2002), Lempken et al. (J Cryptol 22:62---74, 2009), and Svaba and van Trung (J Math Cryptol 4:271---315, 2010) for constructing public key cryptosystems. In this article we describe a new approach for constructing pseudorandom number generators using random covers for large finite groups. We focus, in particular, on the class of elementary abelian 2-groups and study the randomness of binary sequences generated from these generators. We successfully carry out an extensive test of the generators by using the NIST Statistical Test Suite and the Diehard battery of tests. Moreover, the article presents argumentation showing that the generators are suitable for cryptographic applications. Finally, we include performance data of the generators and propose a method of using them in practice.