Design and implementation of a novel cryptographically secure pseudorandom number generator
Juan Di Mauro, Eduardo Salazar, Hugo D. Scolnik
TL;DR
The paper presents a cryptographically secure pseudorandom number generator that blends sequences of modular exponentiations in safe-prime groups with Feistel-like nonlinear mixing. By reducing security to the hardness of the Discrete Logarithm Problem in carefully chosen groups and to the security of a PRF family, it provides a formal, game-based argument that the generator is secure assuming a secure RG primitive and PRF. Extensive statistical testing (NIST and TestU01 Crush) on multi-gigabit sequences demonstrates strong statistical properties, with practical performance on the order of a few thousand cycles per byte using 1024-bit safe primes. The work emphasizes portability and practical implementability, offering a cryptographically sound alternative to existing PRNGs for cryptographic and scientific use, while acknowledging the need for broader-scale testing and optimization in future work.
Abstract
The aim of this paper is to present a new design for a pseudorandom number generator (PRNG) that is cryptographically secure, passes all of the usual statistical tests referenced in the literature and hence generates high quality random sequences, that is compact and easy to implement in practice, of portable design and offering reasonable execution times. Our procedure achieves those objectives through the use of a sequence of modular exponentiations followed by the application of Feistel-like boxes that mix up bits using a nonlinear function. The results of extensive statistical tests on sequences of about 2^40 bits in size generated by our algorithm are also presented.