Efficient and Cryptographically Secure Generation of Chaotic Pseudorandom Numbers on GPU

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In this paper, the authors present a new PseudoRandom Number Generator (PRNG) on Graphics Processing Units (GPU). This PRNG is based on the so-called chaotic iterations. It is firstly proven to be chaotic according to the Devaney's formulation. They thus propose an efficient implementation for GPU that successfully passes the BigCrush tests, deemed to be the hardest battery of tests in TestU01. Experiments show that this PRNG can generate about 20 billion of random numbers per second on Tesla C1060 and NVidia GTX280 cards. It is then established that, under reasonable assumptions, the proposed PRNG can be cryptographically secure. A chaotic version of the Blum-Goldwasser asymmetric key encryption scheme is finally proposed. Randomness is of importance in many fields such as scientific simulations or cryptography.