Efficient and cryptographically secure generation of chaotic pseudorandom numbers on GPU

Abstract

In this paper, we 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. We, 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.

A New Pseudorandom Bit Generator Based on Mixing Three-Dimensional Chen Chaotic System with a Chaotic Tactics

“…Addabbo proposed a random bit generator based on one-dimensional piecewiselinear chaotic map [12]. In [13], a new pseudorandom number generator on graphics processing units is presented, which is based on the chaotic iterations. Szczepanski presented a method of generating pseudorandom numbers by applying discrete chaotic dynamical systems which are ergodic or preferably mixing [14].…”

Developing Efficient Discrete Simulations on Multicore and GPU Architectures

“…Another interesting line to be investigated concerns speeding up the simulation by substituting the pseudorandom number generator by a different type of algorithm that can be faster. A good alternative can be an algorithm that generates pseudorandom numbers based on the calculation of chaotic sequences, such as those presented in [37,38]. Those results suggest that they could reduce the execution overhead, and thus contribute to a further speedup of the implementation of the studied laser CA model.…”

Design and Evaluation of Chaotic Iterations Based Keyed Hash Function

“…In this section, we consider that the strategy (S n ) n∈N is provided by a pseudorandom number generator, leading to a collection of so-called CIPRNGs [3]. The XOR CIPRNGs, for instance, is defined as follows [4]:…”

“…), Linear Congruential Generator (LCG), Mersenne Twister (MT), XORshift, RC4, or the Linear-Feedback Shift Register (LFSR). XOR CIPRNGs, which can be written as general chaotic iterations using the vectorial negation (see [4]), have been proven chaotic. They are able to pass all the most stringent statistical batteries of test, for well-chosen inputted generators.…”