Analysis of the Logistic and Skew Tent Map for Smart Coupling over a Finite Field

International audienceChaotic maps have been proved to be efficient in the design of pseudo- random number generator (PRNG). However, the great majority of chaotic maps use real numbers. Due to the high sensitivity of chaos and the finite precision nature of digital device, when a PRNG based on real numbers is numerically implemented, quantization and round-off errors may occur and consequently lead to security breach. Besides, initial conditions and parameters of chaotic maps constitute the seed of a PRNG and pseudo-chaotic behavior has to be guaranteed for all initial conditions. Logistic map and skew tent map are supposed to exhibit good chaos with well defined parameters, but in some particular initial conditions, their trajectories will be trapped into fixed points and lose the chaos quality. For this, we analyze logistic and skew tent map from the perspective of inverse maps in order to find all these unexpected seeds (fixed points and their preimages). To overcome the drawbacks caused by real numbers, a robust PRNG scheme based on a smart coupling of integer chaotic maps over a 32−bit finite field is proposed in this paper. The coupling method can improve the nonlinear dynamics and enhance the randomness efficiently. Simulation results have demonstrated that the proposed PRNG can produce pseudo-random numbers and this PRNG is suitable for encryption systems or other engineering applications