Robust PRNG based on homogeneously distributed chaotic dynamics
Résumé
This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: T T L RC non-alternate, and T T L SC alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim two new nonlinear CPRNG: M T T L SC 2 and N T T L2 are proposed. The maps successfully passed numerous statistical, graphical and numerical tests, due to proposed ring coupling and injection mechanisms. 1. Introduction tremendous development of new IT technologies, e-banking, e-purchasing, etc. nowadays increases incessantly the needs for new and more secure cryptosystems. The latter are used for information encryption, pushing forward the demand for more efficient and secure pseudo-random number generators [1]. At the same time, chaotic maps show up as perfect candidates able to generate independent and secure pseudo-random sequences (used as information carriers or directly involved in the process of encryption/decryption). However, the majority of well-known chaotic maps are not naturally suitable for encryption [2] and most of them don't exhibit even satisfactory properties for encryption. Generally, it is known [3] that true randomness is only obtained using a nondeterministic physical process like radioactivity, pseudo-randomness corresponds to a mathematical algorithm satisfying statistical properties and chaos is limited to dynamical systems. Some authors [4] refer flawly to true or truly random numbers while they are involving only chaotic numbers in their articles. True randomness is never reproducible, which forbids the use of true random numbers in cryptographic algorithms which need synchronisation. Electronic circuits cannot be used because small variations in temperature change the characteristic function which models the behavior, therefore it could not be exactly reproduced. Therefore, we deal with pseudo-random number generator (PRNG)and in this aim we propose the original idea to couple tent and logistic map, and to add an injection mechanism to keep bounded the escaping orbits. In 1973, sir Robert May, a famous biologist introduced the nonlinear, discrete time dynamical system called logistic equation:
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