Cryptography-Based Chaos via Geometric Undersampling of Ring-Coupled Attractors

17 pages, 19 figuresInternational audienceWe propose a new mechanism for undersampling chaotic numbers obtained by the ringcoupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows thebuilding of a PRNG which passes all NIST Test.This new geometric undersampling is very effective for generating 2 parallel streams of pseudorandomnumbers, as we show, computing carefully their properties, up to sequences of 10^12consecutives iterates of the ring coupled mapping which provides more than 3.35 x 10^10 randomnumbers in very short time. Both 3 and 4 dimension cases can be managed in the same way.In addition we recall a novel method of noise-resisting ciphering. The originality lies in the use ofa chaotic pseudo-random number generator: several co-generated sequences can be used at differentsteps of the ciphering process, since they present the strong property of being uncorrelated. Eachletter of the initial alphabet of the plain text is encoded as a subinterval of [-1,1]. The bounds ofeach interval are defined in function of the known bound of the additive noise. A pseudo-randomsequence is used to enhance the complexity of the ciphering. The transmission consists of asubstitution technique inside a chaotic carrier, depending on another cogenerated sequence. Thisnovel noise-resisting ciphering method can be used with geometric undersampling when 4mappings are coupled