From Chaos to Randomness via Geometric Undersampling

René Lozi (1) , Ina Taralova (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

We propose a new mechanism for undersampling chaotic numbers obtained by the ring coupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows the building of a PRNG which passes all NIST Test. This new geometric undersampling is very effective for generating 2 parallel streams of pseudo-random numbers, as we show, computing carefully their properties, up to sequences of one trillion consecutives iterates of the ring coupled mapping which provides more than 33.5 billions random numbers in very short time.

Mots clés: chaos; Pseudo Random Number generator; geometric undersampling

Domaines: Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]

René Lozi, Ina Taralova. From Chaos to Randomness via Geometric Undersampling. ESAIM: Proceedings and Surveys, 2014, ECIT 2012, 46, pp.177-195. ⟨10.1051/proc/201446015⟩. ⟨hal-00813087⟩