A Pseudo-Random Bit Generator Based on Three Chaotic Logistic Maps and IEEE 754-2008 Floating-Point Arithmetic

Michael François (1) , David Defour (2) , Pascal Berthomé (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
2 DALI - Digits, Architectures et Logiciels Informatiques

A novel pseudo-random bit generator (PRBG), combining three chaotic logistic maps is proposed. The IEEE 754-2008 standard for floating-point arithmetic is adopted and the binary64 double precision format is used. A more efficient processing is applied to better extract the bits, from outputs of the logistic maps. The algorithm enables to generate at each iteration, a block of 32 random bits by starting from three chosen seed values. The performance of the generator is evaluated through various statistical analyzes. The results show that the output sequences possess high randomness statistical properties for a good se- curity level. The proposed generator lets appear significant cryptographic qualities.

Mots clés: Logistic map; Chaotic map; Pseudo-random; PRBG

Domaines: Architectures Matérielles [cs.AR]

Michael François, David Defour, Pascal Berthomé. A Pseudo-Random Bit Generator Based on Three Chaotic Logistic Maps and IEEE 754-2008 Floating-Point Arithmetic. Theory and Applications of Models of Computation, Apr 2014, Chennai, India. pp.229-247, ⟨10.1007/978-3-319-06089-7_16⟩. ⟨hal-00985357⟩