Relations Between Evaluations of NIST Tests and Lyapunov Exponents of Sequences Generated by the Piecewise Logistic Map over Integers In this paper, we focus on binary sequences obtained from piecewise logistic map over integers, and show the relation between the Lyapunov exponents of the maps and results of the NIST tests for the sequences. When the Lyapunov exponent is a negative value, we confirm that the branch diagram is sparse and the bit occurrence rate is also greatly biased. We also give a sample of that the positivenegative signs of the Lyapunov exponents mostly coincide on the evaluations of the NIST tests. From the branching diagram of the piecewise logistic map, we can moreover find that there are many good pseudorandom sequences generated by the individual control parameters of the map.

An Efficient Cryptosystem based on the LogisticChebyshev Map We utilise the LogisticChebyshev map as a cascade discretetime chaotic system to design a new form of a cryptosystem. Based on the LogisticChebyshev map, we present a novel method for constructing substitution boxes or Sboxes. The performance of the proposed Sbox scheme is investigated. Our results shows that the constructed Sbox has significant qualities for viable applications in security related domains. Additionally, we utilise a new pseudorandom number generator (PRNG) scheme for the purpose of generating keystreams for further encryption. We utilise this technique to demonstrate how a PRNG based chaotic system can be utilsied for image encryption. Our simulation results and analysis show that the proposed scheme has efficient performance for cryptographic based image processing applications.