Adaptive Chirikov Map for Pseudo-random Number Generation in Chaos-based Stream Encryption

Abstract

Information security plays an important role in modern technologies. Stream encryption is one of the common tools used for secure communications. The stream encryption algorithms require sequence with pseudo-random properties. The chaotic maps as a source of pseudo-random numbers with desired statistical properties is widely studied in the last decades. One of the known problems of the implementation of the chaos- based pseudo-random number generators implemented with low- precision arithmetic is a short period length. A possible solution of the short-cycle problem is a perturbation of the orbit or the nonlinearity parameter of the chaotic map for breaking out the cycle. In the present article, we propose a new approach for increasing the cycle length by changing the symmetry coefficient of the adaptive Chirikov map. We switch two values of the symmetry coefficient according to the output of the linear feedback shift register. We calculate the estimations of the period length for the perturbed and original Chirikov maps and confirm the efficiency of the proposed approach. Properties verification for the output sequences of generators based on the adaptive Cirikov map is carried out using correlation analysis methods and the NIST statistical test suite. The obtained results can be used in cryptography applications as well as in secure communication systems design.

Keywords

• chirikov map
• chaos-based encryption
• pseudo-random number generator
• nist tests
• correlation analysis
• adaptive map