A cutting-edge approach to generate random bit sequence with confound chaotic maps

Abstract

A random number sequence is a sequence of numbers that exhibit statistical randomness. In other words, all numbers in the sequence have an equal chance and it’s hard to predict the next number in the sequence. They are most commonly used in cryptography to strengthen the security. Same key can be used by sender and receiver to generate the same set of random numbers. The pseudo-random number generation is an important task in computer science with various security features. There are 2 types of random number generators; they are True Random Number Generators (TRNG) and Pseudo Random Number Generators (PRNG). In recent years, PRNGs are implemented in hardware or software using chaotic maps. Some of the chaotic maps used in PRNG are Logistic map, Lorenz map, Henon map, Skew Tent map, Saw tooth map, etc. The Tinker Bell map is a discrete-time chaotic dynamical system with four system parameters. It is a most commonly studied examples of dynamical systems that exhibit chaotic behaviour. Chaotic maps possess several drawbacks such as the discontinuity of ranges, non-uniform distribution, periodicity in chaotic range, and small key space. In this PRNG, the numbers are generating in an unpredictable manner. To improve the uniform distribution and periodicity in random number generation, combination of Logistic and Tinker bell map is proposed. The Logistic map is a polynomial mapping. The Tinker bell map is known to have shorter periods. It is notable for having chaotic solutions for certain parameter values and initial conditions. In the proposed work, the Tinker bell map perturbs Logistic map to increase the chaotic behaviour of Logistic map. Output of the Logistic map is taken as Pseudo random bit sequence or Pseudo random number. NIST statistical test suite is used to verify the randomness of the generated random sequence.