Cryptographically Secure Pseudo-Random Number Generation (CS-PRNG) Design using Robust Chaotic Tent Map (RCTM)

Abstract: Chaos, a nonlinear dynamical system, favors cryptography due to their inherent sensitive dependence on the initial condition, mixing, and ergodicity property. In recent years, the nonlinear behavior of chaotic maps has been utilized as a random source to generate pseudo-random number generation for cryptographic services. For chaotic maps having Robust chaos, dense, chaotic orbits exist for the range of parameter space the occurrence of chaotic attractors in some neighborhoods of parameter space and the absence of periodic windows. Thus, the robust chaotic map shows assertive chaotic behavior for larger parameters space with a positive Lyapunov exponent. This paper presents a novel method to generate cryptographically secure pseudo-random numbers (CSPRNG) using a robust chaotic tent map (RCTM). We proposed a new set of equations featuring modulo and scaling operators that achieve vast parameter space by keeping chaotic orbit globally stable and robust. The dynamic behavior of the RCTM is studied first by plotting the bifurcation diagram that shows chaotic behavior for different parameters, which the positive Lyapunov exponent verifies. We iterated the RCTM to generate pseudo-random bits using a simple thresholding method. Various statistical tests are performed that ascertain the randomness of generated secure pseudo-random bits. It includes NIST 800-22 test suite, ENT statistical test suite, TestU01 test suite, key space analysis, key sensitivity analysis, correlation analysis, histogram analysis, and differential analysis. The proposed scheme has achieved larger key space as compared with existing methods. The results show that the proposed PRBG algorithm can generate CSPRNG.