A pseudo-random number generator on elliptic curves over Galois field using 2D enhanced logistic-quadratic map

This study proposes a high-performance pseudo-random number generator (PRNG) that integrates a nondegenerate two-dimensional enhanced logistic-quadratic map (2D-ELQM) with operations on elliptic curves (ECs) over the finite field GF(p). First, we constructed the 2D-ELQM, which demonstrates a broader chaotic range and enhanced randomness and unpredictability. We conducted a dynamic analysis of the 2D-ELQM using various methods, including bifurcation and phase space diagrams, Lyapunov exponents (LE), Kolmogorov entropy (KE), sample entropy (SE), correlation dimension (CD) and TestU01. Subsequently, we combined the 2D-ELQM with EC operations over GF(p) to design a robust PRNG. Finally, we performed a series of experiments and comprehensive analyses to evaluate the performance of the proposed PRNG, with results indicating its effectiveness and potential application in cryptographic systems.