A BBS-inspired pseudo-random number generator using elliptic curve-enhanced 2D chaotic map

To solve the problem of low output efficiency, insufficient dynamical complexity, and non-standardized parameter selection in the traditional Blum–Blum–Shub (BBS) generator, a BBS-inspired pseudo-random number generator (PRNG) is proposed. A two-dimensional Elliptic Curve Enhanced Chaotic Map (2D-ECHCM) is constructed by integrating a two-dimensional chaotic map with secp256k1 elliptic curve scalar multiplication. The chaotic properties of the 2D-ECHCM are evaluated through numerical simulations. Based on the 2D-ECHCM, a PRNG is designed, by embedding elliptic curve scalar multiplication into the chaotic iteration and outputting 256 bits per iteration, so that the output depends on both the chaotic state and the hardness of the elliptic curve discrete logarithm problem. Meanwhile, a parameter perturbation mechanism over a finite field is adopted to dynamically update the control parameter, thereby standardizing parameter generation and avoiding periodic degradation caused by fixed parameters. The simulation results indicated that the generator passes all applicable statistical tests and maintains a sufficiently large key space, showing strong randomness and capability to withstand brute-force attacks.