Pseudo-random number generator based on asymptotic deterministic randomness

TL;DR

This paper introduces a new pseudorandom number generator based on asymptotic deterministic randomness, combining piecewise linear maps and nonlinear transforms to enhance cryptographic security and resistance to attacks.

Contribution

It proposes a novel PRNG method using asymptotic deterministic randomness with detailed analysis of its properties and security advantages over existing chaos-based generators.

Findings

The generated sequences exhibit good statistical and random-like properties.

The method improves security against entropy and symbolic dynamics attacks.

Theoretical and experimental results confirm the effectiveness of the approach.

Abstract

An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.