A Chaos-Based PRNG Using Delta-Kicked Oscillator Dynamics for Secure Encryption Applications
TL;DR
A novel deterministic pseudorandom source based on a delta-kicked forced oscillator and comprehensively test its discrete output in the exact binary format consumed by downstream ciphers to support the generator as a statistically well-validated and numerically robust candidate for chaos-based cryptographic architectures.
Abstract
Typically, chaotic sources are indirectly assessed through ciphertext-level metrics that cannot isolate the contribution of the source itself, or are rarely complemented with a comprehensive set of analyses specifically tailored to digital chaotic generators. Here, we propose a novel deterministic pseudorandom source based on a delta-kicked forced oscillator (DKO) and comprehensively test its discrete output in the exact binary format consumed by downstream ciphers. The architecture separates key-dependent parameter derivation, nonlinear evolution, transient removal, and digital output generation. An explicit 22-symbol external key is deterministically mapped to the internal DKO parameters, separating user-key capacity from numerical parameter precision. The operating regime is characterized by phase-space analysis, bifurcation diagrams, temporal evolution, and Lyapunov exponents, while statistical quality is evaluated using NIST SP 800-22, DIEHARDER, and TestU01 SmallCrush, Crush, and BigCrush, complemented by byte-distribution, autocorrelation, complexity, bit-plane, key-sensitivity, multi-key, and finite-precision analyses. The generator satisfied all applicable NIST criteria and all 15, 144, and 160 SmallCrush, Crush, and BigCrush statistics, respectively, while DIEHARDER reported no failures. Complementary analyses showed near-uniform distribution, negligible statistical memory, strong key sensitivity, consistent multi-key behavior, and no degradation under double precision. These results support the generator as a statistically well-validated and numerically robust candidate for chaos-based cryptographic architectures and provide a reference for future comparative evaluations.