Image Encryption via Data-Identified Discrete Chaotic Maps

2026-05-20

AI Summary

This work proposes a data-driven image encryption framework that overcomes the limitations of traditional methods relying on predefined chaotic maps, which often lack adaptability to data characteristics and exhibit constrained security. For the first time in image cryptography, the SINDy-PI algorithm is employed to directly identify high-order nonlinear discrete chaotic systems from observed data, which then serve as adaptive encryption mappings. The approach requires no prior assumption about the dynamical structure and uses only initial conditions as the secret key, enabling the encryption mapping to automatically adapt to the input data. Experimental results demonstrate that the encrypted images achieve near-optimal information entropy (~8 bits), with NPCR ≈ 99.6% and UACI ≈ 33.5%, indicating high sensitivity to initial conditions and strong resistance against differential and statistical attacks.

Abstract

In this work, we propose a data-driven image encryption framework that identifies chaotic maps directly from data using the SINDy-PI algorithm. Unlike conventional encryption schemes relying on predefined maps, our method learns the full explicit dynamics -- including cross-terms and higher-order nonlinearities -- from observational data. The validity of this approach is verified on three distinct chaotic systems: the H{é}non map, the three-dimensional logistic map, and the piecewise-linear Lozi map, demonstrating its generality. The encryption key consists solely of initial conditions; the map structure itself becomes data-dependent, introducing an extra layer of security. Moreover, even when the initial conditions are fixed, different training data (e.g., with a tiny noise seed) lead to slightly different maps, which produce completely different ciphertexts (NPCR $\approx 99.6\%$, UACI $\approx 33.5\%$). Numerical experiments on the H{é}non system show near-ideal information entropy ($\approx 8$ bits), negligible inter-pixel correlation, and extreme sensitivity to initial conditions: a perturbation of $10^{-16}$ causes total decryption failure. The scheme resists both differential and statistical attacks, with NPCR and UACI values matching theoretical ideals. Our results establish a new paradigm for chaos-based cryptography beyond fixed maps.

Problem

• image encryption
• chaotic maps
• data-driven
• cryptography
• security

Innovation

• data-driven encryption
• chaotic maps identification
• SINDy-PI algorithm
• adaptive cryptography
• image encryption