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<p>Digital images play a crucial role in the dissemination of information in today’s society. To ensure their secure transmission, this paper introduces a novel pseudo-random number generator for chaotic image encryption. Recognizing that chaotic systems can suffer precision loss during digitization, potentially leading to chaotic degradation, we propose using the Square Unscented Root Kalman Filter (SUKF) to track the digital Coupled Map Lattice (CML) chaotic system. The tracking results are incorporated as disturbance feedback into the CML system, forming the Coupled Map Lattice based on the Square Unscented Root Kalman Filter (SUKFCML) to enhance its chaotic characteristics. We provide a theoretical analysis to validate the advantages of SUKF. And the SUKFCML’s chaotic sequences exhibit: passed NIST SP-800 test, nearing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(50\%\)</EquationSource> </InlineEquation> Bit Change Rate (BCR), optimized correlation, stable Lyapunov exponent, continuous power spectrum, uniform invariant distribution and reduced Equilibrium Degree (ED). Building on this newly developed chaotic pseudo-random number generator, we present an image encryption scheme that applies a generalized Fibonacci matrix and saw-tooth transformations for permutation, followed by image diffusion through multiplication in the GF(257) field. The simulation results show that the scheme features an efficient key space, low correlation, high information entropy, and strong resistance to differential attacks, offering robust security.</p>

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Image encryption algorithm using a novel chaotic pseudo-random number generator combined with square unscented root kalman filter

  • 期刊论文

  • 发表日期：

    2026年4月12日

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  • Chenghui Wang,
  • Shiyuan Wang,
  • Bo Yang

摘要

Digital images play a crucial role in the dissemination of information in today’s society. To ensure their secure transmission, this paper introduces a novel pseudo-random number generator for chaotic image encryption. Recognizing that chaotic systems can suffer precision loss during digitization, potentially leading to chaotic degradation, we propose using the Square Unscented Root Kalman Filter (SUKF) to track the digital Coupled Map Lattice (CML) chaotic system. The tracking results are incorporated as disturbance feedback into the CML system, forming the Coupled Map Lattice based on the Square Unscented Root Kalman Filter (SUKFCML) to enhance its chaotic characteristics. We provide a theoretical analysis to validate the advantages of SUKF. And the SUKFCML’s chaotic sequences exhibit: passed NIST SP-800 test, nearing \(50\%\) Bit Change Rate (BCR), optimized correlation, stable Lyapunov exponent, continuous power spectrum, uniform invariant distribution and reduced Equilibrium Degree (ED). Building on this newly developed chaotic pseudo-random number generator, we present an image encryption scheme that applies a generalized Fibonacci matrix and saw-tooth transformations for permutation, followed by image diffusion through multiplication in the GF(257) field. The simulation results show that the scheme features an efficient key space, low correlation, high information entropy, and strong resistance to differential attacks, offering robust security.