Rubik's Cube Encryption Transformation for Digital Images Using Chaotic Sequences

This article introduces a Rubik's Cube encryption transformation method based on chaotic sequences, which are generated using logistic mapping from nonlinear dynamical systems. The encryption technique employs a pseudo-random number sequence derived from the logistic map equation x_n+1 = μx_n(1-x_n) with μ ∈ [3.57, 4.0] to achieve chaotic behavior. Through this encryption transformation, digital images can be protected during storage and secure transmission. The chaotic sequence generation process involves initializing system parameters and iterating the logistic map to produce unpredictable values that determine pixel permutation patterns. The implementation typically includes three core functions: chaotic sequence generation (using floating-point arithmetic with precision control), pixel position scrambling (simulating Rubik's Cube rotations through matrix transformations), and inverse transformation for decryption. Additionally, the article explores applications in cryptography and information security, discussing advantages like high sensitivity to initial conditions and limitations including computational overhead. Future research directions propose hybrid encryption schemes combining chaotic sequences with traditional cryptographic algorithms to enhance security performance and optimization techniques for real-time processing.