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

Digital image encryption technology plays a crucial role in modern information security, where chaotic sequence-based encryption methods have gained significant attention due to their excellent randomness and sensitivity. This paper presents an encryption approach that utilizes the Logistic map from nonlinear dynamical systems to generate chaotic sequences, combined with Rubik's cube transformation for digital image encryption.

The generation of chaotic sequences forms the core of this encryption method. The Logistic map represents a classic one-dimensional chaotic system whose simple mathematical form can produce complex pseudo-random sequences. By adjusting the map parameters, highly unpredictable sequence values can be generated, making them ideal as key streams in the encryption process. In code implementation, this typically involves iterating the equation xₙ₊₁ = μxₙ(1-xₙ) with carefully chosen μ values between 3.57 and 4.0 to ensure chaotic behavior.

The Rubik's cube transformation serves as the structural processing component in the encryption process. Similar to rotation operations in the Rubik's cube game, this transformation performs specific position permutations and color value confusion on image pixel blocks, disrupting the statistical characteristics of the original image. Algorithmically, this involves dividing the image into smaller blocks and applying cyclic shifts or rotations based on the chaotic sequence values. The transformation not only alters the spatial distribution of pixels but also incorporates chaotic sequences for nonlinear modification of pixel values, resulting in encrypted images exhibiting noise-like characteristics that are difficult to decrypt.

The security of this method primarily manifests in three aspects: first, the extreme sensitivity of chaotic sequences to initial conditions means even minute key differences produce completely different encryption results; second, multiple rounds of Rubik's cube transformation significantly increase decryption difficulty; finally, the combination of both techniques achieves dual encryption effects in both spatial and value domains. Programmatically, this involves implementing multiple iterations where each round applies different permutation patterns derived from the chaotic sequence.

In practical applications, this chaotic-based Rubik's cube transformation encryption algorithm can effectively protect digital image confidentiality, suitable for high-security image transmission and storage scenarios. The algorithm maintains moderate computational complexity, enabling efficient operation on standard computing devices while possessing strong resistance against statistical analysis attacks. Code optimization can focus on parallel processing of image blocks and efficient chaotic sequence generation to enhance performance.