Image encryption based on feedback control discrete switching hyperchaotic system and QR decomposition

Abstract

A two-dimensional switching-controlled hyperchaotic system has been developed that enhances the randomness of the system through dynamic switching of the control parameter. The proposed hyperchaotic system is then applied to image encryption. The encryption process begins with the decomposition of the plaintext image matrix into an upper triangular matrix and an orthogonal matrix via QR decomposition. The orthogonal matrix is modified by multiplying on both sides with multiple random orthogonal matrices, resulting in a matrix denoted as E1. Simultaneously, chaotic sequences are employed to scramble the rows and columns of the upper triangular matrix. A subsequent QR decomposition is performed on E1, followed by the multiplication of the orthogonal matrices and additional random orthogonal matrices on both sides, including the upper triangular matrix. The final encrypted matrix is then subjected to bit-level scrambling using chaotic sequences. The chaotic sequences, generated by the newly proposed two-dimensional hyperchaotic map, are used in a bitwise exclusive OR operation to produce the final encrypted image. The experimental results and theoretical analysis confirm that the proposed method provides a high level of security. Moreover, the strong randomness of the hyper-chaotic system makes it highly promising for applications across various fields of cryptography.