Symmetric Image Encryption Algorithm Based on a New Product Trigonometric Chaotic Map

In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approximate entropy, permutation entropy, time-series diagrams, cobweb graphs, and NIST tests. It is proved that the PTM system has a wider chaotic parameter interval and more complex chaotic performance than the existing sine map system. In addition, a novel PTM based symmetric image encryption scheme is proposed, in which the key is related to the hash value of the image. The algorithm realizes the encryption strategy of one-graph-one-key, which can resist plaintext attack. A two-dimensional coordinate traversal matrix for image scrambling and a one-dimensional integer traversal sequence for image pixel value transformation encryption are generated by the pseudo-random integer generator (PRING). Security analysis and various simulation test results show that the proposed image encryption scheme has good cryptographic performance and high time efficiency.