Improved Sine-Tangent chaotic map with application in medical images encryption

The attractive properties of ergodicity, unpredictability, and initial state sensitivity have made chaotic maps the go-to tools in many applications, including cryptography and cyber–physical systems. Despite this, two challenges arise when using chaos systems in cryptography: (i) some one-dimensional (1D) chaotic maps do not satisfy the unpredictability property, and (ii) although they exhibit a complex and chaotic behavior, high-dimensional (HD) chaotic maps incur higher computational complexity. To address these issues, this paper proposes a new 1D chaotic map dubbed the improved Sine-Tangent map (IST map) that is derived from of the Sine map, a tangent function, and a Chebyshev polynomial of the first kind. Relative to chaotic maps, the proposed IST map provides better unpredictability and ergodicity, a vast chaotic range, enhanced complex behavior, and competitive computational complexity. Based on the IST map, we also introduced an encryption scheme for securing medical images in telemedicine. It consists of two diffusion phases, i.e., a bitwise XOR operation and a bitwise expanded XOR (eXOR) operation, with an intermediated confusion one, i.e., random circular-shift. An overriding step is foremost first completed before performing these cryptography phases, i.e., key generation. The secret key of the IST map is updated using the sine and cosine values of the sum of pixels of the input image. This leads to a unique secret key for each image. That is, one-time chaotic sequences are produced for each input image. The cyclic pattern of the sine and cosine values of the sum of pixels provides a prominent sensibility to small changes in the input image. Thus, the proposed algorithm is capable of resisting any chosen/known plaintext attacks. A performance analysis shows that the proposed algorithm outperforms a set of state-of-the-art comparison algorithms and its variants based on Sine, SE, and ST maps since it allows the best performance/complexity trade-off.