An extendable key space integer image-cipher using 4-bit piece-wise linear cat map

This paper presents a multiplierless image-cipher, with extendable 2048-bit key-space, based on a 4-dimensional (4D) quantized piece-wise linear cat map (PWLCM). The quantized PWLCM exhibits limit-cycles of 4-bit encoded integers with periods greater than 10⁷. The synthesis of the PWLCM in a finite state space allows to eliminate the undesirable finite precision effect due to the hardware realization. The proposed image-cipher combines chaos, modular arithmetic, and lattice-based cryptography to encrypt a color image by performing pixel permutation and diffusion in a single operation. Further, an image-dependent confusion operation based on an 8-bit 2D-PWLCM is performed on the whole image to enhance security. In order to increase the key-space without key duplication, 16 × 16 subimages are modified using sub-keys of different lattice length vectors generated from the external key. Both simulations and security analyses confirm that the proposed algorithm can resist common cipher attacks, in addition to its advantages such as simplicity, ease of implementation on low-end processors and extensibility of key-space that allows it to easily adapt even for future post-quantum computing attacks.