Design of nonlinear component of block cipher using quaternion integers

As the only nonlinear component of many cryptosystems, the block cipher is an integral part of symmetric ciphering techniques that increase confidentiality at the substitution stage and create randomness. Encryption's strength is solely determined by the competence of its nonlinear component (S-box). The creation of S-boxes has gotten a lot of attention in recent years and opened vast research directions in cryptography and most recent method is designing S-boxes through elliptic curves (ECs). Accordingly, for the generation of S-boxes by ECs one has to fix a prime integer and other two parameters. In this paper a novel S-boxes constructing method is introduced based on the quaternion integers. Alike the S-boxes over ECs in this work a prime integer and other two parameters are taken to be fixed and a rigorous scheme for constructing S- boxes via affine mapping is described. The proposed work is developed in such a way that for every input, it generates two S-boxes, whereas, in the design of ECs based S-boxes one may obtained the only one S-box. The strength of S-boxes is measured by applying different security analyses, e.g., strict avalanche criterion, differential approximation probability, nonlinearity, bit independence criterion, and linear approximation probability. A detailed comparison between the newly constructed S-boxes and some existing S-boxes, focusing on some ECs-based S-boxes has been given. The cryptographic analysis reveals that the proposed algorithm can generate many distinct S-boxes that are cryptographically strong and are useful for the applications of secure data communication.