Construction of chaotic quantum magnets and matrix Lorenz systems S-boxes and their applications

When we listen regarding quantum cryptography, the first thinking that comes up to mind is, how can there be any connection between physics and cryptographic ciphers. In fact, it comes into view that is one of the hottest research in the field of cryptology to exploit physics and has been confirmed as the important objective in the protection of digital data. The topic of quantum magnets and matrix Lorenz Systems has begun to draw increasing attention in recent years. In last decade, chaotic systems have been utilized in many encryption algorithms. In this regard, Lorenz chaotic system based on differential equations achieved more recognition because of its fundamental sensitivity to initial conditions and easiness in use. This manuscript has two parts. First, we have constructed substitution boxes (S-Boxes) based on quantum magnets and matrix Lorenz chaotic system and permutation of the symmetric group S256 and then designated an image encryption algorithm based on proposed S-boxes and Lorenz chaotic system. In cryptography, it is essential to construct secure S-Boxes to propose cryptographically strong systems. Recently, some image encryption techniques that are weak against robustness have been proposed based on chaotic S-boxes. In the first part of the manuscript, an S-Box design is proposed. Continuous-time Lorenz system is chosen as the chaotic system. The presented image encryption algorithm is based on two rounds of a novel chaotic substitution-permutation network uses proposed S-boxes for substitution purpose by iterations of the Lorenz chaotic system and special kind of permutation process to get the full cipher image. The proposed algorithms for S-box construction and image encryption give very good and coherent performance results when we analyze them with renowned analyses.