Construction of S-boxes from cyclic group of residue class of noncommutative quaternion integers

Substitution boxes (or S-boxes) are a unique nonlinear part of a substitution-permutation network as a cryptosystem that is utilized to obtain the property of confusion in modern symmetric ciphers and provide resistance to cryptanalysis. The efficiency and security of these ciphers depend mainly on the algebraic construction of S-boxes. The novelty of this research is the simultaneous construction of four S-boxes from a cyclic group of residue class of noncommutative quaternion integers. The proposed S-boxes are analyzed by nonlinearity, differential approximation probability, bit independence criterion, linear approximation probability, and strict avalanche criterion which are the avalanche effect tests. A comparison is done between our newly developed technique and already existing techniques based on elliptic curves over the same prime integer. In this comparison, experimental results show that our proposed approach can generate a large number of distinct, safe, and uncorrelated S-boxes with better nonlinearity.