Affiliations: [a] Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
| [b] Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, Pakistan
| [c] Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Correspondence:
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Corresponding author. Majid Khan, Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, Pakistan. E-mail: mk.cfd1@gmail.com.
Abstract: Designing of nonlinear confusion component of block cipher is one of the most important and inevitable research problem. Nowadays mostly heuristic search schemes were utilized for the construction of these confusion component. To construct, a cryptographically secure confusion component several algebraic structures were utilized. The thirst for new algebraic structure for the construction of these nonlinear confusion component has always been a point of interest. In this communication, we have utilized a maximal cyclic subgroup of unit of Galois ring. The offered algorithm is more general as compared to Galois field. The class of Boolean functions over Galois ring fall in mixed category which are not completely balanced. Boolean functions having higher nonlinearity and others cryptographic aspects added an inevitable significance in the construction of modern block ciphers. The primary idea of this article is to structure non-balanced Boolean functions on n variables, where n is an even integer, sustaining strict avalanche criterion (SAC) and bit independent criterion (BIC). By comparing SAC with available cryptographic Boolean functions, the constructed multivalued Boolean function acquire highest nonlinearity which does not follow the existing nonlinearity bound of Boolean functions. These newly proposed S-boxes consists of n basic Boolean functions which satisfy the balancedness and non-balancedness criterion. Therefore, these S-box structure lies within a less balanced and more bent Boolean function categories.
