Nonlinear Components of a Block Cipher over Eisenstein Integers

In block ciphers, the nonlinear components, also known as substitution boxes (S-boxes), are used with the purpose to induce confusion in cryptosystems. For the last decade, most of the work on designing S-boxes over the points of elliptic curves, chaotic maps, and Gaussian integers has been published. The main purpose of these studies is to hide data and improve the security levels of crypto algorithms. In this work, we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers (EI). The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters. However, in the same way, by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve (EC), chaotic maps, and Gaussian integers. The newly designed pair of S-boxes are assessed by various tests like nonlinearity, bit independence criterion, strict avalanche criterion, linear approximation probability, and differential approximation probability.