A Novel Application of Elliptic Curves in the Dynamical Components of Block Ciphers

The proposed work deals with a distinguished application of complex algebraic-geometric structure in nonlinear dynamical components of block ciphers. Due to the complex algebraic structure of the elliptic curves, their application in public-key cryptography has gained immense importance in recent years. The presented study introduces an effective application of elliptic curves in the nonlinear components, used in a symmetric-key cryptosystem. We propose that the group law defined on the rational points of an elliptic curve, over the binary field, offers extra-ordinary technical advantages, when used in the byte substitution process in block ciphers. For this purpose a specific elliptic curve over the Galois field \({\mathbb {F}}_{2^{4}}\) is selected that is special as its elliptic group is of the same order as that of \({\mathbb {F}}_{2^{4}}\). This feature helps us defining a bijective map between the two structures that renders highly increased level of perplexity and confusion in data. The cryptographic forte of the proposed method is tested through most significant analyses and when compared with one of the most recent schemes, it shows outstanding results.