A Generalization of Algebraic Expression for Nonlinear Component of Symmetric Key Algorithms of Any Characteristic p

Abstract

Recently several block ciphers are proposed which are based on the inversion mapping over binary Galois field with n-input. These proposed block ciphers are Camellia, AES, Square and Hierocrypt in which S-box over binary Galois field with n-input is used. Now with the passage of time it is necessary to increase the security of these blocks ciphers by increasing the key space which can be increased by generalizing this concept over non-binary Galois field with n-input. In this paper, we have designed an innovative techniques through which we can easily find element of nonlinear component of block cipher namely S-box through a single expression instead of matrix algebraic computations. Our main idea here is to reduce the computational complexity while performing calculations for S-box which is one of the most important nonlinear components for any modern block ciphers. Also, we have transformed our existing problem of being using matrix algebra to a symbolic single expression algebra which reduces the tedious calculations of S-boxes.