On Partial Linearization of Byte Substitution Transformation of Rijndael-The AES

Abstract

Rijndael-The AES^[1-3] is 128-bit block cipher based on an elegant algebraic structure over F₂⁸. This cipher employs a simple approach to its substitution, permutation (SP) operations. We take a close look at its internals; the byte substitution transformation function is the only non-linear function in Rijndael - The AES. This transformation comprises of two steps operating on each byte. Here we are trying to remodel this to one step operation using indicator vector matrix representation. This representation is further extended to mathematically represent one complete encryption or decryption round of Rijndael the using indicator vector matrix representation that can be explored for better crypto-analysis^[4,5] of the cipher.