IMPLEMENTATION OF RIJNDAEL S-BOX USING COMBINATIONAL LOGIC

Introduction

This Project presents a combinational logic based Rijndael S-Box implementation for the SubByte transformation in the Advanced Encryption Standard (AES) algorithm for Field Programmable Gate Arrays (FPGAs). Recent publications on AES implementation have shown that the combinational logic based S-Box is proven for its small area occupancy and high throughput, given the fact that pipelining can be applied to this S-Box implementation as compared to the typical ROM based lookup table implementation which access time is fixed and unbreakable. 

The Project deals with a brief introduction to the Advanced Encryption Standard, the SubByte and InvSubByte transformation, and finally a short discussion on the previous h ardware implementations of the SubByte/InvSubByte transformation.

The Advanced Encryption Standard 

The AES algorithm has a fixed block size of 128 bits and a key length of 128, 192 or 256 bits. It generates its key from an input key using the Key Expansion function. The AES operates on a 4x4 array of bytes which is called a state. The state undergoes 4 transformations which are namely the AddRoundKey, SubByte, ShiftRow and MixColumn transformation.The AddRoundKey transformation involves a bitwise XOR operation between the state array and the resulting Round Key that is output from the Key Expansion function. 

SubByte transformation is a highly non-linear byte substitution where each byte in the state array is replaced with another from a lookup table called an S-Box. ShiftRow transformation is done by cyclically shifting the rows in the array with different offsets. Finally, MixColumn transformation is a column mixing operation, where the bytes in the new column are a function of the 4 bytes of a column in the state array.Of all the transformation above, the SubByte transformation is the most computationally heavy.The SubByte and InvSubByte Transformation The SubByte transformation is computed by taking the multiplicative inverse in GF(28) followed by an affine transformation. For its reverse, the InvSubByte transformation, the inverse affine transformation is applied first prior to computing the multiplicative inverse.

The steps involved for both transformation is shown below. 

SubByte: Multiplicative Inversion in GF(28) ->Affine Transformation 

InvSubByte:Inverse Affine Transformation ->Multiplicative Inversion in GF(2*8)