Galois Field Arithmetic Operations using Xilinx FPGAs in Cryptography

Cryptography algorithms are standards for any security-based industry. Internationally widely accepted and used cryptography algorithms like AES, DES rely heavily on finite field arithmetic which needs to be performed efficiently, to meet execution speed and design constraints. This paper aims to provide a concise perspective on designing efficient architectures in finite field arithmetic. In this paper, we propose Galois field arithmetic using irreducible polynomial to generate the S-box for AES using 128, 192, and 256-bit Keys. Cryptographic algorithms are more prone to side-channel attacks, so we implemented this algorithm instead of using a lookup table-based approach. The proposed Galois Field implementation of arithmetic operations are unique which can be extended to any primitive polynomial of any word size GF(2
ⁿ
). A novel scheme is proposed for AES S-box, Inverse S-box, and validated using a Xilinx Virtex-7 FPGA.