Implementation of Low Complexity Finite Field GF (2m) Multiplier Using Irreducible Primitive Polynomials

Advancements in wireless technology led to the evolution of many modern wireless networks and wireless communication applications. Internet of Things (IoT) is a state of art communication technology and Edge devices are fundamental in this kind of communication. Number of edge devices required mainly depends on the complexity of applications. In IoT edge devices security is a major concern, asymmetric algorithms like Elliptic curve cryptography(ECC) can be used to address this issue which depend significantly on finite field GF (2^m) arithmetic operations, where GF denotes Galois Field. In particular, Galois Field multiplication is a complex but important operation as it can also be utilized in important functions like division and inversion. In our work, realization of a low computational complexity finite field GF (2^m) multiplier employing primitive polynomials as field irreducible polynomials is done. Primitive polynomials are employed in an available multiplication algorithm and this modified multiplier is realized in MATLAB. It is observed that computational steps for realizing the multiplication are reduced, which in turn can lead to improvement in time efficiency. A Verilog model is developed and simulated to use as a golden reference for comparing the MATLAB results.