Low Complexity Finite Field Multiplier for a New Class of Fields

Abstract

Finite fields is considered as backbone of many branches in number theory, coding theory, cryptography, combinatorial designs, sequences, error-control codes, and algebraic geometry. Recently, there has been considerable attention over finite field arithmetic operations, specifically on more efficient algorithms in multiplications. Multiplication is extensively utilized in almost all branches of finite fields mentioned above. Utilizing finite field provides an advantage in designing hardware implementation since the ground field operations could be readily converted to VLSI design architecture. Moreover, due to importance and extensive usage of finite field arithmetic in cryptography, there is an obvious need for better and more efficient approach in implementation of software and/or hardware using different architectures in finite fields. This project is intended to utilize a newly found class of finite fields in conjunction with the Mastrovito algorithm to compute the polynomial multiplication more efficiently