A 32 Bit Multiplier Architecture Using Galois Fields

In this paper, a novel architecture for a finite field integer multiplier based on a superset of the triple moduli set {2-1,2,2+1} is presented. The superset is constructed by adding extra moduli of the form 2±1 (for any non-zero integer n) to extend its range. The multiplier uses index transform approach whereby multiplication is carried out by index addition, and is organized into submodules which operate in parallel thereby speeding up the whole operation. For numbers modulo 2, a triplet index set is used. It has been found that in the majority of cases few of the remaining moduli happens to be a prime number and hence index transform approach is efficiently applied by decomposing the modulus into a number of relatively prime submoduli. For the rest of the moduli, a prime factorization yields integers that are either prime or powers of primes or a combination of both. Index transform is readily applied to prime numbers, and an index pair mapping is used for integers that are powers of primes. The beauty of this design is that index transform approach is exclusively applied in the entire design.