Efficient Double Basis Semi-systolic Multipliers over GF(2m) Using Coupled Polynomials

In finite field, the best choice of the polynomial basis (PB)multiplication is selected by a sparse irreducible polynomial to obtain advantageous space and time complexity. In this paper, we introduce a new polynomial basis representation,called the coupled polynomial basis (CPB). By using this basis representation, the irreducible polynomial can be converted into F = β_m + Σ_i=0^n-1, where β₀ = 1 and β_i = xⁱ+x^i-1. This polynomial is called the coupled polynomial. The modified polynomials are abundant, and area half of the Hamming weight as compared with the original polynomials. Here combining the relation of PB and CPB, we obtain low-complexity semi-systolic double basis multiplier as compared with existing multipliers.