Abstract
In finite field, the best choice of the polynomial basis (PB)multiplication is selected by a sparse irreducible polynomialto obtain advantageous space and time complexity. In thispaper, we introduce a new polynomial basis representation,called the coupled polynomial basis (CPB). By using thisbasis representation, the irreducible polynomial can beconverted into F ? ? ? ? £U ????????, where ?? ? 1 and?? ? ?? ? ???? . This polynomial is called the coupledpolynomial. The modified polynomials are abundant, and area half of the Hamming weight as compared with the originalpolynomials. Here combining the relation of PB and CPB, weobtain low-complexity semi-systolic double basis multiplieras compared with existing multipliers.
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