Digit-Level Semi-Systolic and Systolic Structures for the Shifted Polynomial Basis Multiplication Over Binary Extension Fields

Finite field multiplication is one of the most important operations in the finite field arithmetic. In this paper, we study semi-systolic and systolic implementations of the shifted polynomial basis multiplication and propose low time complexity semi-systolic and systolic array structures. We show that our proposed semi-systolic multiplier is faster than its existing counterparts available in the literature. Our application-specified integrated circuit (ASIC) implementation of the proposed semi-systolic multiplier demonstrates that reduction in time complexity is achieved without imposing hardware overhead. Furthermore, our proposed systolic array shifted polynomial basis (SPB) multiplier has a low time complexity for general irreducible polynomials.