Finite Field Polynomial Multiplier with Linear Feedback Shift Register

摘要

We will present an one-dimensional polynomial basis array multiplier for performing multiplications in finite field GF(2~m). A linear feedback shift register is employed in our proposed multiplier for reducing space complexity. As compared to other existing two-dimensional polynomial basis multipliers, our proposed linear array multiplier drastically reduces the space complexity from O(m~2) to O(m). A new two-dimensional systolic array version of the proposed array multiplier is also included in this paper. The proposed two-dimensional systolic array multiplier saves about 30% of space complexity and 27% of time complexity while comparing with other two-dimensional systolic array multipliers.