Design and implementation of pipelined TMVP multiplier using block recombination

Fan and Hasan proposed a new scheme for subquadratic space complexity parallel multiplication in GF(2ⁿ) using Toeplitz matrix-vector products (TMVP). Recently, a recombined version of Fan-Hasan TMVP multiplier is also proposed to achieve lower space complexity. In this paper, optimal ending condition during recursion for the recombined multiplier is discussed. Based on the idea of decomposing building blocks, we present a new method to design pipelined parallel binary field multiplier which has subquadratic space complexity in combinational part and high throughput. ASIC results of this proposed multiplier are shown to have total area saving of 28.8% with even better throughput against designs using brute force algorithm when optimized for speed.