Efficient Modulo Multiplier

Abstract

The paper presents the methodology to compute modulo multiplication with the moduli set 2n, 2n−1, 2n+1. In addition to this, designs of the modulo multipliers, namely 2n, 2n−1, and 2n+1 (with n = 4, 8, and 16), have been proposed which are based on half adders, full adders, 4:3 compressor, 7:3 compressor, and the multi-column compressor namely 5,5:4. The gate level design of 4:3 compressor is carried out by solving the truth table using the K-map reduction. To verify the functionalities we have implemented the proposed modulo multipliers using VHDL coding in Xilinx 14.2 design suite. Simulation using Virtex-6 device has been performed to estimate delay, power consumption, and power-delay product (PDP). Moreover, the modulo multipliers are simulated in Cadence RC compiler using 0.18 µm technology to estimate the area. One of the major contributions to the arts of this work is in the partial product reduction stage which utilizes the multi-column 5,5:4 compressor to reduce power and area. The modulo 2n−1 multiplier of operand size 4-bit shows an improvement of 66.34% in terms of area over the best-reported paper. On the other hand, the modulo 2n+1 multiplier of operand size 4-bit shows an improvement of 58.59% terms of in area and the same of operand size 8-bit shows an improvement of 22.72% over the best-reported paper. The proposed algorithms of moduli multiplication are applicable to Booth multiplication of signed numbers.