High-Speed Modular Multipliers Based on a New Binary Signed-Digit Adder Tree Structure

In this paper, we present multipliers using a modified binary tree of the modulo m signed-digit (SD) number residue adders where m = 2(n) - 1, 2(n), 2(n) + 1. New additions rules are used for generating the intermediate sum and carry with a binary number representation. The sums and carries are directly inputted into the next stage of adders, so that the modulo m multiplier using binary modulo m adder tree proposed in [13] can be improved. Moreover residue multipliers using the SD residue adders are also designed with inputs/outputs in binary number representation. The design and simulation results of the proposed residue arithmetic circuits show that high speed arithmetic circuits can be obtained.