Fast modular multiplication using Booth recoding based on signed-digit number arithmetic

Abstract

Proposes a new algorithm of serial modular multiplication based on signed-digit (SD) number system using Booth recoding method. By introducing a p-digit radix-two SD number system, a modular addition is easily implemented by using one or two SD adders, so that no carry propagation will arise during the additions. A modular multiplication can be performed by repeating the modular addition with modular partial products. In order to implement a high speed modular multiplication, a Booth recoding method is used to reduce the partial products to be added for the modular multiplication. We also give a pipeline architecture with two modular SD adders to realize a faster modular multiplication. The design result by using VHDL shows that a fast modular multiplier can be implemented based on the presented method.