MODULO (2p ± 1) MULTIPLIERS USING A THREE-OPERAND MODULAR SIGNED-DIGIT ADDITION ALGORITHM

Abstract

In this paper, a new three-operand modulo (2p ± 1) addition is implemented by performing a carry-save addition and a two-operand modular addition based on the p-digit radix-two signed-digit (SD) number system. Thus, the delay time of the three-operand modular adder is independent of the word length of the operands. A modulo (2p ± 1) multiplier is constructed as a ternary tree of the three-operand modular SD adders, and the modular multiplication time is proportional to log 3 p. When a serial modular multiplier is constructed using the three-operand modular SD adder, two modular partial products can be added to the sum at the same time. Two kinds of Booth recoding methods are also proposed to reduce the partial products from p to p/2. Therefore, the performance of a parallel modular multiplier can be modified by reducing half of the modular SD adders in the adder tree. For a serial modular multiplication, two partial products are generated from two Booth recoders and added to the sum by using one three-operand modular SD adder, so that the speed of the modular multiplication is three times as fast as the speed without using the three-operand modular SD adder and the Booth recoding method. A very large-scale integration (VLSI) implementation method by VHDL is also discussed. The design and simulation results show that high-speed modular multipliers can be obtained by the algorithms presented.