Low-Cost High-Performance VLSI Architecture for Montgomery Modular Multiplication

Abstract

This paper proposes a simple and efficient Montgomery multiplication algorithm such that the low-cost and high-performance Montgomery modular multiplier can be implemented accordingly. The proposed multiplier receives and outputs the data with binary representation and uses only one-level carry-save adder (CSA) to avoid the carry propagation at each addition operation. This CSA is also used to perform operand precomputation and format conversion from the carry-save format to the binary representation, leading to a low hardware cost and short critical path delay at the expense of extra clock cycles for completing one modular multiplication. To overcome the weakness, a configurable CSA (CCSA), which could be one full-adder or two serial half-adders, is proposed to reduce the extra clock cycles for operand precomputation and format conversion by half. In addition, a mechanism that can detect and skip the unnecessary carry-save addition operations in the one-level CCSA architecture while maintaining the short critical path delay is developed. As a result, the extra clock cycles for operand precomputation and format conversion can be hidden and high throughput can be obtained. Experimental results show that the proposed Montgomery modular multiplier can achieve higher performance and significant area–time product improvement when compared with previous designs.