Improving radix-4 feedforward scalable montgomery modular multiplier by precomputation and double booth-encodings

Abstract

Hardware implementation of multiprecision modular multiplications in public-key cryptography has led to various developments of scalable Montgomery modular multipliers, which are fast enough constrained from limited hardware resources. Among the candidates, the feedforward scalable Montgomery modular multiplier achieves low latency with simple logics and little change in the algorithm. However, the performance of high-radix feedforward scalable Montgomery modular multiplier is deteriorated by quotient determination. In this work, the method of double Booth-encodings and precomputation, which is firstly proposed for a traditional scalable Montgomery modular multiplier by Pinckney et al., is applied to radix-4 feedforward scalable Montgomery modular multiplier. FPGA implementation shows that the critical path is reduced by about 31% while the cost of hardware resources also decreases.

Fast RSA decryption through high-radix scalable Montgomery modular multipliers

“…The scalable Montgomery modular multipliers in [31] and [8] achieves similar performances to that in [10,30] in another low-latency architecture. Also due to dedicated multipliers, this work is faster than [8,31] on FPGA platforms.…”

“…Unlike the interleaved Montgomery algorithm [6,7], the parallel words are allocated in a pipeline. The low-latency scalable architecture is efficient with limited hardware and fast if sufficient resources are available [8][9][10]. Meanwhile, high-radix scalable architecture cuts down the number of clock cycles for one scalable Montgomery modular multiplications, although it has a longer critical path and latency between PEs [11,12].…”

Area and Delay Efficient Compressor Based Montgomery Multiplier

“…A hybrid multiplier with 4-level recursion is constructed by X.Yan [14] by applying the Knuth and Karatsuba algorithm recursively. The double Booth-encodings and precomputation methods is applied to radix-4 Montgomery multiplier by T.Wu [15] which is scalable and feed forward. A fair comparison is provided by S.Kakde [16] and it includes the improved Montgomery multiplier design with CSA stages and parallel register.…”