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

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.