FLALM: A Flexible Low Area-Latency Montgomery Modular Multiplication on FPGA

Montgomery Modular Multiplication (MMM) is widely used in many public key cryptography systems. This paper presents a Flexible Low Area-Latency MMM (FLALM) implementation, which supports Generic Montgomery Modular Multiplication (GMM) and Square Montgomery Modular Multiplication (SMM) operations. A new SMM schedule for the Finely Integrated Product Scanning (FIPS) GMM algorithm is proposed to accelerate SMM with tiny additional design. Furthermore, a new FIPS dual-schedule is proposed to solve the data hazards of this algorithm. Finally, we explore the trade-off between area and latency, and present the FLALM to accelerate GMM and SMM. The FLALM is implemented on FPGA (Virtex-7 platform). The results show that the area*latency (AL) value of FLALM (wordsize $w$ =128) is 38.1% and 44.7% better than the previous state-of-art scalable references when performing 1024-bit and 2048-bit GMM, respectively. Moreover, when computing SMM, the advantage of AL value is raised to 73.7% and 86.3% respectively.