Manipulated Lookup Table Method for Efficient High-Performance Modular Multiplier

Modular multiplication is a fundamental operation in many cryptographic systems, with its efficiency playing a crucial role in the overall performance of these systems. Since many cryptographic systems operate with a fixed modulus, we propose an enhancement to the fixed modulus lookup table (LuT) method used for modular reduction, which we refer to as the manipulated LuT (MLuT) method. Our approach applies to any modulus and has demonstrated comparable performance compared with some specialized reduction algorithms designed for specific moduli. The strength of our proposed method in terms of circuit performance is shown by implementing it on Virtex7 and Virtex Ultrascale+ FPGA as the LUT-based MLuT modular multiplier (LUT-MLuTMM) with generalized parallel counters (GPCs) used in the summation step. In one-stage implementations, our proposed method achieves up to a 90% reduction in area and a 50% reduction in latency compared with the generic LuT method. In multistage implementations, our approach offers the best area-interleaved time product, with improvements of 39%, 13%, and 29% over the current state-of-the-art for ~256-bit, SIKE434, and BLS12-381 modular multipliers, respectively. These results demonstrate the potential of our method for high-performance cryptographic accelerators employing a fixed modulus.