Hardware Optimized Modular Reduction

We introduce a modular reduction method that is optimized for hardware and outperforms conventional approaches. By leveraging calculated reduction cycles and combinatorial logic, we achieve a remarkable 30% reduction in power usage, 27% reduction in Configurable Logic Blocks (CLBs), and 42% fewer look-up tables (LUTs) than the conventional implementation. Our Hardware-Optimized Modular Reduction (HOM-R) system can condense a 256-bit input to a four-bit base within a single 250 MHz clock cycle. Further, our method stands out from prevalent techniques, such as Barrett and Montgomery reduction, by eliminating the need for multipliers or dividers, and relying solely on addition and customizable LUTs. This innovative method frees up FPGA resources typically consumed by power-intensive DSPs, offering a compelling low-power, low-latency alternative for diverse design needs.