Multicore Modular Multiplication of Progressive Multiplier Reduction Algorithm

The global expansion of interconnected edge network components requires immediate strategies for securing low-power computing nodes. Cryptographic algorithms executing over binary extension fields yield considerable computational benefits because their carry-free arithmetic significantly optimizes dynamic power consumption. However, general-purpose silicon architectures lack the dedicated hardware structures to run these finite-field operations efficiently, resulting in severe processing throughput bottlenecks. This study addresses this limitation by introducing a parallelized modular multiplier framework designed to integrate smoothly with the multicore execution environments of modern embedded platforms. Our approach deploys a progressive multiplier reduction (PMR) protocol that segments dense mathematical workloads into distributed structural thread groups. This architectural alignment allows multiplication matrices and spatial field reductions to take place concurrently, balancing localized workloads while decreasing intermediate data buffering demands. We present two distinct topological styles based on column division and row division techniques, deriving comprehensive analytical formulations to capture precise silicon area footprints, critical path delays, and total operational cycle counts. The resulting hardware metrics demonstrate that the parallel PMR design achieves a highly competitive area–delay product alongside optimized dynamic consumption characteristics. This structural paradigm delivers a scalable and robust security alternative for general edge hardware, ensuring system runtime stability while meeting tight environmental power constraints, protecting vital industrial assets, and sustaining emerging macroeconomic infrastructure.