Efficient Barrett Modular Multiplication Based on Toom-Cook Multiplication

The Toom-Cook multiplier (TCM) is the most suitable method for multiplying large integers with key widths typically employed in ECC or RSA due to its computational efficiency. In this brief, we improve the accuracy of hardware TCM algorithm, and propose a TCM-based Barrett modular multiplication algorithm. We provide detailed mathematical proofs for the determination of parameters, error ranges, and input-output bounds, which serve to validate the robustness and reliability of our proposed algorithm. Further, the hardware architecture and the ASIC implementation results under 40nm, 65nm, 90nm process are presented. Compared with existing works, the proposed modular multiplier exhibits superior performance in terms of Area-Time-Product.