Base Extent Optimization for RNS Montgomery Algorithm

Base extent (BE) is the most costly operation in classic RNS Montgomery multiplication. In this paper, we propose a method to optimize Chinese Remainder Theorem (CRT)- based BE, where some common factors are extracted that the precomputed parameters of BEs can be adjusted to some forms with a small Hamming weight if modulo selected properly. Four modulo are selected to demonstrate the advantage of the proposed method. Using the proposed method and four modulo, the 32 multiplications of BEs can be replaced with 40 additions. The most efficient algorithm state of the art requires 48 multiplication for a system of four modulo while the proposed method reduced the number of the required multiplications from 48 to 20. Our method allows faster computation of RNS Montgomery multiplication.