Parallel Modular Multiplication Algorithm in Residue Number System

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Abstract

This paper presents a novel method for the parallelization of the modular multiplication algorithm in the Residue Number System (RNS). The proposed algorithm executes modular reductions using a new lookup table along with the Mixed Radix number System (MRS) and RNS. MRS is used because algebraic comparison is difficult in RNS, which has a non-weighted number representation. Compared with the previous algorithm, the proposed algorithm only requires L moduli which is half the number needed in the previous algorithm. Furthermore, the proposed algorithm reduces the number of MUL operations by 25 %.