An Efficient Implementation of the CRT Algorithm Based on an Interval-Index Characteristic and Minimum-Redundancy Residue Code

The Chinese remainder theorem (CRT), which appeared in ancient China, is widely used in many modern computer applications. This paper presents the CRT implementation by using the interval-index characteristic and minimum redundancy residue code. The proposed algorithm does not use large modulo addition operations and provides low computational complexity compared to conventional non-redundant RNS. The efficiency factors of using the minimally redundant RNS increase with the number k of non-redundant moduli, asymptotically approaching the threshold k/2. The new approach presented here will have a significant impact on many non-modular operations in RNS arithmetic, which currently use the CRT.