An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System




Residue Number System, Chinese Remainder Theorem, residue code, rank of a number, positional characteristics


The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.


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Author Biography

Mikhail Selianinau, Jan Dlugosz University in Czestochowa

Faculty of Science and Technology,

Dr.Sci.Tech., Associate professor



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How to Cite

Selianinau, M. (2020). An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System. Computer Science, 21(2).