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Optimising the New Chinese Remainder Theorem 1 for the Moduli Set

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
John Bosco Aristotle K. Ansuura, Ismail Rashid Fadulilahi

John Bosco Aristotle K Ansuura and Ismail Rashid Fadulilahi. Optimising the New Chinese Remainder Theorem 1 for the Moduli Set. International Journal of Computer Applications 148(4):1-7, August 2016. BibTeX

	author = {John Bosco Aristotle K. Ansuura and Ismail Rashid Fadulilahi},
	title = {Optimising the New Chinese Remainder Theorem 1 for the Moduli Set},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2016},
	volume = {148},
	number = {4},
	month = {Aug},
	year = {2016},
	issn = {0975-8887},
	pages = {1-7},
	numpages = {7},
	url = {},
	doi = {10.5120/ijca2016906811},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


This paper seeks to improve the performance of the New Chinese Remainder Theorem (CRT) using the new moduli set {2^(2n+2)+3,2^(2n+1)+1,2^2n+1,2}. This optimization is very important in order to minimize the cost of hardware implementation and to improve the reverse conversion speed. The major factor responsible for this high hardware cost and high reverse conversion time is the presence of multipliers in the hardware implementation of the reverse converters. This paper proposes the moduli set {2^(2n+2)+3,2^(2n+1)+1,2^2n+1,2}, which is applicable for applications requiring larger dynamic range. The moduli set must be relatively prime integers. The computation of multiplicative inverses can be eliminated. We employ the proposed moduli set to optimize the New CRT-I. This scheme can result in less memory and adder based reverse converters, which is shown to be better than known existing similar state of the art scheme.


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Reverse Conversion, Optimization, Algorithm, Co-prime.