• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.307-316
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• 2008

Real life problems can be expressed as a congruence modulus n and split into a system of congruence equations in modulus factors of n. A system of congruence equations can be combined into a congruence equation under certain conditions. This paper uniquely presents and critically reviews the generalized Chinese Remainder Theorem (CRT) for combining systems of congruence equations into single congruence equations. Sequential and parallel implementation strategies of the generic CRT are outlined. A variety of unique applications of the CRT are discussed.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.377-395
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• 2023

The purpose of this paper is to consider the abstract theory of hypernear rings. In this regard, we derive the isomorphism theorems for hypernear rings as well as Chinese Remainder theorem. Our results can be considered as a generalization for the cases of Krasner hyperrings, near rings and rings.

• Journal of the Korean Mathematical Society
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• v.11 no.1
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• pp.5-6
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• 1974

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.4
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• pp.57-66
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• 2004

This paper proposes the design of a 2,048-bit RSA based on RNS(residue number systems) Montgomery modular multiplier As the systems that RNS processes a fast parallel modular multiplication for a large word partitioned into small words, we introduce Montgomery reduction method(MRM)［1］based on Wallace tree modular multiplier and 33 RNS bases with 64-bit size for RNS Montgomery modular multiplication in this paper. Also, for fast RNS modular multiplication, a modified method based on Chinese remainder theorem(CRT)［2］ is presented. We have verified 2,048-bit RSA based on RNS using Samsung 0.35${\mu}{\textrm}{m}$ technology and the 2,048-bit RSA is performed in 2.54㎳ at 100MHz.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.7
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• pp.3690-3713
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• 2019

According to the main group key management schemes logical key hierarchy (LKH), exclusion basis systems (EBS) and other group key schemes are limited in network structure, collusion attack, high energy consumption, and the single point of failure, this paper presents a group key management scheme for wireless sensor networks based on Lagrange interpolation polynomial characteristic (AGKMS). That Chinese remainder theorem is turned into a Lagrange interpolation polynomial based on the function property of Chinese remainder theorem firstly. And then the base station (BS) generates a Lagrange interpolation polynomial function f(x) and turns it to be a mix-function f(x)' based on the key information m(i) of node i. In the end, node i can obtain the group key K by receiving the message f(m(i))' from the cluster head node j. The analysis results of safety performance show that AGKMS has good network security, key independence, anti-capture, low storage cost, low computation cost, and good scalability.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.93-97
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• 1994

Previously T.Porter [3] has given a relative Chinese Remainder Theorem under the hypothesis that given ring R has at least one .tau.-closed maximal ideal (by his notation Ma $x_{\tau}$(R).neq..phi.). In this short paper we drop his overall hypothesis that Ma $x_{\tau}$(R).neq..phi. and give the proof and some related results with this Theorem. In this paper R will always denote a commutative ring with identity element and all modules will be unitary left R-modules unless otherwise specified. Let .tau. be a given hereditarty torsion theory for left R-module category R-Mod. The class of all .tau.-torsion left R-modules, dented by J is closed under homomorphic images, submodules, direct sums and extensions. And the class of all .tau.-torsionfree left R-modules, denoted by F, is closed under taking submodules, injective hulls, direct products, and isomorphic copies ([2], Proposition 1.7 and 1.10).

• Journal for History of Mathematics
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• v.8 no.1
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• pp.54-60
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• 1995

No Abstract, See Full Text

• Journal for History of Mathematics
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• v.1 no.1
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• pp.80-82
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• 1984

• International Journal of Contents
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• v.11 no.2
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• pp.31-36
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• 2015

Recent years have seen a significant increase in demand for multimedia data over wireless sensor networks for monitoring applications that utilize sensor nodes to collect multimedia data, including sound and video. However, the multimedia streams generate a very large amount of data. When data transmission schemes for traditional wireless sensor networks are applied in wireless multimedia sensor networks, the network lifetime significantly decreases due to the excessive energy consumption of specific nodes. In this paper, we propose a data compression scheme that implements the Chinese remainder theorem to a wireless multimedia sensor network. The proposed scheme uses the Chinese Remainder Theorem (CRT) to compress and split multimedia data, and it then transmits the bit-pattern packets of the remainder to the base station. As a result, the amount of multimedia data that is transmitted is reduced. The superiority of our proposed scheme is demonstrated by comparing its performance to that of an existing scheme. The results of our experiment indicate that our proposed scheme significantly increased the compression ratio and reduced the compression operation in comparison to those of existing compression schemes.

• Journal of Korea Multimedia Society
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• v.16 no.10
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• pp.1163-1170
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• 2013

Digital watermarking techniques have been used as one of the means for copyright protection and authentication of multimedia data. Conventional Chinese Remainder Theorem(CRT)-based spatial domain watermarking techniques do not perform well under JPEG compression. However, it is seen that the CRT-based watermarking technique in Discrete Cosine Transform(DCT) domain performs well for JPEG compression. In this paper, an improved CRT-based image watermarking method in the DCT domain is proposed. The proposed method provides better robustness which decreases changes of absolute difference of residues against rounding errors due to DCT conversion and various attacks. Experimental results show that the proposed method has a good robustness against various attacks compared with the conventional CRT-based watermarking in DCT domain.