• Journal of applied mathematics & informatics
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• 제26권1_2호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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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.

• 대한수학회지
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• 제11권1호
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• pp.5-6
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• 1974

• 대한전자공학회논문지SD
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• 제41권4호
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• pp.57-66
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• 2004

본 논문에서는 RNS(residue number systems) 몽고메리 모듈라 곱셈기 기반의 2,048 비트 RSA 설계를 제안한다. RNS는 긴 워드에 대한 모듈라 연산을 짧은 워드로 분할하여 고속 병렬 모듈라 연산을 처리하는 시스템으로써 본 논문에서는 RNS 몽고메리 모듈라 곱셈 연산을 위해 Wallace 트리 모듈라 곱셈기 기반의 Montgomery reduction method(MRM)［1］와 33개의 64 비트 RNS base 를 도입하였다. 또한, 고속 RNS 모듈라 곱셈 연산을 위해 Chinese remainder theorem(CRT)［2］기반의 개선된 base extension 알고리즘을 제안한다. 본 논문에서 제시한 RNS 기반의 2,048 비트 RSA는 삼성 0.35㎛ 공정을 사용하여 기능을 검증하였으며 100㎒에서 2.53㎳ 연산 속도 결과를 얻었다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권7호
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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.

• 대한수학회보
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• 제31권1호
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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).

• 한국수학사학회지
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• 제8권1호
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• pp.54-60
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• 1995

No Abstract, See Full Text

• 한국수학사학회지
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• 제1권1호
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• pp.80-82
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• 1984

• International Journal of Contents
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• 제11권2호
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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.

• 한국멀티미디어학회논문지
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• 제16권10호
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• pp.1163-1170
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• 2013

디지털 워터마킹은 저작권 보호와 멀티미디어 데이터 인증의 수단으로 사용되어 왔다. 기존의 공간영역에서의 CRT 기반 워터마킹 방법은 JPEG 압축에 취약하여, JPEG 압축에서 잘 동작하는 DCT 영역에서의 CRT 기반 워터마킹이 제안되었다. 본 논문에서는 DCT 영역에서의 향상된 CRT 기반 워터마킹 방법을 제안한다. 제안한 방법은 DCT 변환시 발생되는 rounding 오류 또는 여러 가지 공격에도 나머지들의 차에 대한 절대값의 변화를 감소시켜 견고성을 향상시킨다. 실험을 통하여 제안한 방법이 기존의 DCT 영역에서의 CRT 기반 워터마킹 방법보다 여러 가지 공격에 대하여 견고성이 향상되는 것을 확인하였다.