• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.77-85
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• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Journal of Biomedical Engineering Research
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• v.5 no.1
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• pp.39-46
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• 1984

In order to improve the performance of ultrasonic diagnostic equipment, it is important to development the signal processing considering the ultrasonic properties of biological medium and propagation mechanism in tissue. Attenuation coefficient is not only important factor to analyze propagation properties, but also it is significant to estimate it in view of tissue characterization, so we show one of the method to estimate attenuation coefficient of biological tissue and the results of estimation.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.553-567
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• 2021

In this paper, we introduce concepts of MS-fuzzy ideals of MS-algebras. We reveal the connections between MS-fuzzy ideals and several kinds of fuzzy ideals as fuzzy prime ideals, kernel fuzzy ideals, e-fuzzy ideals and closure fuzzy ideals. We show that many of these classes are proper subclasses of the class of MS-fuzzy ideals. Finally some properties of the homomorphic images, inverse homomorphic images of MS-fuzzy ideals are studied.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.435-447
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• 2019

The notions of a neutrosophic subalgebra and a neutrosohic ideal of a subtraction algebra are introduced. Characterizations of a neutrosophic subalgebra and a neutrosophic ideal are investigated. We show that the homomorphic preimage of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra, and the onto homomorphic image of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.35-51
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• 2022

We give secure parameter suggestions to use sparse secret vectors in LWE based encryption schemes. This should replace existing security parameters, because homomorphic encryption (HE) schemes use quite different variables from the existing parameters. In particular, HE schemes using sparse secrets should be supported by experimental analysis, here we summarize existing attacks to be considered and security levels for each attacks. Based on the analysis and experiments, we compute optimal scaling factors for CKKS.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.465-477
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• 2023

In this paper, the concepts of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are introduced, and their properties are studied. The restricted intersection, the extended intersection, union, AND operation, and the cartesian product of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are established. Moreover, the homomorphic image and homomorphic pre-image of soft PMS-algebras are also studied.

• The Journal of the Korea Contents Association
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• v.21 no.9
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• pp.42-50
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• 2021

As the Internet environment develops, data-analysis-based applications have been widely and extensively used in the past decade. However, these applications potentially have a privacy problem in that users' personal information may be leaked to unauthorized parties. To tackle such a problem, researchers have suggested several techniques including data perturbation and cryptography. The homomorphic encryption algorithm is a relatively new cryptography technology that allows arithmetic operations for encrypted values as it is without decryption. Since original values are not required, we believe that this method provides better privacy protection than other existing solutions. In this work, we propose to apply a homomorphic encryption algorithm that protects personal information while enabling data analysis.

• Journal of Industrial Convergence
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• v.17 no.1
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• pp.1-6
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• 2019

Various cryptographic technologies have been proposed from ancient times and are developing in various ways to ensure the confidentiality of information. Due to exponentially increasing computer power, the encryption key is gradually increasing for security. Technology are being developed; however, security is guaranteed only in a short period of time. With the advent of the 4th Industrial Revolution, encryption technology is required in various fields. Recently, encryption technology using homomorphic encryption has attracted attention. Security threats arise due to the exposure of keys and plain texts used in the decryption processing for the operation of encrypted information. The homomorphic encryption can compute the data of the cipher text and secure process the information without exposing the plain text. When using the homomorphic encryption in processing big data like stored personal information in various services, security threats can be avoided because there is no exposure to key usage and decrypted information.

• Convergence Security Journal
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• v.21 no.1
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• pp.33-44
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• 2021

Data outsourcing utilizing the Cloud faces a problem of the third-party exposure, modulation, and reliability for the provided computational delegation results. In order to solve those problematic security issues, homomorphic encryption(HE) which executes calculation and analysis on encrypted data becomes popular. By extension, a new type of HE with a authentication functionality, homomorphic authenticated encryption(HAE) is suggested. However, a research on the HAE is on the initial stage. Furthermore, based on a message authenticated scheme with HE, the method and analysis to design is still absent. This paper aims to analyze an HAE, with a generic combination of a message authenticated scheme and a HE, known as "Encrypt with Authentication". Following a series of analysis, we show that by adopting a unforgeable message authenticated scheme, the generically constructed HAE demonstrated an unforgeability as well. Though, a strong unforgeability is not the case. This paper concludes that although indistinguishable HE can be applied to design the HAE, a security issue on the possibility of indistinguishability is still not satisfied.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.12
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• pp.1904-1913
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• 2021

With the proliferation of smart phones and the development of IoT technology, it has become possible to collect personal data for public purposes. However, users are afraid of voluntarily providing their private data due to privacy issues. To remedy this problem, mainly three techniques have been studied: data disturbance, traditional encryption, and homomorphic encryption. In this work, we perform simulations to compare them in terms of accuracy, message length, and computation delay. Experiment results show that the data disturbance method is fast and inaccurate while the traditional encryption method is accurate and slow. Similar to traditional encryption algorithms, the homomorphic encryption algorithm is relatively effective in privacy preserving because it allows computing encrypted data without decryption, but it requires high computation costs as well. However, its main cost, arithmetic operations, can be processed in parallel. Also, data analysis using the homomorphic encryption needs to do decryption only once at any number of data.