• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.5
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• pp.2629-2650
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• 2019

It is important to construct fully homomorphic encryption with ciphertext matrix that makes fully homomorphic encryption become very nature and simple. We present a general design method of constructing fully homomorphic encryption whose ciphertext is matrix. By using this design method, we can deduce a fully homomorphic encryption scheme step by step based on a basic encryption scheme. The process of deduction is similar to solving equation and the final output result is a fully homomorphic encryption scheme with ciphertext matrix. The idea of constructing ciphertext matrix is ciphertexts stack, which don't simply stack ciphertexts together but is to obtain the desired homomorphic property. We use decryption structure as tool to analyze homomorphic property and noise growth during homomorphic evaluation. By using this design method, we obtain three corresponding fully homomorphic encryption schemes. Our obtained fully homomorphic encryption schemes are more efficient. Finally, we introduce the adversary advantage and improve the previous method of estimating concert parameters of fully homomorphic encryption. We give the concert parameters of these schemes.

• East Asian mathematical journal
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• v.39 no.3
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• pp.291-298
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• 2023

Recently, a new type of encryption called Homomorphic Authenticated Encryption (HAE) has been proposed. This combines the functionality of homomorphic encryption with authentication. Several concrete HAE schemes have been developed and security results for homomorphic authenticated encryption, designed by combining a homomorphic message authentication scheme with a homomorphic secret-key encryption, have been partially reported. In this paper, we analyze the security of a design method that combines homomorphic message authentication and homomorphic encryption, with a focus on the encryption after authentication (EAA) type. The results of our analysis show that while non-forgeability and indistinguishability are maintained, strong non-forgeability is not.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.237-240
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• 2004

In this study, the digital image processing with image enhancement based on homomorphic filtering was performed using geophysical imaging data such as gravity, magnetic data and sub-scenes of satellite images such as LANDSAT, IKONOS, and KOMPSAT. Windows application program for executing homomorphic filtering was designed and newly implemented. In general, homomorphic filtering is technique that is based on Fourier transform, which enhances the contrast of image by removing the low frequencies and amplifying the high frequencies in frequency domain. We can enhance the image selectively using homomorphic filtering as compared with the existing method, which enhance the image totally. Through several experiment using remotely sensed imagery and geophysical image with this program, it is concluded that homomorphic filtering is more effective to reveal distinct characteristics for some complicated and multi-associated features on image data.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.5
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• pp.2588-2609
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• 2019

Speech homomorphic encryption has become one of the key components in secure speech storing in the public cloud computing. The major problem of speech homomorphic encryption is the huge data expansion of speech cipher-text. To address the issue, this paper presents a speech homomorphic encryption scheme with less data expansion, which is a probabilistic statistics and addition homomorphic cryptosystem. In the proposed scheme, the original digital speech with some random numbers selected is firstly grouped to form a series of speech matrix. Then, a proposed matrix encryption method is employed to encrypt that speech matrix. After that, mutual information in sample speech cipher-texts is reduced to limit the data expansion. Performance analysis and experimental results show that the proposed scheme is addition homomorphic, and it not only resists statistical analysis attacks but also eliminates some signal characteristics of original speech. In addition, comparing with Paillier homomorphic cryptosystem, the proposed scheme has less data expansion and lower computational complexity. Furthermore, the time consumption of the proposed scheme is almost the same on the smartphone and the PC. Thus, the proposed scheme is extremely suitable for secure speech storing in public cloud computing.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.24 no.3
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• pp.461-475
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• 2014

Homomorphic MAC is a cryptographic primitive which protects authenticity of data, while allowing homomorphic evaluation of such protected data. In this paper, we present a new homomorphic MAC, which is based on integers, relying only on the existence of secure PRFs, and having efficiency comparable to the practical Catalano-Fiore homomorphic MAC. Our scheme is unforgeable even when MAC verification queries are allowed to the adversary, and we achieve this by showing strong unforgeability of our scheme.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.231-233
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• 2006

We characterize those commutative semigroups S such that every non-isomorphic homomorphic image of S has smaller cardinality than S. We also characterize commutative groups with the same property.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.4
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• pp.601-608
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• 2023

Homomorphic encryption is a promising technology that has been extensively researched in recent years. It allows computations to be performed on encrypted data, without the need to decrypt it. In this paper, we perform bibliometric analysis to objectively and quantitatively analyze the research trends of homomorphic encryption technology using 6,047 homomorphic encryption papers from the Scopus database. Specifically, we analyze the number of papers by year, keyword co-occurrence, topic clustering, changes in related keywords over time, and country of homomorphic encryption research institutions. Our analysis results provide strategic directions for research and application of homomorphic encryption and can be a great help for subsequent research and industrial applications.

• Journal of Information Processing Systems
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• v.7 no.3
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• pp.549-560
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• 2011

Vote validity proof and verification is an efficiency bottleneck and privacy drawback in homomorphic e-voting. The existing vote validity proof technique is inefficient and only achieves honest-verifier zero knowledge. In this paper, an efficient proof and verification technique is proposed to guarantee vote validity in homomorphic e-voting. The new proof technique is mainly based on hash function operations that only need a very small number of costly public key cryptographic operations. It can handle untrusted verifiers and achieve stronger zero knowledge privacy. As a result, the efficiency and privacy of homomorphic e-voting applications will be significantly improved.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.4
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• pp.123-128
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• 1994

Hardware realization of a digital 2-D homomorphic filter for real time contrast enhancement of video signal is presented. In homomorphic filter, logarithmic and exponential conversion used the memory lookup table method and because the hardware is implemented by multiplierless TTL devices, it can be designed to specific IC. The contrast gain can be controlled externally and the transfer function of homomorphic filter can be easily varied by the change of lookup table memory data.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.3
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• pp.172-177
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• 2009

In this paper, a new morphology-based homomorphic filtering technique is presented to enhance features in medical images. The homomorphic filtering is performed based on the morphological sub-bands, in which an image is morphologically decomposed. An evolutionary design is carried to find an optimal gain and structuring element of each sub-band. As a search algorithm, Differential Evolution scheme is utilized. Simulations show that the proposed filter improves the contrast of the interest feature in medical images.