A General Design Method of Constructing Fully Homomorphic Encryption with Ciphertext Matrix

( Xinxia Song ),( Zhigang Chen ) 한국인터넷정보학회 2019 KSII Transactions on Internet and Information Syst Vol.13 No.5

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.

Secure Outsourced Computation of Multiple Matrix Multiplication Based on Fully Homomorphic Encryption

( Shufang Wang ),( Hai Huang ) 한국인터넷정보학회 2019 KSII Transactions on Internet and Information Syst Vol.13 No.11

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.’s work.We improve Mishra et al.’s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.’s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.’s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

국방 클라우드 컴퓨팅 암호화 효율적 구현 방안 연구

양현상 ( Hyeonsang Yang ) 한국국방기술학회 2020 한국국방기술학회 논문지 Vol.2 No.1

본 연구는 클라우드 컴퓨팅 암호화를 위해 동형암호에 관해 기존 문헌들의 연구 결과를 토대로 동형암호의 장단점에 대한 분석을 근거하여 동형암호 적용방법을 통해 효율적인 구현을 위한 방안을 제시하고자 한다. 이를 위해 동형암호를 IT 기술 구현 및 표준화하려는 방법이 필요하다. 본 연구에서는 동형암호 개념 이해하고 동형암호 구현을 위한 장·단점을 분석하고 효율적 구현 방법을 소개하고자 한다. This study aims to propose a method for efficient implementation through a method of applying isomorphic encryption based on the analysis of the strengths and weaknesses of isomorphic encryption based on the research results of existing literature on isotype encryption for cloud computing encryption. For this, it is necessary to implement and standardize homomorphic cryptography in IT technology. In this study, we intend to understand the concept of homomorphic cryptography, analyze the advantages and disadvantages of implementing homomorphic cryptography, and introduce efficient implementation methods.

완전 동형 암호 라이브러리의 성능 분석

조은지(Eun-Ji Jo),문수빈(Su-Bin Moon),이윤호(Younho Lee) 한국정보기술학회 2018 한국정보기술학회논문지 Vol.16 No.2

According to the coming of era of big data, the importance of data analysis is increasing. This trend emphasizes the importance of managing and controlling confidential information such as personal information derived from nations and companies. Research for ‘Fully Homomorphic Encryption’ which is able to operate encrypted data without decryption to counter this trend is active. In this paper, we compare the features of HElib, TFHE, and SEAL, which are representative libraries of Fully Homomorphic Encryption. We also implement the addition and comparison operations of the encrypted numerical data using the libraries and compare the performance. Based on the results of these features and performance comparison, we provide basic data that can be used for selecting application fields of each library.

통신환경을 이용한 CKKS 동형암호 암호문 초기화 기법

채승재,이준우,이용우,노종선 한국통신학회 2023 韓國通信學會論文誌 Vol.48 No.8

CKKS(Cheon-Kim-Kim-Song) 완전 동형 암호(Fully-Homomorphic Encryption, FHE)는 현재 연구자들의 가장큰 관심을 받고 있다. 완전동형암호를 활용할 수 있는 많은 분야가 있지만, 그중에 연구가 많이 진행되고 있는 정보보호 머신러닝에서는 현재 완전 동형 암호 외에도 다자간 계산(Multi-Party Computation, MPC)를 이용하거나혹은 둘을 혼합한 hybrid한 방식 등 다양한 방식으로 연구가 진행되고 있다. 본 논문에서는 기존 CKKS 완전 동형 암호를 사용하는 경우 가장 많은 연산시간이 소요되는 bootstrapping과정을 통신환경을 이용할 수 있을 때, 랜덤한 값을 생성하여 통신을 통해 암호문 초기화 과정을 설계하고, 이 과정으로 부트스트래핑을 대체할 수 있음을제시한다.

Efficient machine learning over encrypted data with non-interactive communication

Park, Heejin,Kim, Pyung,Kim, Heeyoul,Park, Ki-Woong,Lee, Younho Elsevier 2018 Computer standards & interfaces Vol.58 No.-

<P><B>Abstract</B></P> <P>In this paper, we describe a protocol framework that can perform classification tasks in a privacy-preserving manner. To demonstrate the feasibility of the proposed framework, we implement two protocols supporting Naive Bayes classification. We overcome the heavy computational load of conventional fully homomorphic encryption-based privacy-preserving protocols by using various optimization techniques. The proposed method differs from previous techniques insofar as it requires no intermediate interactions between the server and the client while executing the protocol, except for the mandatory interaction to obtain the decryption result of the encrypted classification output. As a result of this minimal interaction, the proposed method is relatively stable. Furthermore, the decryption key is used only once during the execution of the protocol, overcoming a potential security issue caused by the frequent exposure of the decryption key in memory. The proposed implementation uses a cryptographic primitive that is secure against attacks with quantum computers. Therefore, the framework described in this paper is expected to be robust against future quantum computer attacks.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A privacy-preserving machine learning protocol framework is proposed. </LI> <LI> The proposed protocol preserves the privacy of model, user input, and classification output. </LI> <LI> We realized the Naive–Bayesian classification protocol on our framework. </LI> <LI> We utilized Fully Homomorphic Encryption only for implementation. </LI> <LI> The proposed supports higher security and communication efficiency. </LI> </UL> </P>

클라우드 컴퓨팅 환경에서의 개인정보보호를 위한 완전 동형 암호 적용 방안 고찰

김세환(Sehwan Kim),윤현수(Hyunsoo Yoon) 한국정보보호학회 2014 정보보호학회논문지 Vol.24 No.5

클라우드 컴퓨팅 서비스는 스마트기기의 보급과 맞물려 편리함을 장점으로 수요가 급격히 증가하고 있다. 시장의 관심을 받으면서 클라우드 컴퓨팅 시스템이 정말로 안전한지에 대한 관심도 높아지고 있는 상황이다. 클라우드 환경의 특성상 서비스 제공자는 데이터를 위탁받는 입장에서 사용자의 개인정보를 유출할 수 있게 되는데, 이러한 문제점을 해결하기 위한 방법으로 완전 동형 암호가 대두되고 있다. 완전 동형 암호는 사용자의 암호화된 데이터를 복호화하지 않고 연산을 가능하게 하는 암호체계이다. 완전 동형 암호를 이용하면 기밀성을 보장하면서 암호문에 대한 키가 없어도 연산을 수행할 수 있기 때문에 클라우드 컴퓨팅 환경에서 발생할 수 있는 보안 위협 요소들을 제거하는데 효과적일 것으로 전망하고 있다. 본 논문에서는 클라우드 컴퓨팅 서비스에서 발생할 수 있는 보안 위협 요소들을 조사하고 이를 해결할 수 있는 완전 동형 암호에 대하여 살펴본다. Demands for cloud computing service rapidly increased along with the expansion of supplying smart devices. Interest in cloud system has led to the question whether it is really safe. Due to the nature of cloud system, cloud service provider can get a user"s private information and disclose it. There is a large range of opinion on this issue and recently many researchers are looking into fully homomorphic encryption as a solution for this problem. Fully homomorphic encryption can permit arbitrary computation on encrypted data. Many security threats will disappear by using fully homomorphic encryption, because fully homomorphic encryption keeps the confidentiality. In this paper, we research possible security threats in cloud computing service and study on the application method of fully homomorphic encryption for cloud computing system.

A Hybrid Scheme of Public-Key Encryption and Somewhat Homomorphic Encryption

Jung Hee Cheon,Jinsu Kim IEEE 2015 IEEE transactions on information forensics and sec Vol.10 No.5

<P>We introduce a hybrid homomorphic encryption that combines public-key encryption (PKE) and somewhat homomorphic encryption (SHE) to reduce the storage requirements of most somewhat or fully homomorphic encryption (FHE) applications. In this model, messages are encrypted with a PKE and computations on encrypted data are carried out using SHE or FHE after homomorphic decryption. To obtain efficient homomorphic decryption, our hybrid scheme combines IND-CPA PKE without complicated message padding with SHE with a large integer message space. Furthermore, if the underlying PKE is multiplicative, the proposed scheme has the advantage that polynomials of arbitrary degree can be evaluated without bootstrapping. We construct this scheme by concatenating the ElGamal and Goldwasser-Micali schemes over a ring ℤ<SUB>N</SUB> for a composite integer N whose message space is ℤ<SUB>N</SUB><SUP>×</SUP>. To accelerate the homomorphic evaluation of the PKE decryption, we introduce a method to reduce the degree of the exponentiation circuit at the cost of additional public keys. Using the same technique, we present an efficient partial solution to an open problem which is to evaluate mod q mod p arithmetic homomorphically for large p. As an independent interest, we also obtain a generic method for converting from private-key SHE to public-key SHE. Unlike the method described by Rothblum, we are free to choose the SHE message space.</P>

정수 기반 일괄 동형 암호 응용의 구현 및 성능 비교

임종혁,이문규 한국차세대컴퓨팅학회 2015 한국차세대컴퓨팅학회 논문지 Vol.11 No.6

동형 암호는 암호화된 상태의 데이터를 이용해 연산을 수행할 수 있는 암호화 방법으로, 클라우드 서비스 등 원격서버에 데이터를 저장하고 사용하는 경우에 있어 프라이버시 문제를 해결하는 수단으로 최근 활발하게 연구되고 있다. 최근까지는 완전 동형 암호의 경우 큰 암호문에 한 비트 평문 밖에 저장할 수 없어 동형 암호의 실용성 문제가제기되었으나, 하나의 암호문에 여러 평문을 저장하는 일괄 완전 동형 암호가 Eurocrypt 2013에서 Cheon 등에의해 제시되었다. 본 논문에서는 이러한 일괄 완전 동형 암호 및 이의 응용을 직접 구현하고 성능을 평가하였으며, 추가적으로 멀티코어 환경에서의 병렬처리에 따른 최적화 가능성을 확인하였다. Homomorphic encryption is an encryption scheme where operations are performed over encrypted data. An extensive research on homomorphic encryption has been done to solve the privacy issue in the applications such as cloud computing services that store critical data on remote servers. Until recently, a ciphertext of fully homomorphic encryption was able to deal with only a single plaintext bit, which was an issue from a practical viewpoint. However, in Eurocrypt 2013, Cheon et al. proposed a batch fully homomorphic encryption scheme that encrypts multiple plaintext bits in a single ciphertext. In this paper, we implement this batch fully homomorphic encryption scheme and its application and estimate the performance. In addition, we implemented this scheme on a multi-core environment to verify the effect of a parallel optimization.

Improved Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Can Xiang,Chun-ming Tang 보안공학연구지원센터 2014 International Journal of Security and Its Applicat Vol.8 No.6

Fully homomorphic encryption (FHE) is a “holy grail” of cryptography. However, it is not yet adopted in practice because no known scheme is efficient. In this paper, we mainly focus on how to reduce the public key sizes in FHE. Based on Dijk et al.’s FHE scheme (DGHV) and Gentry’s fully homomorhpic technology, we propose two schemes with shorter public keys by encrypting with a combination of the public key elements to replace a linear form in DGHV scheme and a quadratic form in Coron et al.’s scheme. Compared with DGHV scheme and Coron et al.’s scheme, our schemes can greatly reduce the public key sizes, which make our schemes more efficient. Furthermore, we prove the security of our schemes based on difficulties of the approximate greatest common divisor (AGCD) problem and the sparse subset sum problem.