Secure matrix multiplication based on fully homomorphic encryption

Huang, Hai; Zong, Haoran

doi:10.1007/s11227-022-04850-4

Cited by 9 publications

(7 citation statements)

References 19 publications

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“…No fully homomorphic encryption and Arbitrary matrix multiplication [91] Hypercube Structure, Fully homomorphic (Symmetric) multiplication scheme for arbitrary matrix, Fully homomorphic encryption Experimental findings indicate outstanding performance for matrices of varied dimensions.…”

Section: Swhe and Bgnmentioning

confidence: 99%

Comprehensive Review and Analysis of Cryptography Techniques in Cloud Computing

Sasikumar,

Nagarajan

2024

IEEE Access

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Cloud computing is a fast-growing industry that offers various online services, including software, computing resources, and databases. Its payment model is usage-based, whereas consistency is based on resource-sharing. Cloud storage is popular among individuals and businesses because it reduces cost, increases productivity, boosts performance, and improves security. However, cloud computing comes with security risks as data are stored with third-party providers, and Internet access limits visibility and control. Effective data security and data protection are key issues compared with traditional on-premise computing. There are several methods for ensuring data security in the cloud, of which cryptography is the most important. Cryptography offers a range of security features including authentication, confidentiality, integrity, and availability. However, a thorough examination of the different cryptography methods in a single study is lacking. This study comprehensively examined different cryptography methods, including deoxyribose nucleic acid (DNA), elliptic curve, homomorphic, hybrid, lightweight, and novel methods. The analysis addresses their methodology, algorithms, results, applications, and limitations and provides valuable suggestions for data security in the cloud. This paper proposes the use of elliptic curve cryptography (ECC) to ensure safe communication and lightweight cryptography for Internet of Things (IoT) devices with limited resources. This emphasizes the benefit of combining asymmetric security with symmetric efficiency in hybrid cryptography.

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Section: Swhe and Bgnmentioning

confidence: 99%

Comprehensive Review and Analysis of Cryptography Techniques in Cloud Computing

Sasikumar,

Nagarajan

2024

IEEE Access

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“…Rathee et al [29] proposed to encrypt source matrices into the two-dimensional hypercube structure [24] and then transform the MM problem to a series of matrixvector multiplication problems. Huang et al [30] extended this approach to make it applicable to general MM. As shown in section 3.3, we have developed a more effective algorithm with higher computational efficiency.…”

Section: Related Workmentioning

confidence: 99%

“…3.3.1 m = min{m, l, n} 0 (28) 0 (6) 0 (165) 0 (100) 0 (51) 0 (18) 0 (1) 0 (168) 0 (91) 0 (30) 0 (320) 0 (216) 0 (128) 0 (56) For the HE MM of A m×l × B l×n , Algorithm 1 needs to perform l iterations, with each iteration including one ϵ transformation, one ω transformation, one HE-Add, and one HE-Mult operation. Assuming the matrix is flattened with the columnmajor order, according to Theorem 3.3 and 3.4, one ϵ transformation and one ω transformation would result in no more than (( n l + 1) + 2n) non-zero diagonals in corresponding transformation matrices, with each non-zero diagonal requiring one HE-Add, one HE-Rot, and one HE-CMult operations.…”

Section: The Enhanced Hegmm Algorithmmentioning

confidence: 99%

“…For a general MM A m×l × B l×n , we can transform A m×l and B l×n to two square matrices, A ′ d×d and B ′ d×d with d = max{m, l, n} and use this algorithm to calculate the result; • E2DM-R, which is presented in [27] on rectangular matrix multiplication A r×d × B d×d . For a general MM A m×l ×B l×n , we can expand A m×l and/or B l×n accordingly and use this algorithm to calculate the result; • Huang-MM, which is introduced in [30] and implemented with Pyfhel [10].…”

Section: Experimental Platformmentioning

confidence: 99%

“…We randomly generated 2000 pairs of matrices, with column and row numbers evenly distributed with [1,64], as the test cases. Note that, even though Huang et al [30], HEGMM and HEGMM-Enhanced can handle MM with column or row numbers exceeding 64, as long as the total element is no more than 2 12 , we limited the largest dimension size to 64 so that E2DM-S and E2DM-R can always apply. We assume that σ and τ transformations of E2DM and HEGMM are performed on plaintext, and to be fair, we assume the portion of Huang et al's algorithm, i.e., extracting diagonal vector from matrix, is also performed on plaintext.…”

Section: Experimental Platformmentioning

confidence: 99%

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Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption

Gao,

Gang,

Homsi

et al. 2024

Preprint

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Despite the enormous technical and financial advantages of cloud computing, security and privacy have always been the primary concerns for adopting cloud computing facilities, especially for government agencies and commercial sectors with high-security requirements. Homomorphic Encryption (HE) has recently emerged as an effective tool in ensuring privacy and security for sensitive applications by allowing computing on encrypted data. One major obstacle to employing HE-based computation, however, is its excessive computational cost, which can be orders of magnitude higher than its counterpart based on the plaintext. In this paper, we study the problem of how to reduce the HE-based computational cost for general Matrix Multiplication (MM), i.e., a fundamental building block for numerous practical applications, by taking advantage of the Single Instruction Multiple Data (SIMD) operations supported by HE schemes. Specifically, we develop a novel element-wise algorithm for general matrix multiplication, based on which we propose two HE-based General Matrix Multiplication (HEGMM) Approved for Public Release on 06 Mar 2024. Distribution is Unlimited. Case Number: 2024-0184 (original case number(s): AFRL-2024-0944) algorithms to reduce the HE computation cost. Our experimental results show that our algorithms can significantly outperform the state-of-the-art approaches of HE-based matrix multiplication.

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