Secure outsourcing of large matrix determinant computation

Liu, Jiayang; Bi, Jingguo

doi:10.1007/s11704-019-9189-7

Cited by 11 publications

(11 citation statements)

References 51 publications

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“…However, in practice, the cloud may be malicious. To the best of our knowledge, the existing secure outsourcing algorithms for matrix determinant computation under the malicious model include [4][5][6]. In [5], Lei et al used the block matrix and permutation techniques to protect privacy.…”

Section: Related Work and Comparative Analysismentioning

confidence: 99%

“…In their algorithm, the client's local computations include (2 + l)n 2 + 2m 2 + 4mn + 2n + m multiplications, where m is the increase in dimension after encryption and n is the original dimension of matrix. Liu et al proposed a new matrix determinant secure outsourcing algorithm using the permutation and mix-row/mix-column operations, which avoid the increase in matrix dimension during the encryption and reduces the number of local multiplications to (2 + l)n 2 + 3n [6]. Zhang et al proposed a method that has better privacy [4]; however, because 8n times of elementary column/row transformations are involved in the process of encryption, it has a higher local computational burden than other algorithms, which require (10 + l)n 2 + 6n local multiplications.…”

Section: Related Work and Comparative Analysismentioning

confidence: 99%

“…We use the permutation, mix-row/mix-column, and split operations in our algorithm to protect the privacy of matrix. Besides, we use a new result verification method to improve the cheating detectability, which is different from [4][5][6]. The main idea of the verification method is to ensure that at least the diagonal elements in the results of Low triangle and Up triangle (LU) decomposition returned from the cloud are correct.…”

Section: Secure Outsourcing Of Matrix Determinantmentioning

confidence: 99%

“…In Table 3, the number of multiplications required by every part of the proposed algorithm is demonstrated and compared with three existing algorithms from [4][5][6]. In Table 4, the numbers of additions required by the proposed algorithm are listed and compared in the same way as Table 3.…”

Section: Computational Complexitymentioning

confidence: 99%

“…In all the previous algorithms, the detectability of malicious forged results depends on the rounds of verification, and to achieve a high cheating detectability, multiple rounds of verification are required, which also brings high computational burden to the client. In the previous three algorithms [4][5][6], the succeeding probability of malicious forged results is 1 2 l , where l is the number of verification rounds and recommended to be greater than 20.…”

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confidence: 99%

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Secure Outsourcing of Matrix Determinant Computation under the Malicious Cloud

Song

Sang

2021

Sensors

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Computing the determinant of large matrix is a time-consuming task, which is appearing more and more widely in science and engineering problems in the era of big data. Fortunately, cloud computing can provide large storage and computation resources, and thus, act as an ideal platform to complete computation outsourced from resource-constrained devices. However, cloud computing also causes security issues. For example, the curious cloud may spy on user privacy through outsourced data. The malicious cloud violating computing scripts, as well as cloud hardware failure, will lead to incorrect results. Therefore, we propose a secure outsourcing algorithm to compute the determinant of large matrix under the malicious cloud mode in this paper. The algorithm protects the privacy of the original matrix by applying row/column permutation and other transformations to the matrix. To resist malicious cheating on the computation tasks, a new verification method is utilized in our algorithm. Unlike previous algorithms that require multiple rounds of verification, our verification requires only one round without trading off the cheating detectability, which greatly reduces the local computation burden. Both theoretical and experimental analysis demonstrate that our algorithm achieves a better efficiency on local users than previous ones on various dimensions of matrices, without sacrificing the security requirements in terms of privacy protection and cheating detectability.

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