The highly development of Internet and cloud computing technology makes it possible to share computing power, storage and data. Cloud computing makes users with limited computing resources be able to carry out large computational tasks with the help of cloud. but security is a major concern that hinders the widespread use of outsourcing computing. We focus on outsourcing large matrix multiplication in this paper. Firstly, we exploit Chinese Remainder Theorem(CRT) to construct a large matrix multiplication outsourcing protocol which is highly efficient in the malicious cloud model. Then formal security proof and extensive performance evaluation show that our protocol achieves a higher security level i.e., information-theoretic security for input privacy and adaptive chosen ciphertext attack (CCA2) security for output privacy). Compared with previous works, users in the proposed protocol are able to verify the results received from the cloud with tiny error rate.
The highly development of Internet and cloud computing technology makes it possible to share computing power, storage and data. Cloud computing makes users with limited computing resources be able to carry out large computational tasks with the help of cloud. but security is a major concern that hinders the widespread use of outsourcing computing. We focus on outsourcing large matrix multiplication in this paper. Firstly, we exploit Chinese Remainder Theorem(CRT) to construct a large matrix multiplication outsourcing protocol which is highly efficient in the malicious cloud model. Then formal security proof and extensive performance evaluation show that our protocol achieves a higher security level i.e., information-theoretic security for input privacy and adaptive chosen ciphertext attack (CCA2) security for output privacy). Compared with previous works, users in the proposed protocol are able to verify the results received from the cloud with tiny error rate.
Outsourcing computation to cloud server has recently become popular in cloud computing. Cloud computing technologies enable clients with limited computational resources to outsource their massive computations to powerful cloud servers. Outsourcing computation has some new concerns, such as outsourced data and result privacy, verifiability and efficiency. Matrix multiplication is one of the most basic computational problems. In this paper, we are motivated to design a secure and efficient protocol for outsourcing the massive matrix multiplication computations to the cloud server. The existing works are mostly under amortized model that have an expensive phase as offline mode. Our proposed scheme does not have any expensive phase. So the client can outsource its matrices in online mode in which the efficiency of outsourcing will be increased. In our scheme, the client encrypts two matrices and sends them to a semi-honest cloud server. The cloud server computes matrix multiplication and a proof. After that, it sends the encrypted result to the client and finally the client checks the validity of the computation and decrypts the result. Our proposed scheme achieves privacy protection of outsourced data and multiplication result, unforgeability of proof, verification and high efficiency.
Linear algebra plays an important role in computer science, especially in cryptography. Numerous cryptographic protocols and scientific computations are based on linear algebra, which can be reduced to some core problems, such as matrix multiplication, determinant and the characteristic polynomial of a matrix. However, it is difficult to carry out these expensive computations independently for resource-limited cloud users. Outsourced computation, a service provided by cloud computing, enables a resources-constrained client to outsource his mass computing tasks to the cloud. In this paper, we use data hiding technique to design a secure and verifiable outsourcing protocol for computing the characteristic polynomial and eigenvalues of a matrix. Our protocols achieve several desired features, such as data privacy, verifiability and efficiency. Moreover, no cryptographic assumption is needed in our protocols.
In view of the problem that users’ informations are leaked and tampered possiblely exists at service terminal in existing outsourcing cloud computing protocols,a secure efficient and verifiable outsourcing protocol about determinant computing in the cloud was proposed.Firstly,the outsourcing computing protocol was based on the fuzz matrix technology and needed not under the premise of any difficulty assumptions to ensure the security of users’ informations.Secondly,by means of generating a special kind of transformation matrixes to deal with plaintext matrix,then after the users receive the returned results,the correctness of these results can be verified effectively,and the performance analysis shows this protocol can effectively improve the efficiency of outsourcing cloud computing.Finally,an electronic trading framework for determinant outsourcing computing was proposed,which could be effectively applied to e-commerce and other fields.
Matrix calculation plays an important role in both scientific computation and cryptography. Many cryptographic protocols, scientific computations, and numerical computations are based on matrix calculation. However, it is difficult to finish matrix calculation independently for these customers whose computation abilities are limited. Cloud Computing has a great deal of computational resources, which enable customers with limited computational resources to outsource their mass computing to the cloud. In this paper we design secure, verifiable, and practical outsourcing protocols for matrix calculation, including matrix multiplication, computing the determinant and inverse of a matrix. Compared with those existing outsourcing protocols, our protocols have obvious improvement concerning both efficiency and security. Furthermore, no cryptographic assumption is needed in our protocols. Finally, we give two applications for our outsourcing protocols; one is to construct an outsourcing protocol for solving the large-scale systems of linear equations, and the other is to design an outsourcing protocol for realizing a cryptosystem based on error-correction code.
Cloud-assisted computation empowers resource-constrained clients to efficiently tackle computationally intensive tasks by outsourcing them to resource-rich cloud servers. In the current era of Big Data, the widespread need to solve large-scale modular linear systems of equations (LMLSE) of the formAx≡bmodqposes a significant challenge, particularly for lightweight devices. This paper delves into the secure outsourcing ofLMLSEunder a malicious single-server model and, to the best of our knowledge, introduces the inaugural protocol tailored to this specific context. The cornerstone of our protocol lies in the innovation of a novel matrix encryption method based on sparse unimodular matrix transformations. This novel technique bestows our protocol with several key advantages. First and foremost, it ensures robust privacy for all computation inputs, encompassingA,b,q, and the outputx, as validated by thorough theoretical analysis. Second, the protocol delivers optimal verifiability, enabling clients to detect cloud server misbehavior with an unparalleled probability of 1. Furthermore, it boasts high efficiency, requiring only a single interaction between the client and the cloud server, significantly reducing local-client time costs. For anm-by-nmatrixA, a given parameterλ=ω(logq), andρ=2.371552, the time complexity is diminished fromO(max{mnρ−1,mρ−2n2}⋅(logq)2)toO((mn+m2)λlogq+mn(logq)2). The comprehensive results of our experimental performance evaluations substantiate the protocol's practical efficiency and effectiveness.
The rapid development of cloud computing has probably benefited each of us. However, the privacy risks brought by untrusty cloud servers arise the attention of more and more people and legislatures. In the last two decades, plenty of works seek the way of outsourcing various specific tasks while ensuring the security of private data. Although the addition and multiplication are enough for implementing any functions, the direct utilization of existing schemes like homomorphic encryption will lead to significant efficiency and accuracy loss, which is not suitable for outsourcing computation tasks. The tasks to be outsourced are endless, however, the involved calculations are similar. In this paper, inspired by additive secret sharing and multiplicative secret sharing technologies, we construct a series of novel protocols which support the common secure calculations on numbers (e.g., basic elementary functions) or matrices (e.g., solve eigenvectors) in arbitrary n number of servers (n≥2), and the n-party protocols ensure the security of the original data even if n−1 servers collude. All protocols we designed only need constant interaction rounds, and we demonstrate them under universally composability security. We believe that these protocols can provide a new basic tool for actual outsourced tasks.