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International Conference on Computer and Knowledge Engineering

Online privacy preserving outsourcing of large matrix multiplication

Fatemeh Erfan, Hamid Mala

Published Oct 1, 2017• 3 citations
Publisher

Abstract

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.

DOI
10.1109/iccke.2017.8167882

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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.
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.
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.
With the advent of cloud computing, individuals and companies alike are looking for opportunities to leverage cloud resources not only for storage but also for computation. Nevertheless, the reliance on the cloud to perform computation raises the unavoidable challenge of how to assure the correctness of the delegated computation. In this regard, we introduce two cryptographic protocols for publicly verifiable computation that allow a lightweight client to securely outsource to a cloud server the evaluation of high-degree univariate polynomials and the multiplication of large matrices. Similarly to existing work, our protocols follow the amortized verifiable computation approach. Furthermore, by exploiting the mathematical properties of polynomials and matrices, they are more efficient and give way to public delegatability. Finally, besides their efficiency, our protocols are provably secure under well-studied assumptions.
We give improved protocols for the secure and private outsourcing of linear algebra computations, that enable a client to securely outsource expensive algebraic computations (like the multiplication of large matrices) to a remote server, such that the server learns nothing about the customer's private input or the result of the computation, and any attempted corruption of the answer by the server is detected with high probability. The computational work performed at the client is linear in the size of its input and does not require the client to locally carry out any expensive encryptions of such input. The computational burden on the server is proportional to the time complexity of the current practically used algorithms for solving the algebraic problem (e.g., proportional to n3 for multiplying two n x n matrices). The improvements we give are: (i) whereas the previous work required more than one remote server and assumed they do not collude, our solution works with a single server (but readily accommodates many, for improved performance); (ii) whereas the previous work required a server to carry out expensive cryptographic computations (e.g., homomorphic encryptions), our solution does not make use of any such expensive cryptographic primitives; and (iii) whereas in previous work collusion by the servers against the client revealed to them the client's inputs, our scheme is resistant to such collusion. As in previous work, we maintain the property that the scheme enables the client to detect any attempt by the server(s) at corruption of the answer, even when the attempt is collusive and coordinated among the servers.
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 nnn number of servers (n≥2n \geq 2n≥2), and the nnn-party protocols ensure the security of the original data even if n−1n-1n−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.
We give protocols for the secure and private outsourcing of linear algebra computations, that enable a client to securely outsource expensive algebraic computations (like the multiplication of huge matrices) to two remote servers, such that the servers learn nothing about the customer's private input or the result of the computation,and any attempted corruption of the answer by the servers is detected with high probability. The computational work done locally by the client is linear in the size of its input and does not require the client to carry out locally any expensive encryptions of such input.The computational burden on the servers is proportional to the time complexity of the current practically used algorithms for solving the algebraic problem (e.g., proportional to n3for multiplying two ntimesn matrices). If the servers were to collude against the client,then they would only find out the client's private inputs, but they would not be able to corrupt the answer without detection by the client.