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.
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.
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.
Matrix calculation, which has been considered as one of the most expensive operations, plays an important role in most current cryptosystems. In this paper, we propose three new and secure outsourcing schemes of matrix calculation by using one untrusted cloud server. The first one is for matrix multiplication, the second is for the inverse of a matrix, and the third is for the determinant of a matrix. Compared with other proposed schemes, our schemes are superior in efficiency owing to the reduction of user cost. In particular, the user's computation cost in our schemes is at most 1/4, 1/4, 7/16 of the corresponding schemes in the state-of-the-art algorithms, respectively. In addition, the efficiency and security of our schemes are analysed and proved.
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.
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.
Abstract. Linear algebra plays an important role in computer science, especially in cryptography.Numerous cryptog-raphic protocols, scientific computations, and numerical computations are based on linear algebra. Many linear algebra tasks can be reduced to some core problems, such as matrix multiplication, determinant of matrix and the characteristic polynomial of matrix. However, it is difficult to execute these tasks independently for client whose computation abilities are weaker than polynomial-time computational ability. Cloud Computing is a novel eco-nomical paradigm which provides powerful computational resources that enables resources-constrained client to outsource their mass computing tasks to the cloud. In this paper, we propose a new verifiable and secure outsourcing protocol for the problem of computing the characteristic polynomial and eigenvalues of matrix. These protocols are not only effi-cient and secure, but also unnecessary for any cryptographic assumption.