Biblio

In cloud computing application scenarios involving computationally weak clients, the natural need for applied cryptography solutions requires the delegation of the most expensive cryptography algorithms to a computationally stronger cloud server. Group exponentiation is an important operation used in many public-key cryptosystems and, more generally, cryptographic protocols. Solving the problem of delegating group exponentiation in the case of a single, possibly malicious, server, was left open since early papers in the area. Only recently, we have solved this problem for a large class of cyclic groups, including those commonly used in cryptosystems proved secure under the intractability of the discrete logarithm problem. In this paper we solve this problem for an important class of non-cyclic groups, which includes RSA groups when the modulus is the product of two safe primes, a common setting in applications using RSA-based cryptosystems. We show a delegation protocol for fixed-exponent exponentiation in such groups, satisfying natural correctness, security, privacy and efficiency requirements, where security holds with exponentially small probability. In our protocol, with very limited offline computation and server computation, a client can delegate an exponentiation to an exponent of the same length as a group element by only performing two exponentiations to an exponent of much shorter length (i.e., the length of a statistical parameter). We obtain our protocol by a non-trivial adaptation to the RSA group of our previous protocol for cyclic groups.

Group exponentiation is an important operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is outsourced from a computationally weaker client to a computationally stronger server, possibly implemented in a cloud-based architecture. While preliminary solutions to this problem considered mostly honest servers, or multiple separated servers, some of which honest, solving this problem in the case of a single (logical), possibly malicious, server, has remained open since a formal cryptographic model was introduced in [20]. Several later attempts either failed to achieve privacy or only bounded by a constant the (security) probability that a cheating server convinces a client of an incorrect result. In this paper we solve this problem for a large class of cyclic groups, thus making our solutions applicable to many cryptosystems in the literature that are based on the hardness of the discrete logarithm problem or on related assumptions. Our main protocol satisfies natural correctness, security, privacy and efficiency requirements, where the security probability is exponentially small. In our main protocol, with very limited offline computation and server computation, the client can delegate an exponentiation to an exponent of the same length as a group element by performing an exponentiation to an exponent of short length (i.e., the length of a statistical parameter). We also show an extension protocol that further reduces client computation by a constant factor, while increasing offline computation and server computation by about the same factor.

Now a day's cloud technology is a new example of computing that pays attention to more computer user, government agencies and business. Cloud technology brought more advantages particularly in every-present services where everyone can have a right to access cloud computing services by internet. With use of cloud computing, there is no requirement for physical servers or hardware that will help the computer system of company, networks and internet services. One of center services offered by cloud technology is storing the data in remote storage space. In the last few years, storage of data has been realized as important problems in information technology. In cloud computing data storage technology, there are some set of significant policy issues that includes privacy issues, anonymity, security, government surveillance, telecommunication capacity, liability, reliability and among others. Although cloud technology provides a lot of benefits, security is the significant issues between customer and cloud. Normally cloud computing technology has more customers like as academia, enterprises, and normal users who have various incentives to go to cloud. If the clients of cloud are academia, security result on computing performance and for this types of clients cloud provider's needs to discover a method to combine performance and security. In this research paper the more significant issue is security but with diverse vision. High performance might be not as dangerous for them as academia. In our paper, we design an efficient secure and verifiable outsourcing protocol for outsourcing data. We develop extended QP problem protocol for storing and outsourcing a data securely. To achieve the data security correctness, we validate the result returned through the cloud by Karush\_Kuhn\_Tucker conditions that are sufficient and necessary for the most favorable solution.

Cloud computing platforms are becoming increasingly prevalent and readily available nowadays, providing us alternative and economic services for resource-constrained clients to perform large-scale computation. In this work, we address the problem of secure outsourcing of large-scale nonnegative matrix factorization (NMF) to a cloud in a way that the client can verify the correctness of results with small overhead. The input matrix protection is achieved by a lightweight, permutation-based encryption mechanism. By exploiting the iterative nature of NMF computation, we propose a single-round verification strategy, which can be proved to be effective. Both theoretical and experimental results are given to demonstrate the superior performance of our scheme.

The massive amount of data that is being collected by today's society has the potential to advance scientific knowledge and boost innovations. However, people often lack sufficient computing resources to analyze their large-scale data in a cost-effective and timely way. Cloud computing offers access to vast computing resources on an on-demand and pay-per-use basis, which is a practical way for people to analyze their huge data sets. However, since their data contain sensitive information that needs to be kept secret for ethical, security, or legal reasons, many people are reluctant to adopt cloud computing. For the first time in the literature, we propose a secure outsourcing algorithm for large-scale quadratic programs (QPs), which is one of the most fundamental problems in data analysis. Specifically, based on simple linear algebra operations, we design a low-complexity QP transformation that protects the private data in a QP. We show that the transformed QP is computationally indistinguishable under a chosen plaintext attack (CPA), i.e., CPA-secure. We then develop a parallel algorithm to solve the transformed QP at the cloud, and efficiently find the solution to the original QP at the user. We implement the proposed algorithm on the Amazon Elastic Compute Cloud (EC2) and a laptop. We find that our proposed algorithm offers significant time savings for the user and is scalable to the size of the QP.