text: Cloud business intelligence is an increasingly popular choice to deliver decision support capabilities via elastic, pay-per-use resources. However, data security issues are one of the top concerns when dealing with sensitive data. In this paper, we propose a novel approach for securing cloud data warehouses by flexible verifiable secret sharing, fVSS. Secret sharing encrypts and distributes data over several cloud service providers, thus enforcing data privacy and availability. fVSS addresses four shortcomings in existing secret sharing-based approaches. First, it allows refreshing the data warehouse when some service providers fail. Second, it allows on-line analysis processing. Third, it enforces data integrity with the help of both inner and outer signatures. Fourth, it helps users control the cost of cloud warehousing by balancing the load among service providers with respect to their pricing policies. To illustrate fVSS' efficiency, we thoroughly compare it with existing secret sharing-based approaches with respect to security features, querying power and data storage and computing costs.
  @cite_14: In this paper, we propose the new (t i , n) threshold multi secret sharing scheme. In our scheme, each user keeps only one share and the secret vectors K i = k i , 1 ,…, k i , mi are shared according to independent (t i , n) threshold access structures (i = l,…, h). Here note that a (t i , n) threshold multi-secret sharing scheme has been proposed by [1]. Unfortunately, however, there is a serious attack on Shi's scheme that can reconstruct all elements of K i with only t 1 shares. In this paper, we shall give the solution to this problem by using one-way functions. Furthermore, Shi's scheme has a drawback such that the dimension of the secret vector K i cannot exceed t i . On the other hand, our scheme has no such a restriction. Finally, we demonstrate that our scheme is more efficient than Shi's scheme by showing that our scheme is more efficient than the three naive improvements on the protocol of
  @cite_4: In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme, based on one-dimensional cellular automata where the number of secrets is not restricted by n or t. We show that our scheme can be used to solve an open problem proposed recently in (2008) [G. Alvarez, L. Hernandez Encinas, A. Martin del Rey, A multisecret sharing scheme for color images based on cellular automata, Information Sciences 178 (2008) 4382-4395].
  @cite_7: Cloud computing helps reduce costs, increase business agility and deploy solutions with a high return on investment for many types of applications, including data warehouses and on-line analytical processing. However, storing and transferring sensitive data into the cloud raises legitimate security concerns. In this paper, the authors' propose a new multi-secret sharing approach for deploying data warehouses in the cloud and allowing on-line analysis processing, while enforcing data privacy, integrity and availability. The authors' first validate the relevance of their approach theoretically and then experimentally with both a simple random dataset and the Star Schema Benchmark. The authors also demonstrate its superiority to related methods.
  @cite_9: A new multi-secret sharing (t, n) threshold scheme is proposed in this paper. The scheme uses the Lagrange interpolating polynomial to split and reconstruct the secrets based on Shamir secret sharing scheme, and verifies the legality of data by NTRU algorithm and one-way hashing function. Compared with other public key cryptosystems such as elliptic curve cryptography, the proposed is simpler in design, which requires less calculation and fewer storage spaces. It can detect effectively a variety of cheating and forgery behaviors, which guarantee that the reconstruction of secret is the secure and trustworthy.
  @cite_0: In the secret sharing schemes already published, the security of the scheme is mostly established upon difficult mathematical problems such as the solution of discrete logarithm and the factoring of large number. However, such schemes take up lots of resources while result in low speed. In this paper we propose a new secret-sharing scheme, which is based on shamir secret sharing scheme and use the NTRU and one-way hashing function to verify the validity of data. The security of our scheme is built on quick and efficient NTRU algorithm. It can use the public channel to issue information, detect effectively a variety of cheating or forgery behaviors, and ensure the credibility of resumption of secret.
  @cite_2: 
  @cite_13: Highlights? We propose an efficient (n, t, n)-VSS. ? We propose a (n, t, n)-MSS. ? We propose a (n, t, n)-VMSS. ? All our (n, t, n) SS are unconditionally secure. Recently, Harn and Lin introduced a notion of strong t-consistency of a (t, n) secret sharing scheme and proposed a strong (n, t, n) verifiable secret sharing (VSS). In this paper, we propose a strong (n, t, n) VSS which is more efficient than Harn and Lin's VSS. Using the same approach, we propose a (n, t, n) multi-secret sharing scheme (MSS) to allow shareholders to share n-t+1 secrets. Also, the proposed (n, t, n) MSS can be modified to include the verifiable feature. All proposed schemes are unconditionally secure and are based on Shamir's (t, n) secret sharing scheme.
  @cite_12: A secret-sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. Secret-sharing schemes are an important tool in cryptography and they are used as a building box in many secure protocols, e.g., general protocol for multiparty computation, Byzantine agreement, threshold cryptography, access control, attribute-based encryption, and generalized oblivious transfer. In this survey, we describe the most important constructions of secret-sharing schemes; in particular, we explain the connections between secret-sharing schemes and monotone formulae and monotone span programs. We then discuss the main problem with known secret-sharing schemes - the large share size, which is exponential in the number of parties. We conjecture that this is unavoidable. We present the known lower bounds on the share size. These lower bounds are fairly weak and there is a big gap between the lower and upper bounds. For linear secret-sharing schemes, which is a class of schemes based on linear algebra that contains most known schemes, super-polynomial lower bounds on the share size are known. We describe the proofs of these lower bounds. We also present two results connecting secret-sharing schemes for a Hamiltonian access structure to the NP vs. coNP problem and to a major open problem in cryptography - constructing oblivious-transfer protocols from one-way functions.
  @cite_17: In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D . This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
summary: Among encryption techniques, only secret sharing @cite_12 handles both data privacy and availability, which is why we focus on this family of approaches. The principle of secret sharing @cite_17 is based on the fact that @math points define a polynomial @math of degree @math . The secret is the polynomial's constant term and the remaining terms are usually randomly selected. Each data piece is transformed into @math shares @math corresponding to points of the polynomial. Reconstruction of the secret is achieved through Lagrange interpolation @cite_2 : there is only one polynomial @math such that @math and @math . Then the secret is @math . Moreover, modern secret sharing schemes, such as multi-secret sharing @cite_7 @cite_13 @cite_14 , verifiable secret sharing @cite_0 , and verifiable multi-secret sharing @cite_9 @cite_4 , also help reduce shared data volume, verify the honesty of CSPs, and both, respectively. We classify secret sharing-based approaches for securing DBs and DWs into two families.