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.
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.
@cite_14 @cite_4 @cite_7 @cite_9 @cite_0 @cite_2 @cite_13 @cite_12 @cite_17
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A secret sharing scheme is a method to store information securely and reliably. Particularly, in a threshold secret sharing scheme , a secret is encoded into @math shares, such that any set of at least @math shares suffice to decode the secret, and any set of at most @math d @math t_ 1 d n$ . The scheme is based on a generalization of Shamir’s secret sharing scheme and preserves its simplicity and efficiency. In addition, we consider the setting of secure distributed storage where the proposed communication efficient secret sharing schemes not only improve decoding bandwidth but further improve disk access complexity during decoding. 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. We consider the problem of threshold secret sharing in groups with hierarchical structure. In such settings, the secret is shared among a group of participants that is partitioned into levels. The access structure is then determined by a sequence of threshold requirements: a subset of participants is authorized if it has at least k0 0 members from the highest level, as well as at least k1 > k0 members from the two highest levels and so forth. Such problems may occur in settings where the participants differ in their authority or level of confidence and the presence of higher level participants is imperative to allow the recovery of the common secret. Even though secret sharing in hierarchical groups has been studied extensively in the past, none of the existing solutions addresses the simple setting where, say, a bank transfer should be signed by three employees, at least one of whom must be a department manager. We present a perfect secret sharing scheme for this problem that, unlike most secret sharing schemes that are suitable for hierarchical structures, is ideal. As in Shamir's scheme, the secret is represented as the free coefficient of some polynomial. The novelty of our scheme is the usage of polynomial derivatives in order to generate lesser shares for participants of lower levels. Consequently, our scheme uses Birkhoff interpolation, i.e., the construction of a polynomial according to an unstructured set of point and derivative values. A substantial part of our discussion is dedicated to the question of how to assign identities to the participants from the underlying finite field so that the resulting Birkhoff interpolation problem will be well posed. In addition, we devise an ideal and efficient secret sharing scheme for the closely related hierarchical threshold access structures that were studied by Simmons and Brickell. 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.