Private-keyless access, serving as an implementation mechanism within policy-based data custody, enables control and authorization based on predefined policies without requiring users to possess a private key. The unforgeability of both user identity and authorization decisions is ensured by the cryptosystem in private-keyless data custody. Hereby, we introduce a novel Cryptographic Resource Enabled Framework (CREF) to simplify key management, enhance security, and increase flexibility of access authorization. Firstly, in the data custody phase, data resource and its session key are uploaded in ciphertext form to CREF, and the access authorization complies with multiple policies designated by the provider. Secondly, in the dynamic authorization phase, traditional keys or keycards are replaced with adequate one-time attribute credentials issued by multiple authorities. CREF makes dynamically cryptographic policy decision according to the credentials and the cryptographic policy (cryptopolicy). Technically, we design the Credentials-Driven Cryptosystem (CDC) over ideal lattice to build anti-quantum confidence for CREF. In CDC, preimage Gaussian sampler is adopted to sample short vector as real-time attribute credential instead of user's private key. Small policy matrix is implemented to convert monotone policies into optimized cryptopolicies in order to reduce accumulated error. The security analysis confirms that both credentials and cryptopolicies are existentially unforgeable, ensuring the semantic security of the whole CREF. Experimental results indicate CREF has lower storage and computational costs than existing schemes. Meanwhile, with policies' continuous improvements as system evolves, CREF only need to select a suitable policy among multiple candidates to make authorization decisions without having to reencrypt data.

In this article, our primary focus is on the current lack of privacy-preserving queries tailored to real-number fields rather than integers. We take multisource private data counting on real numbers (R-PDC) within IoT architecture as a breakthrough point to enable diverse query services without revealing sensitive data. The advantage of this is that the parameters required for queries remain stable and minimal in the scenario of wide numerical domain and dynamic changed data set. First, we present a general R-PDC method based on curve approximation, in which an approximate query function (AQF) is established to approximate the constructed ideal counting curve for element queries on target set. We also demonstrate curve construction process of AQF and provide the feasibility theorem of AQF for counting a target element within an allowable error. By integrating the R-PDC method with fixed-point fully homomorphic encryption, an efficient R-PDC scheme is presented to perform multiparty collaborative queries in IoT. In security aspect, the R-PDC scheme on$(m,\epsilon)$-AQF is proved to be statistically secure against chosen element attack (CEA) for cumulative error$\epsilon $and data set size$m$. Moreover, the scheme achieves$O(nm\gamma)$computation and$O(n^{2}m\gamma)$communication complexities for$n$servers and$\gamma $-length fraction. Finally, as an extension of AQF over single attribute, multidimensional R-PDC method is applied into privacy-preserving Naive Bayes classifier and Apriori algorithm over multiple attributes. Our work provides substantial support and insights for the advancement of privacy computation.

To face urgent concern of privacy leakage on mobile crowdsourcing, some Lattice-Based Cryptographic (LBC) schemes have been applied to the cloud-fog-edge data sharing platform for privacy protection. As an important factor of LBC’s security, current key generation usually involves Preimage Gaussian Sampling for Lattice Trapdoor (PGS-LT) to sample short preimage vector from dual lattice. However, there lacks researches on the implementation of PGS-LT according to entities’ computation and storage capacities. To address this issue, we present a fast double-perturbation scheme that is applied to the cloud-fog-edge data sharing platform. Firstly, we design a fast spherical G-lattice sampling algorithm including two samplers: G-perturbation sampler and G-lattice sampler. Among them, the fast non-spherical G-lattice sampling algorithm is extended to arbitrary bases, and deployed on the G-lattice sampler. Meanwhile, the G-perturbation sampler is designed to sample G-perturbation for converting the non-spherical distribution of output G-lattice vector to the spherical one. Secondly, we optimize the assignment of computational tasks in PGS-LT by considering entities’ abilities in the cloud-fog-edge platform. Moreover, we analyze three types of delegated preimage sampling in terms of Gaussian quality and complexity. The analysis and experimental results show that fast spherical G-lattice sampling provides high Gaussian quality of output vector. Meanwhile, in the aspect of complexity, the G-perturbation sampler has lower time & space complexity than the existing works. The G-lattice sampler remains good performance as it only involves extra integer multiplications in linear time complexity.

In this article, we address the problem of data privacy in multisource data mining. To do it, we present a new multiparty fully homomorphic encryption (MP-FHE) scheme, in which all participants are completely fair to perform the same computation. At first, the proposed MP-FHE scheme is divided into five stages (i.e., calculation, configuration, recombination, resharing, and reconstruction stage) to achieve the unified computation form of addition and multiplication. Meanwhile, random bivariate polynomials and commutative encryption are used to achieve the degree reduction of polynomials and the continuity of computation. Moreover, we prove that the scheme meets result consistency and program termination under the fail-stop adversary model. Especially, three kinds of error detection criteria are presented to find errors in three different stages (i.e., recombination, resharing, and reconstruction stage), which provides the monitor basis for the fail-stop adversary model. In addition, the MP-FHE scheme is applied into privacy preserving k-means clustering algorithm. Finally, we evaluate the computation and communication performance of our scheme from both theoretical and experimental aspects, and the evaluation results show that the scheme is efficient enough for multisource data mining.

In this article, we address the problem of secure sensitive data sharing for the specified recipients in Blockchain Internet of Things (BIoT). To do it, we present a cryptographic solution to meet the requirements of decentralization and convenience through key management and programmable ciphertext. First, we design a new ciphertext-policy decentralized-key attribute-based encryption (CP-DK-ABE) scheme. After the master secret key is shared into all full nodes in the form of threshold secret sharing, a decentralized multiparty computation protocol is used to generate the user’s private key in an interactive way. Meanwhile, the attribute subkeys associated with the private key can be reconstructed by obtaining a fragment from each of full nodes, so as to achieve the cooperative management of attribute key through all of full nodes. Furthermore, following the blockchain’s script system, we introduce five new opcodes to represent ciphertext in the programmable format. Such a mechanism provides flexible capability to represent the logical relationship of the access control policy among attribute subciphers in the CP-DK-ABE ciphertext by the scripting language. As a result, the processes of encryption and decryption are implemented entirely by the script interpreter on the blockchain node, thereby greatly improving the convenience of programming in BIoT devices. In addition, we prove that the proposed CP-DK-ABE scheme is key private and semantically secure for a limited number of corrupted full nodes under the decisional linear and bilinear Diffie–Hellman assumption, respectively.

In the past decade, the researchers paid more attention to the cheating problem in visual cryptography (VC) so that many cheating prevention visual cryptography schemes (CPVCS) have been proposed. In this paper, the authors propose a novel method, which first makes use of Latin square to prevent cheating in VC. Latin squares are utilised to guide the choosing of authentication regions in different rows and columns of each divided block of the shares, which ensures that the choosing of authentication regions is both random and uniform. Without pixel expansion, the new method provides random regions authentication in each divided block of all shares. What is important is that the proposed method is applicable to both ( k , n )‐deterministic visual cryptography scheme (( k , n )‐DVCS) and ( k , n )‐probabilistic visual cryptography scheme (( k , n )‐PVCS). Experimental results and properties analysis are given to show the effectiveness of the proposed method.

The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time . In this paper, we prove that for the 2-URMS networks: 1) the solvability can be determined with time O(|E|); 2) a solution can be constructed with time O(|E|); 3) an optimal solution can be obtained in polynomial time; 4) the number of encoding links required to achieve a solution is upper-bounded by max{3,2N - 2}; and 5) the field size required to achieve a linear solution is upper-bounded by max{2, ⌊√{2N-7/4}+1/2⌋}, where |E| is the number of links and N is the number of sinks of the underlying network. Both bounds are shown to be tight.

We consider a directed acyclic network with two source-sink pairs {s1, t1} and {s2, t2}. The source s1wishes to communicate a message X1to the sink t1and the source s2wishes to communicate two messages X2and X3to the sink t2, where Xi, i = 1,2,3, are independent random variables of unit rate. We give a simple characterization for linear solvability of such networks under the condition that the minimum cut from {s1, s2} to t2equals 3. We develop a region decomposition method for proving this result, which we believe can be an effective approach for non-multicast network coding problem.

This paper consists of an erratum to the previously published Enumerating Typical Circulant Covering Projections onto a Circulant Graph.

Enumerating the isomorphism classes of several types of graph covering projections is one of the central research topics in enumerative topological graph theory (see [S. F. Du, D. Marusic, and A. O. Waller, J. Combin. Theory Ser. B, 74 (1998), pp. 276--290], [S. F. Du, J. H. Kwak, and M. Y. Xu, J. Combin. Theory Ser. B, 93 (2005), pp. 73--93], [R. Feng, J. H. Kwak, J. Kim, and J. Lee, SIAM J. Discrete Math., 11 (1998), pp. 265--272], [R. Feng. and J. H. Kwak, Discrete Math.}, 277 (2004), pp. 73--85], [C. D. Godsil and A. D. Hensel, J. Combin. Theory Ser. B., 56 (1992), pp. 205--238], [M. Hofmeister, Discrete Math., 143 (1995), pp. 87--97], [M. Hofmeister, SIAM J. Discrete Math., 8 (1995), pp. 51--61], [M. Hofmeister, SIAM J. Discrete Math., 11 (1998), pp. 286--292], [J. H. Kwak, J. Chun, and J. Lee, SIAM J. Discrete Math., 11 (1998), pp. 273--285], [J. H. Kwak and J. Lee, Canad. J. Math., 42 (1990), pp. 747--761], and [J. H. Kwak and J. Lee, Combinatorial and Computational Mathematics: Present and Future, (2001), pp. 97--161]). A covering projection is called circulant if its covering graph is circulant. A covering projection p from a Cayley graph ${\rm Cay} ({\cal A},X)$ onto another ${\rm Cay} ({\cal Q},Y)$ is called typical if the map $p: {\cal A}\rightarrow {\cal Q}$ on the vertex sets is a group homomorphism from ${\cal A}$ onto ${\cal Q}$. In [R. Feng. and J. H. Kwak, Discrete Math., 277 (2004), pp. 73--85], the authors enumerated the isomorphism classes of typical circulant double covering projections onto a circulant graph. As a continuation of this work, we enumerate in this paper the isomorphism classes of those covering projections of any folding number. An erratum to this article has been appended at the end of the pdf file.

Hofmeister introduced the notion of a concrete (resp., concrete regular) covering of a graph G and gave formulas for enumerating the isomorphism classes of concrete (resp., concrete regular) coverings of G [Ars Combin., 32 (1991), pp. 121--127; SIAM J. Discrete Math., 8 (1995), pp. 51--61]. In this paper, we show that the number of the isomorphism classes of n-fold concrete (resp., concrete regular) coverings of G is equal to that of the isomorphism classes of n-fold (resp., regular) coverings of a new graph, the join $G+\infty$ of G and an extra vertex $\infty$. As a consequence, we can enumerate the isomorphism classes of concrete (resp., concrete regular) coverings of a graph by using known formulas for enumerating the isomorphism classes of coverings (resp., regular coverings) of a graph.