Qualified Subsets Research Articles

Sorting Center Value Identification of "Internet + Recycling" Based on Transfer Clustering.

As the core link of the “Internet + Recycling” process, the value identification of the sorting center is a great challenge due to its small and imbalanced data set. This paper utilizes transfer fuzzy c-means to improve the value assessment accuracy of the sorting center by transferring the knowledge of customers clustering. To ensure the transfer effect, an inter-class balanced data selection method is proposed to select a balanced and more qualified subset of the source domain. Furthermore, an improved RFM (Recency, Frequency, and Monetary) model, named GFMR (Gap, Frequency, Monetary, and Repeat), has been presented to attain a more reasonable attribute description for sorting centers and consumers. The application in the field of electronic waste recycling shows the effectiveness and advantages of the proposed method.

Practical attacks on a class of secret image sharing schemes based on Chinese Remainder Theorem

Chinese Remainder Theorem based secret image sharing schemes provide an efficient way to store secret image files securely in a distributed manner. Two basic properties required for designing such schemes are — availability and confidentiality. The first property ensures the retrieval of secret image from a qualified subset of shares and the latter guarantees the secrecy of the image against a coalition of non-qualified subset of shares. To model practical attacks on such schemes, in this paper, more powerful active adversaries are considered who can tamper with some shares to modify the reconstructed secret image. We show that an active adversary can tamper with one single share to make the honest parties reconstruct a false secret image of her choice. Our mathematical analysis along with the experimental data exhibit the practicality of our attacks for large class of existing schemes.

A perfect secret sharing scheme for general access structures

The secret sharing (SS) scheme has been widely used as the de facto paradigm for group key management in cryptography and distributed computation. An SS scheme for a general access structure (GSS) has drawn more and more attention since it allows flexible access control. However, previous solutions to GSS need to either assign multiple shares to each participant or to solve a complex nonlinear integer programming. In this paper, we propose a novel strategy to address the two problems simultaneously based on the Chinese Remainder Theorem (CRT) for a polynomial ring over a finite field. We classify general access structures satisfying the monotone property into the two families of maximum forbidden subsets and minimum qualified subsets conforming to the security condition and the revealing condition. The moduli used in the scheme are pairwise coprime polynomials and can take the irreducible polynomials. To find the degrees of these polynomials, we only need to solve an integer linear programming (ILP) by minimizing the sum of the degrees of all the moduli. The proposed scheme is inherently a weighted SS scheme and may have no solution which commonly exists in all GSS schemes. To ensure a solution, we put forth a preprocessing algorithm which separates the original access structure into several subaccess structures based on graph theory. The proposed scheme only assigns a share for each participant and achieves perfect security. It has good generalization and provides a universal approach to program the scheme construction for SS schemes with general access structures, threshold access structures and weighted access structures.

Ideal secret sharing schemes on graph-based $3$-homogeneous access structures

‎The characterization of the ideal access structures is one of the main open problems in secret sharing and is important from both practical and theoretical points of views‎. ‎A graph-based $3-$homogeneous access structure is an access structure in which the participants are the vertices of a connected graph and every subset of the vertices is a minimal qualified subset if it has three vertices and induces a connected graph‎. ‎In this paper‎, ‎we introduce the graph-based $3-$homogeneous access structures and characterize the ideal graph-based $3$-homogeneous access structures‎. ‎We prove that for every non-ideal graph-based $3$-homogeneous access structure over the graph $G$ with the maximum degree $d$ there exists a secret sharing scheme with an information rate $frac{1}{d+1}$‎. ‎Furthermore‎, ‎we mention three forbidden configurations that are useful in characterizing other families of ideal access structures‎.

An efficient verifiable (t,n)-threshold secret image sharing scheme with ultralight shares

A secret sharing scheme partitions a secret into a set of shares and distributes them among the eligible participants, with each participant receiving one share of the secret. The sharing technique allows any qualified subset of participants to recover the secret. In (t,n)-threshold secret sharing schemes, the secret is distributed among n participants in the form of shares, such that every participant holds exactly one share. Individual share reveals nothing about the secret. Any subset of participants of size t or more (t ≤ n) can combine their shares and compute the secret, while any subset of size < t is not able to do so. This paper proposes a verifiable (t,n)-threshold secret image sharing (VSIS) scheme. In the proposed scheme, a secret image is shared among n participants with an intention that if t or more (t ≤ n) participants collaborate, then the secret image can be computed successfully. Still, any less than t participants get nothing. The scheme makes use of polynomial-based secret sharing and XOR operations to construct the shares and recover the secret image. Our scheme’s main advantage is that it presents the public shares as integer numbers (not image matrices produced in previous SIS schemes), much smaller than the secret image. It also generates a public share-image of the size the same as that of the secret image. Thus, the public shares can be efficiently transferred over the public network and efficiently stored in memory. The scheme applies to both grayscale and color images. The use of Elliptic Curve Cryptography (ECC) enables the participants to choose their own secret shadows and compute the pseudo shares (integer numbers) independently. Hence the entire communications can take place safely on public channels. The pseudo shares are verifiable to the participants as well as the combiner. The combination of small public shares and the elliptic curve cryptosystem makes this scheme ideal for resource-constrained devices. In contrast, public share-image can be safely stored with a Cloud Service Provider (CSP).

Threshold-Based Post-Quantum Secure Verifiable Multi-Secret Sharing for Distributed Storage Blockchain

Blockchain systems store transaction data in the form of a distributed ledger where each node stores a copy of all data, which gives rise to storage issues. It is well-known that the tremendous storage and distribution of the block data are common problems in blockchain systems. In the literature, some types of secret sharing schemes are employed to overcome these problems. The secret sharing method is one of the most significant cryptographic protocols used to ensure the privacy of the data. The main purpose of this paper is to improve the recent distributed storage blockchain systems by proposing an alternative secret sharing method. We first propose a secure threshold verifiable multi-secret sharing scheme that has the verification and private communication steps based on post-quantum lattice-based hard problems. We then apply the proposed threshold scheme to the distributed storage blockchain (DSB) system to share transaction data at each block. In the proposed DSB system, we encrypt the data block with the AES-256 encryption algorithm before distributing it among nodes at each block, and both its secret key and the hash value of the block are privately shared among nodes simultaneously by the proposed scheme. Thereafter, in the DSB system, the encrypted data block is encoded by the Reed–Solomon code, and it is shared among nodes. We finally analyze the storage and recovery communication costs and the robustness of the proposed DSB system. We observe that our approach improves effectively the recovery communication cost and makes it more robust compared to the previous DSB systems. It also improves extremely the storage cost of the traditional blockchain systems. Furthermore, the proposed scheme brings to the DSB system the desirable properties such as verification process and secret communication without private channels in addition to the known properties of the schemes used in the previous DSB systems. As a result of the flexibility on the threshold parameter of the scheme, a diverse range of qualified subsets of nodes in the DSB system can privately recover the secret values.

Smallest Graphs Achieving the Stinson Bound

Perfect secret sharing scheme is a method to distribute a secret information s among participants such that only predefined coalitions, called qualified subsets of participants can recover the secret, while any other coalitions, the unqualified subsets, cannot determine anything about the secret. The most important property is the efficiency of the system, which is measured by the information ratio. It can be shown that for graphs the information ratio is at most (δ + 1)/2 where δ is the maximum degree of the graph. Blundo et al. constructed a family of δ-regular graphs with information ratio (δ + 1)/2 on at least c · 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</sup> vertices. We improve this result by constructing a significantly smaller graph family on c · 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</sup> vertices achieving the same upper bound both in the worst and the average case.

Finding the maximal adversary structure from any given access structure

Secure multi-party computation is an important research area in cryptography, and the secret sharing scheme (SSS) is one of the main tools for constructing multi-party computation protocols. The access structure and the adversary structure are two important subsets of participants in an SSS. In general, the collection of all qualified subsets that can reconstruct the secret s, is known as an access structure, while no information regarding this secret is available to any unqualified subsets, and the collection of unqualified subsets is described as an adversary structure. The maximal adversary, which will become a qualified subset if any one participant not in this unqualified subset is added. At present, there is no effective algorithm to determine the maximal adversary structure for any given access structure. In this paper, we propose two algorithms to determine the maximal adversary structure from any given access structure, in which a binary tree is introduced to construct such algorithms. Moreover, a special type of access structure is established, from which the maximal adversary structure can be directly characterized, and the maximal adversary structure in this case is shown to be the largest when the number of participants of each qualified polynomial in the access structure is three.

An Efficient Verifiable Threshold Multi-Secret Sharing Scheme With Different Stages

Secret sharing is one of the most important cryptographic primitives used for data outsourcing. The threshold-based secret sharing scheme is one of the well-known secret sharing schemes in cryptography. A single secret sharing scheme has low efficiency and multiple secret sharing schemes can greatly improve the efficiency of secret sharing. We present an efficient verifiable threshold multi-secret sharing scheme with different stages in which multiple secrets are shared among participants during one sharing process. In such a way, some qualified subsets of participants can collectively recover these secrets. The verifiable nature means that the participant can verify his/her own share. Our proposed scheme can share multiple secrets and each secret has its own threshold access structure. Moreover, each participant only keeps one share, and however they can reconstruct all secrets in recovery stages. This scheme is a multi-stage-use secret sharing scheme, in which the size of the participant's share is the same as that of each secret and the amount of information disclosed reaches the optimal lower bound. Compared with the previous verifiable (t,n) -threshold multi-secret sharing scheme, this scheme is of stronger computational security and practicability.

Cutting-edge cryptography through the lens of secret sharing

Secret sharing is a mechanism by which a trusted dealer holding a secret “splits” the secret into many “shares” and distributes the shares to a collection of parties. Associated with the sharing is a monotone access structure, that specifies which parties are “qualified” and which are not: any qualified subset of parties can (efficiently) reconstruct the secret, but no unqualified subset can learn anything about the secret. In the most general form of secret sharing, the access structure can be any monotone NP language.In this work, we consider two very natural extensions of secret sharing. In the first, which we call distributed secret sharing, there is no trusted dealer at all, and it can be thought of as combining the features of multiparty non-interactive key exchange and standard secret sharing. Qualified sets can agree on a key which remains pseudorandom for unqualified sets. Our second notion is called functional secret sharing, which incorporates some of the features of functional encryption into secret sharing by providing more fine-grained access to the secret. Qualified subsets of parties do not learn the secret, but instead learn some function applied to the secret, with each set of parties potentially learning a different function.Our main result is that both of the extensions above are equivalent to several recent cutting-edge primitives. In particular, general-purpose distributed secret sharing is equivalent to witness PRFs, and general-purpose functional secret sharing is equivalent to indistinguishability obfuscation. Thus, our work shows that it is possible to view some of the recent developments in cryptography through a secret sharing lens, yielding new insights about both these cutting-edge primitives and secret sharing.

How to Share a Secret, Infinitely

Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collection of qualified subsets is called an access structure . The best known example is the $k$ -threshold access structure, where the qualified subsets are those of size at least $k$ . When $k=2$ and there are $n$ parties, there are schemes for sharing an $\ell $ -bit secret in which the share size of each party is roughly $\max \{\ell ,\log n\}$ bits, and this is tight even for secrets of 1 b. In these schemes, the number of parties $n$ must be given in advance to the dealer. In this paper, we consider the case where the set of parties is not known in advance and could potentially be infinite. Our goal is to give the ${t} {^{\mathrm{ th}}}$ party arriving the smallest possible share as a function of $t$ . Our main result is such a scheme for the $k$ -threshold access structure and 1-bit secrets where the share size of party $t$ is $(k-1)\cdot \log t + \mathsf {poly}(k)\cdot o(\log t)$ . For $k=2$ we observe an equivalence to prefix codes and present matching upper and lower bounds of the form $\log t + \log \log t + \log \log \log t + O(1)$ . Finally, we show that for any access structure there exists such a secret sharing scheme with shares of size $2^{t-1}$ .

A construction method of [formula omitted]-essential secret image sharing scheme

Secret image sharing (SIS) is a technique to decompose a secret image into multiple shadows distributed to the corresponding participants. Only qualified subsets of the shadows can reveal the secret image. Usually all shadows have the same importance. However, in some application scenario, some shadows are accorded with the special privilege due to the status or importance of the corresponding participants. A (t, k, n) essential secret image sharing (ESIS) scheme share a secret image into n shadows including t essential shadows and n–t non-essential shadows. A qualified subset of the shadows should contain at least k shadows including all t essential shadows. In this paper, we propose a construction method of (t, k, n) essential secret image sharing (ESIS) scheme. In our scheme, all shadows have the size 1/k times of the secret image. It also resolves the problems in the previous ESIS schemes, such as different shadow sizes, concatenation of sub-shadows, using multiple SIS schemes and so on. Theoretical analyses and experimental results show that the proposed scheme is secure and effective.

Estimator learning automata for feature subset selection in high‐dimensional spaces, case study: Email spam detection

SummaryOne of the difficult challenges facing data miners is that algorithm performance degrades if the feature space contains redundant or irrelevant features. Therefore, as a critical preprocess task, dimension reduction is used to build a smaller space containing valuable features. There are 2 different approaches for dimension reduction: feature extraction and feature selection, which itself is divided into wrapper and filter approaches. In high‐dimensional spaces, feature extraction and wrapper approaches are not applicable due to the time complexity. On the other hand, the filter approach suffers from inaccuracy. One main reason for this inaccuracy is that the subset's size is not determined considering specifications of the problem.In this paper, we propose ESS (estimator learning automaton‐based subset selection) as a new method for feature selection in high‐dimensional spaces. The innovation of ESS is that it combines wrapper and filter ideas and uses estimator learning automata to efficiently determine a feature subset that leads to a desirable tradeoff between the accuracy and efficiency of the learning algorithm. To find a qualified subset for a special processing algorithm that functions on an arbitrary dataset, ESS uses an automaton to score each candidate subset upon the scale of the subset and accuracy of the learning algorithm using it. In the end, the subset with the highest score is returned. We have used ESS for feature selection in the framework of spam detection, a text classification task for email as a pervasive communication medium. The results show achievement in reaching the goal stated above.

Reduced access structures with four minimal qualified subsets on six participants

In this paper, we discuss a point about applying known decomposition techniques in their most general form. Three versions of these methods, which are useful for obtaining upper bounds on the optimal information ratios of access structures, are known as: Stinson's $λ$-decomposition, $(λ, ω)$-decomposition and $λ$-weighted-decomposition, where the latter two are generalizations of the first one. We continue by considering the problem of determining the exact values of the optimal information ratios of the reduced access structures with exactly four minimal qualified subsets on six participants, which remained unsolved in Marti-Farre et al.'s paper [Des. Codes Cryptogr. 61 (2011), 167-186]. We improve the known upper bounds for all the access structures, except four cases, determining the exact values of the optimal information ratios. All three decomposition techniques are used while some cases are handled by taking full advantage of the generality of decompositions.

Boolean operations-based visual secret sharing for general access structures

Compared to conventional visual secret sharing (VSS), Boolean operations-based VSS solves the problems of the large pixel expansion (pe) and the complex computation involved in the decryption process. However, the existing VSS schemes based on Boolean operations are limited only to (2, n), (n, n) and (k, n). In this paper, we propose a Boolean operations-based VSS scheme for general access structures. The proposed scheme encodes the secret image into several shares such that the secret image can be reconstructed only by any qualified subset of the shares. The proposed scheme has lossless secret reconstruction with an acceptable pixel expansion (0 < pe < 1.5) and fast decoding process. The correctness of the proposed scheme is validated by formal security analysis and the experimental results.

Visual cryptographic schemes using combined Boolean operations

Visual Cryptographic scheme (VCS) is a variant form of secret sharing method to encode a secret image into n distinct shares. The dealer distributes shares to each participants in such a way that, while certain qualified subsets of participants can visually recover the secret, but other forbidden sets of participants have no information on the secret. Such a system is the general access structures in VCS. The essential access structure (k, n)* is a type of threshold scheme were one participant is the leader who holds the essential share and the remaining n-1 shares are given to n-1 participants. The secret image cannot be retrieved in the absence of leader and the leader needs the support of at least k-1 remaining participants to recover the secret image. Small pixel expansion and maximum contrast are the basic parameters for measuring the quality of the VCS. In the literature there are constructions for both deterministic and probabilistic (k, n)*-VCS. The following are the important contributions of this paper. (1) A deterministic (k, n)*-VCS with improved contrast. (2) A deterministic (k, n)- VCS for t essential participants with improved contrast and less pixel expansion. (3) An ideal contrast general access structure construction with AND operation for grey scale images. (4) An ideal contrast (k, n)*-VCS construction for both binary and grey scale images. (5) An ideal contrast (k, n)-VCS for t essential participants for both binary and grey scale images.

Essential secret image sharing scheme with the same size of shadows

Secret image sharing is a method to decompose a secret image into shadow images (shadows) so that only qualified subset of shadows can be used to reconstruct the secret image. Usually all shadows have the same importance. Recently, an essential SIS (ESIS) scheme with different importance of shadows was proposed. All shadows are divided into two group: essential shadows and non-essential shadows. In reconstruction, the involved shadows should contain at least a required number of shadows, including at least a required number of essential shadows. However, there are two problems in previous ESIS scheme: unequal size of shadows and concatenation of sub-shadow images. These two problems may lead to security vulnerability and complicate the reconstruction. In this paper, we propose a novel ESIS scheme based on derivative polynomial and Birkhoff interpolation. A single shadow with the same-size is generated for each essential and non-essential participant. The experimental results demonstrate that our scheme can avoid above two problems effectively.

A quantum secret sharing scheme on access structure

Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.

A multi-threshold secret image sharing scheme based on the generalized Chinese reminder theorem

In a multi-secret image sharing scheme, participants are able to share multiple secret images such the way that each secret image can be reconstructed according to the corresponding access structure. In this paper, employing Chan and Chang's multi-secret sharing, we propose a new multi-threshold secret image sharing scheme. In the secret image sharing process, based on the generalized CRT, secret values are produced according to the associated access structures. The shadow images can be generated by embedding the secret values into a cover image using the quantization operation. The new scheme allows a qualified subset of participants to retrieve the related secret image. Moreover, any monotone access structure can be realized with a deletion procedure. The experiments demonstrate that secret images can be recovered without distortion. Besides, the quality of the shadow images is satisfactory and the capacity of embedded secret values is acceptable especially under binary images.

General Access Structure Secret Sharing in Matrix Projection

Image Secret Sharing is a technique which provides security to confidential images by dispersed storages. General access structure image secret sharing provides flexibility for deciding qualified subsets of participants which can reconstruct the original secret image. Non qualified subsets of participants cannot get any information about original secret image. This paper proposes general access structure image secret sharing based on matrix projection. The experimental results show high accuracy, high security and less overhead in the network due to highly reduced size of image shares.