Generic construction of an $$\mathrm {}$$-secure key exchange protocol in the standard model

LaMacchia, Lauter and Mityagin presented a strong security model for authenticated key agreement, namely the \(\mathrm {eCK}\) model. They also constructed a protocol, namely the NAXOS protocol, that enjoys a simple security proof in the \(\mathrm {eCK}\) model. However, the NAXOS protocol uses a random oracle-based technique to combine the long-term secret key and the per session randomness, so-called NAXOS trick, in order to achieve the \(\mathrm {eCK}\) security definition. For NAXOS trick-based protocols, the leakage of per session randomness modeled in the \(\mathrm {eCK}\) model is somewhat unnatural, because the \(\mathrm {eCK}\) model leaks per session randomness, while the output of the NAXOS trick computation remains safe. In this work, we present a standard model \(\mathrm {eCK}\)-secure protocol construction, eliminating the NAXOS trick. Moreover, our protocol is a generic construction, which can be instantiated with arbitrary suitable cryptographic primitives. Thus, we present a generic \(\mathrm {eCK}\)-secure, NAXOS-free, standard model key exchange protocol. To the best of our knowledge this is the first paper on generic transformation of a \(\mathrm {CCA2}\)-secure public-key encryption scheme to an \(\mathrm {eCK}\)-secure key exchange protocol in the standard model.     

Spatial-spectral-combined sparse representation-based classification for hyperspectral imagery

Recently, sparse representation-based classification (SRC), which assigns a test sample to the class with minimum representation error via a sparse linear combination of all the training samples, has successfully been applied to hyperspectral imagery. Alternatively, spatial information, which means the adjacent pixels belong to the same class with a high probability, is a valuable complement to the spectral information. In this paper, we have presented a new spectral-spatial-combined SRC method, abbreviated as SSSRC or \(\mathrm{S}^{3}\mathrm{RC}\), to jointly consider the spectral and spatial neighborhood information of each pixel to explore the spectral and spatial coherence by the SRC method. Furthermore, a fast interference-cancelation operation is adopted to accelerate the classification procedure of \(\mathrm{S}^{3}\mathrm{RC}\), named \(\mathrm{FS}^{3}\mathrm{RC}\). Experimental results have shown that both the proposed SRC-based approaches, \(\mathrm{S}^{3}\mathrm{RC}\) and \(\mathrm{FS}^{3}\mathrm{RC}\), could achieve better performance than the other state-of-the-art methods.     

New asymmetric quantum codes over $$F_{q}$$

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length \(n=q^{m}-1\) over \(F_{q}\), where \(q\ge 5\) is a prime power. The second one is the asymmetric quantum codes with length \(n=3^{m}-1\). These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set \(T_{1}=T_{2}^{-q}\), then the real Z-distance of our asymmetric quantum codes are much larger than \(\delta _\mathrm{max}+1\), where \(\delta _\mathrm{max}\) is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature.     

Two families of BCH codes and new quantum codes

In this paper, two families of non-narrow-sense (NNS) BCH codes of lengths \(n=\frac{q^{2m}-1}{q^2-1}\) and \(n=\frac{q^{2m}-1}{q+1}\) (\(m\ge 3)\) over the finite field \(\mathbf {F}_{q^2}\) are studied. The maximum designed distances \(\delta ^\mathrm{new}_\mathrm{max}\) of these dual-containing BCH codes are determined by a careful analysis of properties of the cyclotomic cosets. NNS BCH codes which achieve these maximum designed distances are presented, and a sequence of nested NNS BCH codes that contain these BCH codes with maximum designed distances are constructed and their parameters are computed. Consequently, new nonbinary quantum BCH codes are derived from these NNS BCH codes. The new quantum codes presented here include many classes of good quantum codes, which have parameters better than those constructed from narrow-sense BCH codes, negacyclic and constacyclic BCH codes in the literature.     

Subspace Learning by $$\ell ^{0}$$-Induced Sparsity

Subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure. Such methods with sparsity prior, such as sparse subspace clustering (SSC) (Elhamifar and Vidal in IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781, 2013) with the sparsity induced by the \(\ell ^{1}\)-norm, are demonstrated to be effective in subspace clustering. Most of those methods require certain assumptions, e.g. independence or disjointness, on the subspaces. However, these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods. In this paper, we propose \(\ell ^{0}\)-induced sparse subspace clustering (\(\ell ^{0}\)-SSC). In contrast to the required assumptions, such as independence or disjointness, on subspaces for most existing sparse subspace clustering methods, we prove that \(\ell ^{0}\)-SSC guarantees the subspace-sparse representation, a key element in subspace clustering, for arbitrary distinct underlying subspaces almost surely under the mild i.i.d. assumption on the data generation. We also present the “no free lunch” theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding \(\ell ^{0}\) sparse representation problem of \(\ell ^{0}\)-SSC. A novel approximate algorithm named Approximate \(\ell ^{0}\)-SSC (A\(\ell ^{0}\)-SSC) is developed which employs proximal gradient descent to obtain a sub-optimal solution to the optimization problem of \(\ell ^{0}\)-SSC with theoretical guarantee. The sub-optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results. Extensive experimental results on various data sets demonstrate the superiority of A\(\ell ^{0}\)-SSC compared to other competing clustering methods. Furthermore, we extend \(\ell ^{0}\)-SSC to semi-supervised learning by performing label propagation on the sparse similarity matrix learnt by A\(\ell ^{0}\)-SSC and demonstrate the effectiveness of the resultant semi-supervised learning method termed \(\ell ^{0}\)-sparse subspace label propagation (\(\ell ^{0}\)-SSLP).     

Entanglement witness criteria of strong-<Emphasis Type="Italic">k</Emphasis>-separability for multipartite quantum states

Let \(H_{1}, H_{2},\ldots ,H_{n}\) be separable complex Hilbert spaces with \(\dim H_{i}\ge 2\) and \(n\ge 2\). Assume that \(\rho \) is a state in \(H=H_1\otimes H_2\otimes \cdots \otimes H_n\). \(\rho \) is called strong-k-separable \((2\le k\le n)\) if \(\rho \) is separable for any k-partite division of H. In this paper, an entanglement witnesses criterion of strong-k-separability is obtained, which says that \(\rho \) is not strong-k-separable if and only if there exist a k-division space \(H_{m_{1}}\otimes \cdots \otimes H_{m_{k}}\) of H, a finite-rank linear elementary operator positive on product states \(\Lambda :\mathcal {B}(H_{m_{2}}\otimes \cdots \otimes H_{m_{k}})\rightarrow \mathcal {B}(H_{m_{1}})\) and a state \(\rho _{0}\in \mathcal {S}(H_{m_{1}}\otimes H_{m_{1}})\), such that \(\mathrm {Tr}(W\rho )<0\), where \(W=(\mathrm{Id}\otimes \Lambda ^{\dagger })\rho _{0}\) is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.     

Finite approximation of the first passage models for discrete-time Markov decision processes with varying discount factors

This paper deals with the finite approximation of the first passage models for discrete-time Markov decision processes with varying discount factors. For a given control model \(\mathcal {M}\) with denumerable states and compact Borel action sets, and possibly unbounded reward functions, under reasonable conditions we prove that there exists a sequence of control models \(\mathcal {M}_{n}\) such that the first passage optimal rewards and policies of \(\mathcal {M}_{n}\) converge to those of \(\mathcal {M}\), respectively. Based on the convergence theorems, we propose a finite-state and finite-action truncation method for the given control model \(\mathcal {M}\), and show that the first passage optimal reward and policies of \(\mathcal {M}\) can be approximated by those of the solvable truncated finite control models. Finally, we give the corresponding value and policy iteration algorithms to solve the finite approximation models.     

On congruences of weak lattices

We characterize when an equivalence relation on the base set of a weak lattice \(\mathbf{L}=(L,\sqcup ,\sqcap )\) becomes a congruence on \(\mathbf{L}\) provided it has convex classes. We show that an equivalence relation on L is a congruence on \(\mathbf{L}\) if it satisfies the substitution property for comparable elements. Conditions under which congruence classes are convex are studied. If one fundamental operation of \(\mathbf{L}\) is commutative then \(\mathbf{L}\) is congruence distributive and all congruences of \(\mathbf{L}\) have convex classes.     

Shrinking one-way cellular automata

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (\(\text{OCA}\)) with the additional property that during a computation any cell of the \(\text{OCA}\) has the ability to dissolve itself, so-called shrinking one-way cellular automata (\(\text{SOCA}\)). It turns out that real-time \(\text{SOCA}\) are more powerful than real-time \(\text{OCA}\), since they can accept certain linear-time \(\text{OCA}\) languages. On the other hand, linear-time \(\text{OCA}\) are more powerful than real-time \(\text{SOCA}\), which is witnessed even by a unary language. Additionally, a construction is provided that enables real-time \(\text{SOCA}\) to accept the reversal of real-time iterative array languages. Finally, restricted real-time \(\text{SOCA}\) are investigated. We distinguish two limitations for the dissolving of cells. One restriction is to bound the total number of cells that are allowed to dissolve by some function. In this case, an infinite strict hierarchy of language classes is obtained. The second restriction is inspired by an approach to limit the amount of nondeterminism in \(\text{OCA}\). Compared with the first restriction, the total number of cells that may dissolve is still unbounded, but the number of time steps at which a cell may dissolve is bounded. The possibility to dissolve is allowed only in the first k time steps, where \(k\ge 0\) is some constant. For this mode of operation an infinite, tight, and strict hierarchy of language classes is obtained as well.     

Flexible bandwidth assignment with application to optical networks

We introduce two scheduling problems, the flexible bandwidth allocation problem (\(\textsc {FBAP}\)) and the flexible storage allocation problem (\(\textsc {FSAP}\)). In both problems, we have an available resource, and a set of requests, each consists of a minimum and a maximum resource requirement, for the duration of its execution, as well as a profit accrued per allocated unit of the resource. In \(\textsc {FBAP}\), the goal is to assign the available resource to a feasible subset of requests, such that the total profit is maximized, while in \(\textsc {FSAP}\) we also require that each satisfied request is given a contiguous portion of the resource. Our problems generalize the classic bandwidth allocation problem (BAP) and storage allocation problem (SAP) and are therefore \(\text {NP-hard}\). Our main results are a 3-approximation algorithm for \(\textsc {FBAP}\) and a \((3+\epsilon )\)-approximation algorithm for \(\textsc {FSAP}\), for any fixed \(\epsilon >0 \). These algorithms make nonstandard use of the local ratio technique. Furthermore, we present a \((2+\epsilon )\)-approximation algorithm for \(\textsc {SAP}\), for any fixed \(\epsilon >0 \), thus improving the best known ratio of \(\frac{2e-1}{e-1} + \epsilon \). Our study is motivated also by critical resource allocation problems arising in all-optical networks.     

Symmetric triangular approximations of fuzzy numbers under a general condition and properties

We consider the set \(\mathcal {P}\) of real parameters associated to a fuzzy number, in a general form which includes the most important characteristics already introduced for fuzzy numbers. We find the set \(\mathcal {P}_{\mathrm{s}}\subset \mathcal {P}\) with the property that for any given fuzzy number there exists at least a symmetric triangular fuzzy number which preserves a fixed parameter \(p\in \mathcal {P}\). We compute the symmetric triangular approximation of a fuzzy number which preserves the parameter \(p\in \mathcal {P }_{\mathrm{s}}\). The uniqueness is an immediate consequence; therefore, an approximation operator is obtained. The properties of scale and translation invariance, additivity and continuity of this operator are studied. Some applications related with value and expected value, as important parameters, are given too.     

On topological systems

We establish the reflectivity of the subcategories of \(T_{0}\) and sober topological systems in the category \(\mathbf {TopSys}\) of topological systems. We also introduce a Sierpinski object in the category \(\mathbf {TopSys}\) and point out its connection with \(T_{0}\) and sober topological systems and also with injective \(T_{0}\)-topological systems.     

Data assimilation and sampling in Banach spaces

This paper studies the problem of approximating a function f in a Banach space \(\mathcal{X}\) from measurements \(l_j(f)\), \(j=1,\ldots ,m\), where the \(l_j\) are linear functionals from \(\mathcal{X}^*\). Quantitative results for such recovery problems require additional information about the sought after function f. These additional assumptions take the form of assuming that f is in a certain model class \(K\subset \mathcal{X}\). Since there are generally infinitely many functions in K which share these same measurements, the best approximation is the center of the smallest ball B, called the Chebyshev ball, which contains the set \(\bar{K}\) of all f in K with these measurements. Therefore, the problem is reduced to analytically or numerically approximating this Chebyshev ball. Most results study this problem for classical Banach spaces \(\mathcal{X}\) such as the \(L_p\) spaces, \(1\le p\le \infty \), and for K the unit ball of a smoothness space in \(\mathcal{X}\). Our interest in this paper is in the model classes \(K=\mathcal{K}(\varepsilon ,V)\), with \(\varepsilon >0\) and V a finite dimensional subspace of \(\mathcal{X}\), which consists of all \(f\in \mathcal{X}\) such that \(\mathrm{dist}(f,V)_\mathcal{X}\le \varepsilon \). These model classes, called approximation sets, arise naturally in application domains such as parametric partial differential equations, uncertainty quantification, and signal processing. A general theory for the recovery of approximation sets in a Banach space is given. This theory includes tight a priori bounds on optimal performance and algorithms for finding near optimal approximations. It builds on the initial analysis given in Maday et al. (Int J Numer Method Eng 102:933–965, 2015) for the case when \(\mathcal{X}\) is a Hilbert space, and further studied in Binev et al. (SIAM UQ, 2015). It is shown how the recovery problem for approximation sets is connected with well-studied concepts in Banach space theory such as liftings and the angle between spaces. Examples are given that show how this theory can be used to recover several recent results on sampling and data assimilation.     

ν-twin support vector machine with Universum data for classification

A novel ν-twin support vector machine with Universum data (\(\mathfrak {U}_{\nu }\)-TSVM) is proposed in this paper. \(\mathfrak {U}_{\nu }\)-TSVM allows to incorporate the prior knowledge embedded in the unlabeled samples into the supervised learning. It aims to utilize these prior knowledge to improve the generalization performance. Different from the conventional \(\mathfrak {U}\)-SVM, \(\mathfrak {U}_{\nu }\)-TSVM employs two Hinge loss functions to make the Universum data lie in a nonparallel insensitive loss tube, which makes it exploit these prior knowledge more flexibly. In addition, the newly introduced parameters ν₁, ν₂ in the \(\mathfrak {U}_{\nu }\)-TSVM have better theoretical interpretation than the penalty factor c in the \(\mathfrak {U}\)-TSVM. Numerical experiments on seventeen benchmark datasets, handwritten digit recognition, and gender classification indicate that the Universum indeed contributes to improving the prediction accuracy. Moreover, our \(\mathfrak {U}_{\nu }\)-TSVM is far superior to the other three algorithms (\(\mathfrak {U}\)-SVM, ν-TSVM and \(\mathfrak {U}\)-TSVM) from the prediction accuracy.     

Optimal noise functions for location privacy on continuous regions

Users of location-based services are highly vulnerable to privacy risks since they need to disclose, at least partially, their locations to benefit from these services. One possibility to limit these risks is to obfuscate the location of a user by adding random noise drawn from a noise function. In this paper, we require the noise functions to satisfy a generic location privacy notion called \(\ell \)-privacy, which makes the position of the user in a given region \(\mathcal {X}\) relatively indistinguishable from other points in \(\mathcal {X}\). We also aim at minimizing the loss in the service utility due to such obfuscation. While existing optimization frameworks regard the region \(\mathcal {X}\) restrictively as a finite set of points, we consider the more realistic case in which the region is rather continuous with a nonzero area. In this situation, we demonstrate that circular noise functions are enough to satisfy \(\ell \)-privacy on \(\mathcal {X}\) and equivalently on the entire space without any penalty in the utility. Afterward, we describe a large parametric space of noise functions that satisfy \(\ell \)-privacy on \(\mathcal {X}\), and show that this space has always an optimal member, regardless of \(\ell \) and \(\mathcal {X}\). We also investigate the recent notion of \(\epsilon \)-geo-indistinguishability as an instance of \(\ell \)-privacy and prove in this case that with respect to any increasing loss function, the planar Laplace noise function is optimal for any region having a nonzero area.     

Non-determinism in Gödel’s System <Emphasis Type="Italic">T</Emphasis>

The calculus T^? is a successor-free version of Gödel’s T. It is well known that a number of important complexity classes, like e.g. the classes logspace, \(\textsc{p}\), \(\textsc{linspace}\), \(\textsc{etime}\) and \(\textsc{pspace}\), are captured by natural fragments of T^? and related calculi. We introduce the calculus T^∽, which is a non-deterministic variant of T^?, and compare the computational power of T^∽ and T^?. First, we provide a denotational semantics for T^∽ and prove this semantics to be adequate. Furthermore, we prove that \(\textsc{linspace}\subseteq \mathcal {G}^{\backsim }_{0} \subseteq \textsc{linspace}\) and \(\textsc{etime}\subseteq \mathcal {G}^{\backsim }_{1} \subseteq \textsc{pspace}\) where \(\mathcal {G}^{\backsim }_{0}\) and \(\mathcal {G}^{\backsim }_{1}\) are classes of problems decidable by certain fragments of T^∽. (It is proved elsewhere that the corresponding fragments of T^? equal respectively \(\textsc{linspace}\) and \(\textsc{etime}\).) Finally, we show a way to interpret T^∽ in T^?.     

From LTL to deterministic automata

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula \(\varphi \). The automaton is the product of a co-Büchi automaton for \(\varphi \) and an array of Rabin automata, one for each \({\mathbf {G}}\)-subformula of \(\varphi \). The Rabin automaton for \({\mathbf {G}}\psi \) is in charge of recognizing whether \({\mathbf {F}}{\mathbf {G}}\psi \) holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed to standard procedures based on Safra’s determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.     

Toward practical encrypted email that supports private,regular-expression searches

In this paper, we develop a protocol to enable private regular-expression searches on encrypted data stored at a \(\mathsf {server}\). A novelty of the protocol lies in allowing a user to securely delegate an encrypted search query to a \(\mathsf {proxy}\), which interacts with the \(\mathsf {server}\) where the user’s data are stored encrypted to produce the search result for the user. The privacy of the query and the data are both provably protected against an arbitrarily malicious \(\mathsf {server}\) and an honest-but-curious \(\mathsf {proxy}\) under rigorous security definitions. We then detail a series of optimizations to our initial design that achieve an order-of-magnitude performance improvement over the original protocol. We demonstrate the practicality of the resulting protocol through measurements of private regular-expression searches on a real-world email dataset.     

Ordering states with Tsallis relative $$\alpha $$-entropies of coherence

In this paper, we study the ordering states with Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative \(\alpha \)-entropies of coherence for \(\alpha =2, 1, \frac{1}{2}\) and show these three measures and \(l_{1}\) norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between \(l_{1}\) norm of coherence and Tsallis relative \(\alpha \)-entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.     

Connecting unextendible maximally entangled base with partial Hadamard matrices

We study the unextendible maximally entangled bases (UMEB) in \(\mathbb {C}^{d}\bigotimes \mathbb {C}^{d}\) and connect the problem to the partial Hadamard matrices. We show that for a given special UMEB in \(\mathbb {C}^{d}\bigotimes \mathbb {C}^{d}\), there is a partial Hadamard matrix which cannot be extended to a Hadamard matrix in \(\mathbb {C}^{d}\). As a corollary, any \((d-1)\times d\) partial Hadamard matrix can be extended to a Hadamard matrix, which answers a conjecture about \(d=5\). We obtain that for any d there is a UMEB except for \(d=p\ \text {or}\ 2p\), where \(p\equiv 3\mod 4\) and p is a prime. The existence of different kinds of constructions of UMEBs in \(\mathbb {C}^{nd}\bigotimes \mathbb {C}^{nd}\) for any \(n\in \mathbb {N}\) and \(d=3\times 5 \times 7\) is also discussed.