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.     

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^?.     

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.     

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.     

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.     

A Framework for Certified Boolean Branch-and-Bound Optimization

We consider optimization problems of the form (S, cost), where S is a clause set over Boolean variables x ₁?...?x _n , with an arbitrary cost function \(\mathit{cost}\colon \mathbb{B}^n \rightarrow \mathbb{R}\), and the aim is to find a model A of S such that cost(A) is minimized. Here we study the generation of proofs of optimality in the context of branch-and-bound procedures for such problems. For this purpose we introduce \(\mathtt{DPLL_{BB}}\), an abstract DPLL-based branch-and-bound algorithm that can model optimization concepts such as cost-based propagation and cost-based backjumping. Most, if not all, SAT-related optimization problems are in the scope of \(\mathtt{DPLL_{BB}}\). Since many of the existing approaches for solving these problems can be seen as instances, \(\mathtt{DPLL_{BB}}\) allows one to formally reason about them in a simple way and exploit the enhancements of \(\mathtt{DPLL_{BB}}\) given here, in particular its uniform method for generating independently verifiable optimality proofs.     

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.     

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.     

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.     

In All But Finitely Many Possible Worlds: Model-Theoretic Investigations on ‘<Emphasis Type="Italic">Overwhelming Majority</Emphasis>’ Default Conditionals

Defeasible conditionals are statements of the form ‘if A then normally B’. One plausible interpretation introduced in nonmonotonic reasoning dictates that (\(A\Rightarrow B\)) is true iff B is true in ‘most’ A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of ‘overwhelming majority’, defined as ‘truth in a cofinite subset of \(\omega \)’, the first infinite ordinal. One approach employs the modal logic of the frame \((\omega , <)\), used in the temporal logic of discrete linear time. We introduce and investigate conditionals, defined modally over \((\omega , <)\); several modal definitions of the conditional connective are examined, with an emphasis on the nonmonotonic ones. An alternative interpretation of ‘majority’ as sets cofinal (in \(\omega \)) rather than cofinite (subsets of \(\omega \)) is examined. For these modal approaches over \((\omega , <)\), a decision procedure readily emerges, as the modal logic \({\mathbf {K4DLZ}}\) of this frame is well-known and a translation of the conditional sentences can be mechanically checked for validity; this allows also for a quick proof of \(\mathsf {NP}\)-completeness of the satisfiability problem for these logics. A second approach employs the conditional version of Scott-Montague semantics, in the form of \(\omega \)-many possible worlds, endowed with neighborhoods populated by collections of cofinite subsets of \(\omega \). This approach gives rise to weak conditional logics, as expected. The relative strength of the conditionals introduced is compared to (the conditional logic ‘equivalent’ of) KLM logics and other conditional logics in the literature.     

New q-ary quantum MDS codes with distances bigger than $$\frac{ q}{2}$$

The construction of quantum MDS codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474–1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantum MDS \([[n,n-2d+2,d]]_q\) codes with minimum distances \(d>\frac{q}{2}\) for sparse lengths \(n>q+1\). In the case \(n=\frac{q^2-1}{m}\) where \(m|q+1\) or \(m|q-1\) there are complete results. In the case \(n=\frac{q^2-1}{m}\) while \(m|q^2-1\) is neither a factor of \(q-1\) nor \(q+1\), no q-ary quantum MDS code with \(d> \frac{q}{2}\) has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over \(\mathbf{F}_{q^2}\). Then we give some new q-ary quantum codes in this case. Moreover many new q-ary quantum MDS codes with lengths of the form \(\frac{w(q^2-1)}{u}\) and minimum distances \(d > \frac{q}{2}\) are presented.     

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.     

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.     

Reductions to Graph Isomorphism

We show that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem. In particular we show that if a set is many-one logspace reducible to GI, then it is in fact many-one \(\textsf{AC}^{0}\) reducible to GI. For the case of Turing reducibilities we show that for any k≥0 an \(\textsf{NC}^{k+1}\) reduction to GI can be transformed into an \(\textsf{AC}^{k}\) reduction to the same problem.     

The remote set problem on lattices

We initiate studying the Remote Set Problem (\({\mathsf{RSP}}\)) on lattices, which given a lattice asks to find a set of points containing a point which is far from the lattice. We show a polynomial-time deterministic algorithm that on rank n lattice \({\mathcal{L}}\) outputs a set of points, at least one of which is \({\sqrt{\log n / n} \cdot \rho(\mathcal{L})}\) -far from \({\mathcal{L}}\) , where \({\rho(\mathcal{L})}\) stands for the covering radius of \({\mathcal{L}}\) (i.e., the maximum possible distance of a point in space from \({\mathcal{L}}\)). As an application, we show that the covering radius problem with approximation factor \({\sqrt{n / \log n}}\) lies in the complexity class \({\mathsf{NP}}\) , improving a result of Guruswami et al. (Comput Complex 14(2): 90–121, 2005) by a factor of \({\sqrt{\log n}}\) .Our results apply to any \({\ell_p}\) norm for \({2 \leq p \leq \infty}\) with the same approximation factors (except a loss of \({\sqrt{\log \log n}}\) for \({p = \infty}\)). In addition, we show that the output of our algorithm for \({\mathsf{RSP}}\) contains a point whose \({\ell_2}\) distance from \({\mathcal{L}}\) is at least \({(\log n/n)^{1/p} \cdot \rho^{(p)}(\mathcal{L})}\) , where \({\rho^{(p)}(\mathcal{L})}\) is the covering radius of \({\mathcal{L}}\) measured with respect to the \({\ell_p}\) norm. The proof technique involves a theorem on balancing vectors due to Banaszczyk (Random Struct Algorithms 12(4):351–360, 1998) and the “six standard deviations” theorem of Spencer (Trans Am Math Soc 289(2):679–706, 1985).     

Improved Algorithms for Maximum Agreement and Compatible Supertrees

Consider a set of labels L and a set of unordered trees \(\mathcal{T}=\{\mathcal{T}^{(1)},\mathcal{T}^{(2)},\ldots ,\allowbreak \mathcal{T}^{(k)}\}\) where each tree \(\mathcal{T}^{(i)}\) is distinctly leaf-labeled by some subset of L. One fundamental problem is to find the biggest tree (denoted as supertree) to represent \(\mathcal{T}\) which minimizes the disagreements with the trees in \(\mathcal{T}\) under certain criteria. In this paper, we focus on two particular supertree problems, namely, the maximum agreement supertree problem (MASP) and the maximum compatible supertree problem (MCSP). These two problems are known to be NP-hard for k≥3. This paper gives improved algorithms for both MASP and MCSP. In particular, our results imply the first polynomial time algorithms for both MASP and MCSP when both k and the maximum degree D of the input trees are constant.     

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.     

Characterizing the Existence of Potential Functions in Weighted Congestion Games

Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let \(\mathcal{C}\) be an arbitrary set of locally bounded functions and let \(\mathcal{G}(\mathcal{C})\) be the set of weighted congestion games with cost functions in \(\mathcal{C}\). We show that every weighted congestion game \(G\in\mathcal{G}(\mathcal{C})\) admits an exact potential if and only if \(\mathcal{C}\) contains only affine functions. We also give a similar characterization for w-potentials with the difference that here \(\mathcal{C}\) consists either of affine functions or of certain exponential functions. We finally extend our characterizations to weighted congestion games with facility-dependent demands and elastic demands, respectively.