Assume that Alice, Bob, and Carol, each of whom privately holds a one-bit input, want to learn the output of some Boolean function, say the majority function, of their inputs without revealing more of their own secret inputs than necessary. In this paper, we show that such a secure three-input function evaluation can be performed with a deck of real cards; specifically, the three players can learn only the output of the function using eight physical cards — four black and four red cards — with identical backs.

Suppose one of the edges is attacked in a graph G, where some number of guards are placed on some of its vertices. If a guard is placed on one of the end-vertices of the attacked edge, she can defend such an attack to protect G by passing over the edge. For each of such attacks, every guard is allowed either to move to a neighboring vertex, or to stay at where she is. The eternal vertex cover number τ^∞(G) is the minimum number of guards sufficient to protect G from any length of any sequence of edge attacks. This paper derives the eternal vertex cover number τ^∞(G) of such graphs constructed by replacing each edge of a tree by an arbitrary elementary bipartite graph (or by an arbitrary clique), in terms of easily computable graph invariants only, thereby showing that τ^∞(G) can be computed in polynomial time for such graphs G.

A hinge vertex is a vertex in an undirected graph such that there exist two vertices whose removal makes the distance between them longer than before. Identifying hinge vertices in a graph can help detect critical nodes in communication network systems, which is useful for making them more stable. For finding them, an O(n³) time algorithm was developed for a simple graph, and, linear time algorithms were developed for interval and permutation graphs, respectively. Recently, the maximum detour hinge vertex problem is defined by Honma et al. For a hinge vertex u in a graph, the detour degree of u is the largest value of distance between any pair of x and y (x and y are adjacent to u) by removing u. A hinge vertex with the largest detour degree in G is defined as the maximum detour hinge vertex of G. This problem is motivated by practical applications, such as network stabilization with a limited cost, i.e., by enhancing the reliability of the maximum detour hinge vertex, the stability of the network is much improved. We previously developed an O(n²) time algorithm for solving this problem on an interval graph. In this study, we propose an algorithm that identifies the maximum detour hinge vertex on a permutation graph in O(n²) time, where n is the number of vertices in the graph.

We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.

A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar bipartite graphs of maximum degree four. However, we show that the problem is solvable in linear time for graphs having tree-like structures, more specifically, for bounded treewidth graphs, chordal graphs and cographs. We then give a fixed-parameter algorithm for planar graphs when parameterized by the solution size. Such a fixed-parameter algorithm is already known for general graphs, but our algorithm is exponentially faster than the known one.

A binary tree is regarded as a prefix-free binary code, in which the weighted sum of the lengths of root-leaf paths is equal to the expected codeword length. Huffman's algorithm computes an optimal tree in O(n log n) time, where n is the number of leaves. The problem was later generalized by allowing each leaf to have its own function of its depth and setting the sum of the function values as the objective function. The generalized problem was proved to be NP-hard. In this paper we study the case where every function is a unit step function, that is, a function that takes a lower constant value if the depth does not exceed a threshold, and a higher constant value otherwise. We show that for this case, the problem can be solved in O(n log n) time, by reducing it to the Coin Collector's problem.

A term tree pattern is a rooted ordered tree pattern which consists of ordered tree structures with edge labels and structured variables with labels. All variables with the same label in a term tree pattern can be simultaneously replaced with ordered trees isomorphic to the same rooted ordered tree. Then, a term tree pattern is suitable for representing structural features common to tree structured data such as XML documents on the web, the secondary structures of RNA in biology and parse trees describing grammatical structures of natural languages. Let $ott$ be the set of all term tree patterns which have one or more variables with the same label. Let $lott$ be the set of all term tree patterns t such that all variables in t have distinct labels. We remark that $lottsubsetneq ott$ holds. In this paper, we consider a problem, called Matching problem for term tree patterns, of deciding whether or not a given rooted ordered tree T is obtained from a given term tree pattern t by replacing variables in t with rooted ordered trees. We show that Matching problem for term tree patterns in $ott$ is NP-complete, by giving a reduction from the string pattern matching problem, which is NP-complete. Next, by giving operations on an interval, which is a set containing all integers between two given integers representing vertex identifiers, we propose an efficient algorithm for solving Matching problem for term tree patterns in $lottsubsetneq ott$. Then, we show that, when an ordered tree having N vertices and a term tree pattern $t in lott$ having n vertices are given, the proposed matching algorithm correctly solves this problem in O(nN) time.

For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.

In this paper, we improve a width-3 joint sparse form proposed by Okeya, Katoh, and Nogami. After the improvement, the representation can attain an asymtotically optimal complexity found in our previous work. Although claimed as optimal by the authors, the average computation time of multi-scalar multiplication obtained by the representation is 563/1574n+o(n)≈0.3577n+o(n). That number is larger than the optimal complexity 281/786n+o(n)≈0.3575n+o(n) found in our previous work. To optimize the width-3 joint sparse form, we add more cases to the representation. After the addition, we can show that the complexity is updated to 281/786n+o(n)≈0.3575n+o(n), which implies that the modified representation is asymptotically optimal. Compared to our optimal algorithm in the previous work, the modified width-3 joint sparse form uses less dynamic memory, but it consumes more static memory.

Recently a compact code of mosaic floorplans with ƒ inner face was proposed by He. The length of the code is 3ƒ-3 bits and asymptotically optimal. In this paper, we propose a new code of mosaic floorplans with ƒ inner faces including k boundary faces. The length of our code is at most $3f - rac{k}{2} - 1$ bits. Hence our code is shorter than or equal to the code by He, except for few small floorplans with k=ƒ≤3. Coding and decoding can be done in O(ƒ) time.

The correct detection of the start of burst is very important in wideband networking radio operation as it directly affects the Time Division Multiple Access (TDMA) adaptive time slot algorithm. In this paper, we propose a robust Data Aided (DA) algorithm for burst detection in a hybrid CDMA/Adaptive TDMA based wideband networking waveform of a software defined radio. The proposed algorithm is based on a novel differentially modulated training sequence designed by using precoding sequence. The training sequence structure and precoding sequence are exploited in the calculation of proposed timing metric which is normalized by the signal energy. The precoding sequence is adequately designed for the timing metric to have a sharp peak. The algorithm shows excellent performance for multiuser scenario. It is shown through computer simulations that by increasing the active users from 1 to 8, the performance degradation is only about 1∼2dB. The proposed algorithm is compared with other algorithms and found to outperform them even in the presence of multipath fading effects. The proposed algorithm has been implemented on Field Programmable Gate Array (FPGA) platform for high data rate applications and it is shown that the results from hardware are identical to the simulation results.

This paper proposes a novel greedy algorithm, called Creditability-Estimation based Matching Pursuit (CEMP), for the compressed sensing signal recovery. As proved in the algorithm of Stagewise Orthogonal Matching Pursuit (StOMP), two Gaussian distributions are followed by the matched filter coefficients corresponding to and without corresponding to the actual support set of the original sparse signal, respectively. Therefore, the selection for each support point is interpreted as a process of hypothesis testing, and the preliminarily selected support set is supposed to consist of rejected atoms. A hard threshold, which is controlled by an input parameter, is used to implement the rejection. Because the Type I error may happen during the hypothesis testing, not all the rejected atoms are creditable to be the true support points. The creditability of each preliminarily selected support point is evaluated by a well-designed built-in mechanism, and the several most creditable ones are adaptively selected into the final support set without being controlled by any extra external parameters. Moreover, the proposed CEMP does not necessitate the sparsity level to be a priori control parameter in operation. In order to verify the performance of the proposed algorithm, Gaussian and Pulse Amplitude Modulation sparse signals are measured in the noiseless and noisy cases, and the experiments of the compressed sensing signal recoveries by several greedy algorithms including CEMP are implemented. The simulation results show the proposed CEMP can achieve the best performances of the recovery accuracy and robustness as a whole. Besides, the experiment of the compressed sensing image recovery shows that CEMP can recover the image with the highest Peak Signal to Noise Ratio (PSNR) and the best visual quality.

The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2p^m+1qⁿ⁺¹. Furthermore, we establish the formula of the linear complexity of proposed sequences. The results reveal that such sequences with period 2p^m+1qⁿ⁺¹ have a good balance property and high linear complexity.

The MQ problem, which consists of solving a system of multivariate quadratic polynomials over a finite field, has attracted the attention of researchers for the development of public-key cryptosystems because (1) it is NP-complete, (2) there is no known polynomial-time algorithm for its solution, even in the quantum computational model, and (3) it enables cryptographic primitives of practical interest. In 2011, Sakumoto, Shirai and Hiwatari presented two new zero-knowledge identification protocols based exclusively on the MQ problem. The 3-pass identification protocol of Sakumoto et al. has impersonation probability 2/3. In this paper, we propose an improvement that reduces the impersonation probability to 1/2. The result is a protocol that reduces the total computation time, the total communication needed and requires a smaller number of rounds for the same security level. We also present a new extension that achieves an additional communication reduction with the use of some smaller hash commitments, but maintaining the same security level.

The main contribution of this paper is to characterize the hyperbentness of two infinite classes of Boolean functions via Dillon-like exponents, and give new classes of semibent functions with Dillon-like exponents and Niho exponents. In this paper, the approaches of Mesnager and Wang et al. are generalized to Charpin-Gong like functions with two additional trace terms. By using the partial exponential sums and Dickson polynomials, it also gives the necessary and sufficient conditions of the hyperbent properties for their subclasses of Boolean functions, and gives two corresponding examples on F_2³⁰. Thanks to the result of Carlet et al., new classes of semibent functions are obtained by using new hyperbent functions and the known Niho bent functions. Finally, this paper extends the Works of Lisonek and Flori and Mesnager, and gives different characterizations of new hyperbent functions and new semibent functions with some restrictions in terms of the number of points on hyperelliptic curves. These results provide more nonlinear functions for designing the filter generators of stream ciphers.

Wyner has shown in his seminal paper on (discrete memoryless) wiretap channels that if the channel between the sender and an eavesdropper is a degraded version of the channel between the sender and the legitimate receiver, then the sender can reliably and securely transmit a message to the receiver, while the eavesdropper obtains absolutely no information about the message. Later, Leung-Yan-Cheong and Hellman extended Wyner's result to the case where the noise is white Gaussian. In this paper we extend the white Gaussian wiretap channel to the colored Gaussian case and show the finite block length secrecy capacity of colored Gaussian wiretap channels. We also show the asymptotic secrecy capacity of a specific colored Gaussian wiretap channel for which optimal power allocation can be found by a water-filling procedure.

In this correspondence, a generic method of constructing optimal p²-ary low correlation zone sequence sets is proposed. Firstly p²-ary column sequence sets are constructed, then p²-ary LCZ sequence sets with parameters (pⁿ-1, p^m-1, (pⁿ-1)/(p^m-1),1) are constructed by using column sequences and interleaving technique. The resultant p²-ary LCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound.

We propose a novel bias-free adaptive beamformer employing an affine projection algorithm with the optimal regularization parameter. The generalized sidelobe canceller affine projection algorithm suffers from a bias of a weight vectors under the condition of no reference signals for output of an array in the beamforming application. First, we analyze the bias in the algorithm and prove that the bias can be eliminated through a large regularization parameter. However, this causes slow convergence at the initial state, so the regularization parameter should be controlled. Through the optimization of the regularization parameter, the proposed method achieves fast convergence without the bias at the steady-state. Experimental results show that the proposed beamformer not only removes the bias but also achieves both fast convergence and high steady-state output signal-to-interference-plus-noise ratio.

In the traditional time delay estimation methods, it is usually implicitly assumed that the observed signals are either only direct path propagate or coherently received. In practice, the multipath propagation and incoherent reception always exist simultaneously. In response to this situation, the joint maximum likelihood (ML) estimation of multipath delays and system error is proposed, and the estimation of the number of multipath is considered as well for the specific incoherent signal model. Furthermore, an algorithm based Gibbs sampling is developed to solve the multi-dimensional nonlinear ML estimation. The efficiency of the proposed estimator is demonstrated by simulation results.

Since the conventional cascade controller for electric motor drives requires accurate information about the system parameters and load conditions to achieve a desired performance, this paper presents a new practical control structure to improve the robust performance against parameter uncertainties. Two first-order disturbance observers (DOB) are incorporated with the cascade structure, to preserve the nominal performance. The analysis of the robust performance of the DOB is presented by using the singular perturbation theory. Simulation results suggest that the proposed controller can be used effectively as an additional compensator to the conventional cascade scheme.

In this letter, we derive two lower bounds for the number of terms in a double-base number system (DBNS), when the digit set is {1}. For a positive integer n, we show that the number of terms obtained from the greedy algorithm proposed by Dimitrov, Imbert, and Mishra [1] is $Thetaleft(rac{log n}{log log n} ight)$. Also, we show that the number of terms in the shortest double-base chain is Θ(log n).

The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σ_ƒ=2²ⁿ+2ⁿ⁺³ is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σ_ƒ=2²ⁿ+2ⁿ⁺³ for n≥4, if the hamming weight of one decomposition function belongs to the interval Q^*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2^n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.

Password-based anonymous authentication schemes provide not only password-based authentication but also user anonymity. In [15], Yang et al., proposed a password-based anonymous authentication scheme (we call it YZWB10 scheme) using the password-protected credentials. This scheme has being standardized in ISO/IEC 20009-4 that was approved to proceed to the CD stage in the 49th ISO/IEC JTC 1/SC 27 Mexico meeting. In this paper, we analyze unlinkability of the YZWB10 scheme [15]. In particular, we show that a (malicious) server in the YZWB10 scheme can specify which user actually sent the login request to the server. Unlike Yang et al.,'s claim, the YZWB10 scheme [15] does not provide unlinkability against server.

Information-theoretic limits of a multi-way relay channel with direct links (MWRC-DL), where multiple users exchange their messages through a relay terminal and direct links, are discussed in this paper. Under the assumption that a restricted encoder is employed at each user, an outer bound on the capacity region is derived first. Then, a decode-and-forward (DF) strategy is proposed and the corresponding rate region is characterized. The explicit outer bound and the achievable rate region for the Gaussian MWRC-DL are also derived. Numerical examples are provided to demonstrate the performance of the proposed DF strategy.

The mappings from independent binary variables to quadrature amplitude modulation (QAM) symbols are developed. Based the proposed mappings and the existing binary mutually uncorrelated complementary sequence sets (MUCSSs), a construction producing QAM periodic complementary sequence sets (PCSSs) is presented. The resultant QAM PCSSs have the same numbers and periods of sub-sequences as the binary MUCSSs employed, and the family size of new sequence sets is increased with exponent of periods of sub-sequences. The proposed QAM PCSSs can be applied to CDMA or OFDM communication systems so as to suppress multiple access interference (MAI) or to reduce peak-to-mean envelope power ratio (PMEPR), respectively.

In Xu, Chen, and Liu's letter, two constructions producing perfect 8-QAM+/8-QAM sequences were given. We show that their constructions are equivalent to Zeng, et al.'s constructions under unit constant transform. Since the autocorrelation of a perfect sequence under unit constant transform is invariable, Xu, et al.'s constructions are the special case of Zeng, et al.'s constructions.

Generally, in order to extend the cell coverage of a mobile station, relay stations are used at a cell edge in a cellular system. But, received signals in a relay station of a cell edge have a large error because a neighboring cell transmits the signals for other users. Since the transmitted signals for other users are interference for received signals in the relay station of the cell edge, the relay station has a negative effect on the bit error ratio performance. The cell coverage can not be extended stably. In order to expand the cell coverage stably, the inter-cell interference has to cancel. Thus, in this paper, the technique that the inter-cell interference (ICI) is canceled by cooperative relays is proposed. Also, diversity gain is obtained by cooperative relays.

In this letter, an enhanced detection scheme using threshold and lattice-reduction algorithm is proposed. The first step of the proposed detection scheme finds another basis channel matrix H^' which has good properties from the channel matrix H by using lattice-reduction algorithm. And QRD-M detection scheme using threshold algorithm is executed in the next step. Simulation results show that the proposed method has better performance than the conventional QRD-M detection scheme at high SNR. Also, it reduces candidate symbols because of the threshold algorithm.

In cognitive radio (CR), superposition cooperative spectrum sensing (SPCSS) is able to offer a much improved sensing reliability compared to individual sensing. Because of the differences in sensing channel condition, the reporting order for each cognitive radio user (CU) will highly affect the sensing performance of the network. In this paper, we propose an algorithm to assign the best reporting order to each CU in order to maximize sensing performance under SPCSS. The numerical results show that the proposed scheme can obtain the same performance as the optimal scheme.

In this paper, we propose an efficient tracking method that is formulated as a multi-task reverse sparse representation problem. The proposed method learns the representation of all tasks jointly using a customized APG method within several iterations. In order to reduce the computational complexity, the proposed tracking algorithm starts from a feature selection scheme that chooses suitable number of features from the object and background in the dynamic environment. Based on the selected feature, multiple templates are constructed with a few candidates. The candidate that corresponds to the highest similarity to the object templates is considered as the final tracking result. In addition, we present a template update scheme to capture the appearance changes of the object. At the same time, we keep several earlier templates in the positive template set unchanged to alleviate the drifting problem. Both qualitative and quantitative evaluations demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods.