Let f be a Boolean function in n variables. The Möbius transform and its converse of f can describe the transformation behaviors between the truth table of f and the coefficients of the monomials in the algebraic normal form representation of f. In this letter, we develop the Möbius transform and its converse into a more generalized form, which also includes the known result given by Reed in 1954. We hope that our new result can be used in the design of decoding schemes for linear codes and the cryptanalysis for symmetric cryptography. We also apply our new result to verify the basic idea of the cube attack in a very simple way, in which the cube attack is a powerful technique on the cryptanalysis for symmetric cryptography.

In this paper, we present an algorithm that counts the number of empty quadrilaterals whose corners are chosen from a given set S of n points in general position. Our algorithm can separately count the number of convex or non-convex empty quadrilaterals in O(T) time, where T denotes the number of empty triangles in S. Note that T varies from Ω(n2) and O(n3) and the expected value of T is known to be Θ(n2) when the n points in S are chosen uniformly and independently at random from a convex and bounded body in the plane. We also show how to enumerate all convex and/or non-convex empty quadrilaterals in S in time proportional to the number of reported quadrilaterals, after O(T)-time preprocessing.

Multivariate public key cryptosystem (MPKC) is one of the major post quantum cryptosystems (PQC), and the National Institute of Standards and Technology (NIST) recently selected four MPKCs as candidates of their PQC. The security of MPKC depends on the hardness of solving systems of algebraic equations over finite fields. In particular, the multivariate quadratic (MQ) problem is that of solving such a system consisting of quadratic polynomials and is regarded as an important research subject in cryptography. In the Fukuoka MQ challenge project, the hardness of the MQ problem is discussed, and algorithms for solving the MQ problem and the computational results obtained by these algorithms are reported. Algorithms for computing Gröbner basis are used as the main tools for solving the MQ problem. For example, the F4 algorithm and M4GB algorithm have succeeded in solving many instances of the MQ problem provided by the project. In this paper, based on the F4-style algorithm, we present an efficient algorithm to solve the MQ problems with dense polynomials generated in the Fukuoka MQ challenge project. We experimentally show that our algorithm requires less computational time and memory for these MQ problems than the F4 algorithm and M4GB algorithm. We succeeded in solving Type II and III problems of Fukuoka MQ challenge using our algorithm when the number of variables was 37 in both problems.

In this letter, an efficient hybrid direction-of-arrival (DOA) estimation scheme is devised for massive uniform rectangular array. In this scheme, the DOA estimator based on a two-dimensional (2D) discrete Fourier transform is first applied to acquire coarse initial DOA estimates for single data snapshot. Then, the fine DOA is accurately estimated through using the iterative search estimator within a very small region. Meanwhile, a Nyström-based method is utilized to correctly compute the required noise-subspace projection matrix, avoiding the direct computation of full-dimensional sample correlation matrix and its eigenvalue decomposition. Therefore, the proposed scheme not only can estimate DOA, but also save computational cost, especially in massive antenna arrays scenarios. Simulation results are included to demonstrate the effectiveness of the proposed hybrid estimate scheme.

This paper presents an approach to nonlinear impedance measurement exploiting an oscilloscope and Möbius transformation. Proposed system consists of a linear 4-port network and an oscilloscope. One of the port is excited by a high power source. The power is delivered to the second port, which is loaded with a DUT. Another set of two ports are used to observe a voltage set. This voltage set gives the impedance of the DUT through Möbius transformation. We formulated measurability M of the system, and derived the condition that M becomes constant for any DUT. To meet the condition, we propose a linear 4-port network consisting of a quarter-wavelength transmission line and resistors. We confirm the validity and utility of the proposed system by measuring the impedance of incandescent bulbs and an RF diode rectifier.

The copy-move or region duplication forgery technique is a very common type of image manipulation, where a region of the image is copied and then pasted in the same image in order to hide some details. In this paper, a keypoint-based method for copy-move forgery detection is proposed. Firstly, the feature points are detected from the image by using the Förstner Operator. Secondly, the algorithm extracts the features by using MROGH feature descriptor, and then matching the features. Finally, the affine transformation parameters can be estimated using the RANSAC algorithm. Experimental results are presented to confirm that the proposed method is effective to locate the altered region with geometric transformation (rotation and scaling).

We propose a multi-label feature selection method that considers feature dependencies. The proposed method circumvents the prohibitive computations by using a low-rank approximation method. The empirical results acquired by applying the proposed method to several multi-label datasets demonstrate that its performance is comparable to those of recent multi-label feature selection methods and that it reduces the computation time.

A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.

Currently there is not any prospect of realizing quantum computers which can compute prime factorization, which RSA relies on, or discrete logarithms, which ElGamal relies on, of practical size. Additionally the rapid growth of Internet of Things (IoT) is requiring practical public key cryptosystems which do not use exponential operation. Therefore we constituted a cryptosystem relying on the difficulty of factoring the product of two large prime numbers, based on the Chinese Remainder Theorem, fully exploiting another strength of MPKC that exponential operation is not necessary. We evaluated its security by performing the Gröbner base attacks with workstations and consequently concluded that it requires computation complexity no less than entirely random quadratic polynomials. Additionally we showed that it is secure against rank attacks since the polynomials of central map are all full rank, assuming the environment of conventional computers.

We calculated propagation constants of supermodes for two-dimensional two-slab waveguides, with small core gap, using second-order perturbation expansion from gapless slab waveguide system, and compared our results with the existing works. In the perturbation calculation, we used trapezoidal method to calculate the integral over the transverse direction in space and obtained second-order expansion of (core gap)/(core width) for propagation constants. Our result can explain the qualitative relationship between the propagation constants and the gap distance in the neighbor of (core gap)/(core width) being zero.

A novel multiple programming method for a phase change nonvolatile random access memory (NVRAM) is proposed. The resistance of the chalcogenide semiconductors (phase change materials, e.g. SeSbTe) stacked on the memory cell is controlled by the number of the applied current pulses, and we have observed experimentally 4-valued resistance in the range of 42 k-2.1kΩ at the SeSbTe discrete memory cell. On the basis of this experimental results, the 4-valued memory circuit was designed with CMOS 0.35 µm process. It has been confirmed with a circuit simulation that the multi-bit read circuit proposed works successfully under a read cycle operation over 100 MHz at 3.3 V supply voltage and the read operation is completed within 3 nsec.

We propose an equivalent circuit model described by the Rössler equation. Then we can consider a coupled Rössler system with a physical meaning on the connection. We consider an oscillatory circuit such that two identical Rössler circuits are coupled by a resistor. We have studied three routes to entirely and almost synchronized chaotic attractors from phase-locked periodic oscillations. Moreover, to simplify understanding of synchronization phenomena in the coupled Rössler system, we investigate a mutually coupled map that shows analogous locking properties to the coupled Rössler System.

In the paper a problem of wave scattering from a local penetrable inhomogeneity inside a planar dielectric waveguide is studied. The surface potentials method is applied for the problem and the set of systems of BIE is obtained and analyzed from the view-point of their numerical solution. The effective numerical algorithm based on the Nyström method is proposed. The equations for a scattering diagram and mode conversion coefficients are derived.

Ultrashort pulsed-beam propagation in a Kerr-type bulk medium is studied theoretically through classical and quantum field solutions of a higher-order nonlinear Schrödinger equation, which is valid for transversely localized femtosecond pulses in an anomalous dispersion regime. Quantum-mechanical stability analysis via a Hartree approximation to interacting bosons shows that within a certain range of a parameter the solitary wave could be stabilized even in the three-dimensional transverse space-time. This feature admits of an exotic route to multidimensional solitons.