Binary solutions to large systems of linear equations

The concept of generic computational complexity has been extended to generalized register machines over an ordered field. In this case, the machine halts at every input and gives a meaningful answer at almost every input, but it can abandon the calculation using explicit notification, that is, there exists the vague halting state. Note that the machine does not make any error. A generic polynomial time algorithm is proposed to recognize systems of linear equations without any binary solution, when the number of equations m is close to the number of unknowns n. More precisely, two conditions are required. Firstly, the inequality 2n ≥(n-m+1)(n-m+2) holds. Such systems are called large because the number of equations is close to the number of unknowns. Secondly, some assumptions of generality of the system of equations are fulfilled. Our approach is based on finding a positive definite quadratic form among the set of forms that depend on parameters. On the other hand, a counterexample has been found, whicht shows the inapplicability of this method for checking the absence of any binary solution to one equation.

Homotopy analysis method applied to second-order frequency mixing in nonlinear optical dielectric media

The classical problem of three-wave mixing in a nonlinear optical medium is investigated using the homotopy analysis method (HAM). We show that the power series basis builds a generic polynomial expression that can be used to study three-wave mixing for arbitrary input parameters. The phase-mismatched and perfectly phase matched cases are investigated. Parameters that result in generalized sum- and difference-frequency generation are studied using HAM with a power series basis and compared to an explicit finite-difference approximation. The convergence region is extended by increasing the auxiliary parameter.

Power Analysis on NTRU Prime

This paper applies a variety of power analysis techniques to several implementations of NTRU Prime, a Round 2 submission to the NIST PQC Standardization Project. The techniques include vertical correlation power analysis, horizontal indepth correlation power analysis, online template attacks, and chosen-input simple power analysis. The implementations include the reference one, the one optimized using smladx, and three protected ones. Adversaries in this study can fully recover private keys with one single trace of short observation span, with few template traces from a fully controlled device similar to the target and no a priori power model, or sometimes even with the naked eye. The techniques target the constant-time generic polynomial multiplications in the product scanning method. Though in this work they focus on the decapsulation, they also work on the key generation and encapsulation of NTRU Prime. Moreover, they apply to the ideal-lattice-based cryptosystems where each private-key coefficient comes from a small set of possibilities.

Identification of In-Flight Wingtip Folding Effects on the Roll Characteristics of a Flexible Aircraft

Wingtip folding is a means by which an aircraft’s wingspan can be extended, allowing designers to take advantage of the associated reduction in induced drag. This type of device can provide other benefits if used in flight, such as flight control and load alleviation. In this paper, the authors present a method to develop reduced order flight dynamic models for in-flight wingtip folding, which are suitable for implementation in real-time pilot-in-the-loop simulations. Aspects such as the impact of wingtip size and folding angle on aircraft roll dynamics are investigated along with failure scenarios using a time domain aeroservoelastic framework and an established system identification method. The process discussed in this paper helps remove the need for direct connection of complex physics based models to engineering flight simulators and the need for tedious programming of large look-up-tables in simulators. Instead, it has been shown that a generic polynomial model for roll aeroderivatives can be used in small roll perturbation conditions to simulate the roll characteristics of an aerodynamic derivative based large transport aircraft equipped with varying fold hinge lines and tip deflections. Moreover, the effects of wing flexibility are also considered.

A Very Fast Heuristic for Combinatorial Optimization With Specific Application to Priority Rule Sequencing in Operations Management

This article presents mathematics of a generic polynomial-time heuristic which can be integrated into approaches for hard combinatorial optimization problems. The proposed method evaluates objects in a way that combines fuzzy reasoning with a greedy mechanism, thereby exploiting a fuzzy solution space using greedy methods. The effectiveness and efficiency of the proposed method are demonstrated on job-shop scheduling as one of the most challenging classical sequencing problems in the area of combinatorial optimization.