Solutions of xqk+⋯+xq+x=ax^{q^k}+\cdots+x^{q}+x=a in GF2nGF{2^n}

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field

Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions

To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known general theory for this task is much far from giving the exact dimension when applied to a specific linearized polynomial. The first contribution of this paper is to give a better general method to get more precise upper bound on the root number of any given linearized polynomial. We anticipate this result would be applied as a useful tool in many research branches of finite field and cryptography. Really we apply this result to get tighter estimations of the lower bounds on the second order nonlinearities of general cubic Boolean functions, which has been being an active research problem during the past decade, with many examples showing great improvements. Furthermore, this paper shows that by studying the distribution of radicals of derivatives of a given Boolean functions one can get a better lower bound of the second-order nonlinearity, through an example of the monomial Boolean function $g_{\mu}=Tr(\mu x^{2^{2r}+2^r+1})$ over any finite field \GF{n}

A NUMERICAL STUDY ON THE OPEN WATER PERFORMANCE OF A PROPELLER WITH SINUSOIDAL PITCH MOTION

When a ship operates in waves, the ship moves with 6 degrees-of-freedom, and a propeller at the stern of the ship cannot avoid moving due to the ship motion. Therefore, it is important to analyse the propulsion performance while considering the ship motion in waves for efficient ship operation. The pitch motion of the ship has a dominant effect on the variation of the propeller performance and results in sinusoidal pitch motion of the propeller. In this study, a numerical analysis was done using a KP458 model propeller with a diameter of 10 cm, which was designed for the KLVCC2 body plan. The propeller performance was calculated using computational fluid dynamics (CFD) at several constant tilt angles. Numerical simulations were then conducted with sinusoidal pitch motion in several conditions of varying pitch angle. The variations of the thrust and torque of the propeller in sinusoidal pitch motion were compared with the results obtained in constant tilt angles

Increasing the Durability of Piezoelectric Impact-based Micro Wind Generator in Real Application

AbstractThe purpose of this study is to increase the durability of piezoelectric impact-based micro wind generator (PIMWG) in real application. Using new PIMWG design, numerical simulation, and experimental comparison analysis, we improved the durability of PIMWGs in real application. The experimental results show that the optimized PIMWG generated 2.4 mW (RMS value), and it did not crack within 40h. In this study, we improved the durability of PIMWGs for real application

Speeding up Elliptic Curve Scalar Multiplication without Precomputation

This paper presents a series of Montgomery scalar multiplication algorithms on general short Weierstrass curves over odd characteristic fields, which need only 12 field multiplications plus 12 ~ 20 field additions per scalar bit using 8 ~ 10 field registers, thus significantly outperform the binary NAF method on average. Over binary fields, the Montgomery scalar multiplication algorithm which was presented at the first CHES workshop by L´opez and Dahab has been a favorite of ECC implementors, due to its nice properties such as high efficiency outperforming the binary NAF, natural SPA-resistance, generality coping with all ordinary curves and implementation easiness. Over odd characteristic fields, the new scalar multiplication algorithms are the first ones featuring all these properties. Building-blocks of our contribution are new efficient differential addition-and-doubling formulae and a novel conception of on-the-fly adaptive coordinates which softly represent points occurring during a scalar multiplication not only in accordance with the basepoint but also bits of the given scalar. Importantly, the new algorithms are equipped with built-in countermeasures against known side-channel attacks, while it is shown that previous Montgomery ladder algorithms with the randomized addressing countermeasure fail to thwart attacks exploiting address-dependent leakage

Analysis of Long-Range Transport of Carbon Dioxide and Its High Concentration Events over East Asian Region Using GOSAT Data and GEOS-Chem Modeling

This study aims to evaluate the long-range transport of CO2 in East Asian region, using concentration data in a surface measurement site (Gosan Station), column averaged concentration data of satellite-borne instrument (GOSAT), and GEOS-Chem modeling results for the period of June 2009 to May 2011. We perform a validation of the data from GOSAT and GEOS-Chem with total column observations (TCCON). The analysis of the long-range transport and high concentration (HC) events using surface/satellite observations and modeling results is conducted. During the HC events, the concentrations in CO2 and other air pollutants such as SO2 and CO are higher than that of all episodes. It means that CO2, known as a globally well-mixed gas, may also act as a fingerprint of human activity with unique regional characteristics like other air pollutants. This comprehensive analysis, in particular with GOSAT CO2 observation data, shows that CO2 plume with high concentration can be long-range transported with 1-2 days' duration with regional scale. We can find out with GEOS-Chem tagging simulation that more than 45% of the elevated CO2 concentration over central/eastern China, Korea, and Japan on high concentration days can be explained by emission sources of East Asia mainland.open0