Lattice-Based Cryptography: A Survey*

Most of current public key cryptosystems would be vulnerable to the attacks of the future quantum computers.Post-quantum cryptography offers mathematical methods to secure information and communications against such attacks,and therefore has been receiving a significant amount of attention in recent years.Lattice-based cryptography,built on the mathematical hard problems in(high-dimensional) lattice theory,is a promising post-quantum cryptography family due to its excellent efficiency,moderate s...     

Efficient algorithms for Koblitz curves over fields of characteristic three

The nonadjacent form method of Koblitz [Advances in Cryptology (CRYPTO'98), in: Lecture Notes in Comput. Sci., vol. 1462, 1998, pp. 327–337] is an efficient algorithm for point multiplication on a family of supersingular curves over a finite field of characteristic 3. In this paper, a further discussion of the method is given. A window nonadjacent form method is proposed and its validity is proved. Efficient reduction and pre-computations are given. Analysis shows that more than 30% of saving can be achieved.     

Thermal conductivity and thermal expansivity of thermotropic liquid crystalline polymers

The thermal conductivity and thermal expansivity of a thermotropic liquid crystalline copolyesteramide with draw ratio λ from 1.3 to 15 have been measured parallel and perpendicular to the draw direction from 120 to 430 K. The sharp rise in the axial thermal conductivity K_par; and the drastic drop in the axial expansivity α_∥ at low λ, and the saturation of these two quantities at λ > 4 arise from the corresponding increase in the degree of chain orientation revealed by wide-angle x-ray diffraction. In the transverse direction, the thermal conductivity and expansivity exhibit the opposite trends but the changes are relatively small. The draw ratio dependences of the thermal conductivity and expansivity agree reasonably with the predictions of the aggregate model. At high orientation, K_par; of the copolyesteramide is slightly higher than that of polypropylene but one order of magnitude lower than that of polyethylene. In common with other highly oriented polymers such as the lyotropic liquid crystalline polymer, Kevlar 49, and flexible chain polymer, polyethylene, α_par; of the copolyesteramide is negative, with a room temperature value differing from those of Kevlar 49 and polyethylene by less than 50%. Both the axial and transverse expansivity show transitions at about 390 and 270 K, which are associated with large-scale segmental motions of the chains and local motions of the naphthalene units, respectively. ©1995 John Wiley & Sons, Inc.     

一阶非线性椭圆型复方程的间断Riemam边值问题

§1 问题的提法 本文讨论一阶非线性一致椭圆型复方程 的间断非线性Riemann边值问题。以E表示复平面,D~ 表示有界N 1连通区域,其边界由     

用于等离子体诊断的30keV锂束源

本文描述用于等离子体诊断的30keV锂束源的结构,调试及实验结果。对锂辉石和β-锂霞石的发射性能进行了对比。在能量为30.5keV时,引出离子流为376μA。     

Vanishing viscosity limit for the 3D magnetohydrodynamic system with generalized Navier slip boundary conditions

In this paper, we investigate the vanishing viscosity limit problem for the 3D incompressible magnetohydrodynamic (MHD) system in a general bounded smooth domain of R ³ with the generalized Navier slip boundary conditions. We also obtain rates of convergence of the solution of viscous MHD to the corresponding ideal MHD. Copyright © 2016 John Wiley & Sons, Ltd.     

Global Aromaticity in Macrocyclic Cyclopenta‐Fused Tetraphenanthrenylene Tetraradicaloid and Its Charged Species

A stable cyclopenta‐fused tetraphenanthrenylene macrocycle, CPTP‐M , was synthesized, and the structure was confirmed by X‐ray crystallographic analysis. It exhibits a large radical character (number of unpaired electron, N_U=3.52) and a small singlet–triplet energy gap (ΔE_S‐T=?2.8 kcal mol^?1 by SQUID). Its backbone contains 60 ([4n]) conjugated π electrons and is globally antiaromatic. NMR measurements and theoretical calculations revealed that its dication/dianion is globally aromatic owing to the existence of [4n?2]/[4n+2] π‐conjugated electrons. Remarkably, the ring‐current map of the tetraanion shows a unique ring‐in‐ring structure, with a diamagnetic outer ring and a paramagnetic inner ring. Accordingly, both the inner‐rim and outer‐rim protons are deshielded in its ¹H NMR spectrum. The tetraanion can be regarded as an isoelectronic structure of the known octulene, which shows similar electronic properties.     

GLOBAL FINITE ENERGY WEAK SOLUTION TO THE VISCOUS QUANTUM NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL MODEL IN 2-DIMENSION

In this paper, we prove the global existence of the weak solution to the viscous quantum Navier-Stokes-Landau-Lifshitz-Maxwell equations in two-dimen- sion for large data. The main techniques are the Faedo-Galerkin approximation and weak compactness theory.     

同主语同标签Vague命题的Lawry逻辑

给出了Lawry不确定模型的新的性质.基于Lawry模型,引入了同主语同标签Vague命题的Lawry真度的概念.由此,提出了一种非经典逻辑,称为同主语同标签Vague命题的Lawry逻辑,简称Lawry逻辑.其逻辑规律表明它与经典逻辑具有优良的和谐性.     

A lattice Boltzmann model for two‐dimensional sound wave in the small perturbation compressible flows

A multi‐entropy‐level lattice Boltzmann model for two‐dimensional sound wave equation in the small perturbation flows is presented. In this model, we used higher‐order moment method, multi‐scale technique and the Chapman–Enskog expansion, and multi‐entropy‐level to obtain sound wave equation with isentropic equation. As numerical examples, the Doppler effects in the sound wave propagation, the sound scattering from circular cylinder are simulated. The numerical results show that this model can be used to simulate sound wave propagation. Copyright © 2010 John Wiley & Sons, Ltd.