Key-dependent side-channel cube attack on CRAFT

CRAFT is a tweakable block cipher introduced in 2019 that aims to provide strong protection against differential fault analysis. In this paper, we show that CRAFT is vulnerable to side-channel cube attacks. We apply side-channel cube attacks to CRAFT with the Hamming weight leakage assumption. We found that the first half of the secret key can be recovered from the Hamming weight leakage after the first round. Next, using the recovered key bits, we continue our attack to recover the second half of the secret key. We show that the set of equations that are solvable varies depending on the value of the key bits. Our result shows that 99.90% of the key space can be fully recovered within a practical time.     

连续波半主动雷达制导空空导弹截获跟踪距离计算

分析了连续波半主动雷达制导导弹导引头工作电磁环境和对武器系统攻击区的影响，建立了热噪声和杂波干扰环境下导引头截获距离方程，分析推导了直波泄漏干扰，地杂波干扰的计算公式，并在此基础上给出了导弹允许攻击区计算公式。     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

Around Multicolour Disordered Lattice Gas

We consider a system of multicolour disordered lattice gas, following closely the (monocolour) introduced by Faggionato and Martinelli^(3,4). We study the projection on the monocolour system and we derive an estimate of the closeness between grand canonical and canonical Gibbs measures. AMS Classification: Primary: 60K35, 82C20, 82C22     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)