This paper is a survey of modern post-quantum cryptographic schemes based on codes and isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, for code-based cryptosystems we describe the information set decoding and the support splitting algorithm as main attacks, and for cryptosystems based on isogenies we describe in detail the Castryck–Decru attack on SIDH/SIKE.
Seismic images of subsurface structures are the most valuable outcome of seismic data processing. The image quality is strongly affected by the accuracy of background velocity model. In this paper, we develop a gradient-descent velocity update algorithm based on our original high-frequency asymptotics of the Double Square Root equation, i.e., a special one-way approximation of the wave equation describing single-scattered wave field only. We propose a loss function consistent with widely adopted imaging condition and derive equations for its gradient computation. We test our method on noise-free synthetic datasets in 2D settings.
In 1961, L.M. Gluskin proved that a given set ( X ) with an arbitrary nontrivial quasiorder ( rho ) is determined up to isomorphism or anti-isomorphism by the semigroup ( T_rho (X) ) of all isotone transformations of ( (X,rho ) ), i.e., the transformations of ( X ) preserving ( rho ). Subsequently, L.M. Popova proved a similar statement for the semigroup ( P_rho (X) ) of all partial isotone transformations of ( (X,rho ) ); here the relation ( rho ) does not have to be a quasiorder but can be an arbitrary nontrivial reflexive or antireflexive binary relation on the set ( X ). In the present paper, under the same constraints on the relation ( rho ), we prove that the semigroup ( B_rho (X) ) of all isotone binary relations (set-valued mappings) of ( (X,rho ) ) determines ( rho ) up to an isomorphism or anti-isomorphism as well. In addition, for each of the conditions ( T_rho (X)=T(X) ), ( P_rho (X)=P(X) ), and ( B_rho (X)=B(X) ), we enumerate all ( n )-ary relations ( rho ) satisfying the given condition.
To study the flow in a far plane turbulent wake in a passively stratified medium, we use a mathematical model that includes differential equations for the balance of turbulence energy, the transfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and the vertical component of the mass flux vector. Algebraic truncation of the last equation leads to a well-known gradient relation for the vertical component of the mass flux vector. It is established that under a certain constraint on the values of empirical constants in the mathematical model and the law of time scale growth consistent with the mathematical model, this relation is a differential constraint for the model. The equivalence of the local equilibrium approach for the vertical component of the mass flux vector and the zero Poisson bracket for the dimensionless turbulent diffusion coefficient and the averaged density is shown. The results of numerical experiments illustrating the theoretical results are presented.
A set ( J_k ) of graph vertices is said to be ( k )-dominating independent ( ( k geq 1 )) if its vertices are pairwise adjacent and every vertex not in ( J_k ) is adjacent to at least ( k ) vertices in ( J_k ). In the present paper, we obtain new upper bounds for the number of ( k )-dominating independent sets for ( k geq 2 ) in some planar graph classes.
The paper considers the spectral problem associated with the study of local characteristics of weakly coupled systems in reactor physics. The method of associated invariant subspaces based on the matrix spectrum dichotomy method is described. With its help, distributions are found that reflect multiplicating properties of local areas in the system.
Arden and Lee proposed a class of chordal ring networks of degree three as communication networks for multicomputer systems, derived a formula for the diameter, and produced an algorithm for finding the shortest paths for them. In this paper, it is shown that the formula for the diameter and the routing algorithm presented by them are inaccurate. We have obtained a large dataset containing parameters for describing optimal diameter chord rings for all the numbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ring networks. A new method is proposed and the algorithms for automatic search for analytical descriptions of families of optimal chordal rings are realized based on an analysis of the database. Using the latter, analytical descriptions of over 500 new families of optimal chordal ring networks for many values of the number of nodes are found (only six families have been known until now in the literature).
In this paper, for the first time, we present a new model of current distribution in a tungsten sample and of substance evaporation when the surface is heated by an electron beam. The model is based on solving electrodynamics equations in a cylindrical coordinate system using a model temperature distribution in the sample and a thin layer of evaporated tungsten. The model is analyzed in a simplified formulation at constant values of electrical resistance and thermoelectric power in gas and metal. The dependence of the amplitude and isolines of thermal currents on the distribution of temperature at the sample surface is shown. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility, created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.
The following game of two persons is formalized and solved in the paper. Player 1 is asked a question. Player 2 knows the correct answer. Moreover, both players know all possible answers and their a priori probabilities. Player 2 must choose a subset of the given cardinality of deception answers. Player 1 chooses one of the proposed answers. Player 1 wins one from Player 2 if he/she guessed the correct answer and zero otherwise. This game is reduced to a matrix game. However, the game matrix is of large dimension, so the classical method based on solving a pair of dual linear programming problems cannot be implemented for each individual problem. Therefore, it is necessary to develop a method to radically reduce the dimension.
The whole set of such games is divided into two classes. The superuniform class of games is characterized by the condition that the largest of the a priori probabilities is greater than the probability of choosing an answer at random, and the subuniform class corresponds to the opposite inequality—each of the a priori probabilities when multiplied by the total number of answers presented to Player 1 does not exceed one. For each of these two classes, the solving the extended matrix game is reduced to solving a linear programming problem of a much smaller dimension. For the subuniform class, the game is reformulated in terms of probability theory. The condition for the optimality of a mixed strategy is formulated using the Bayes theorem. For the superuniform class, the solution of the game uses an auxiliary problem related to the subuniform class. For both classes, we prove results on the probabilities of guessing the correct answer when using optimal mixed strategies by both players. We present algorithms for obtaining these strategies. The optimal mixed strategy of Player 1 is to choose an answer at random in the subuniform class and to choose the most probable answer in the superuniform class. Optimal mixed strategies of Player 2 have much more complex structure.
The paper proposes a fractional-differential modification of the mathematical model of the process of nonstationary charging of polar dielectric materials under conditions of irradiation with medium-energy electron beams. The mathematical formalization is based on a spherically symmetric diffusion–drift equation with a fractional time derivative. An implicit finite-difference scheme is constructed using the Caputo derivative approximation. An application program has been developed in Matlab software that implements the designed computational algorithm. Verification of an approximate solution of the problem is demonstrated using a test example. The results of computational experiments to evaluate the characteristics of field effects of injected charges in ferroelectrics when varying the order of fractional differentiation in subdiffusion regimes are presented.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：