一类广义Bent型S-Box的构造

S-box是密码理论与实践中十分重要的一种装置 ,它的密码性能由其分量函数所决定 .于是 ,选择适当的分量函数来构造 S-box就成了一个重要的研究课题 .在一定意义上 ,Bent函数是最优良的密码函数 .本文通过函数序列半群和置换群来构造其任何非零线性组合为 Bent函数与线性函数之和的函数组 ,从而可由 Bent函数构造出具有高度非线性度和其他良好性状的 S-box     

Construction of highly nonlinear resilient S-boxes with given degree

We provide two new construction methods for nonlinear resilient S-boxes with given degree. The first method is based on the use of linear error correcting codes together with highly nonlinear S-boxes. Given a [u, m, t + 1] linear code where u = n?d?1, d > m, we show that it is possible to construct (n, m, t, d) resilient S-boxes which have currently best known nonlinearity. Our second construction provides highly nonlinear (n, m, t, d) resilient S-boxes which do not have linear structure, then an improved version of this construction is given.     

Elliptic PDEs with Fibered Nonlinearities

In ℝ ^m ×ℝ ^n−m , endowed with coordinates x=(x′,x″), we consider bounded solutions of the PDE

A novel method for designing S-boxes based on chaotic maps

A method for obtaining cryptographically strong 8 × 8 S-boxes based on chaotic maps is presented and the cryptographical properties such as bijection, nonlinearity, strict avalanche criterion, output bits independence criterion and equiprobable input/output XOR distribution of these S-boxes are analyzed in detail. The results of numerical analysis also show that the S-boxes proposed are of the above properties and can resist the differential attack. Furthermore, our approach is suitable for practical application in designing cryptosystem.     

A block cipher with dynamic S-boxes based on tent map

In this paper, a block encryption scheme based on dynamic substitution boxes (S-boxes) is proposed. Firstly, the difference trait of the tent map is analyzed. Then, a method for generating S-boxes based on iterating the tent map is presented. The plaintexts are divided into blocks and encrypted with different S-boxes. The cipher blocks are obtained by 32 rounds of substitution and left cyclic shift. To improve the security of the cryptosystem, a cipher feedback is used to change the state value of the tent map, which makes the S-boxes relate to the plaintext and enhances the confusion and diffusion properties of the cryptosystem. Since dynamic S-boxes are used in the encryption, the cryptosystem does not suffer from the problem of fixed structure block ciphers. Theoretical and experimental results indicate that the cryptosystem has high security and is suitable for secure communications.     

Elliptic Systems with Nonlinearities of Arbitrary Growth

In this paper we study the existence of nontrivial solutions for the following system of coupled semilinear Poisson equations: where is a bounded domain in We assume that and the function f is superlinear and with no growth restriction (for example f(s) = s e^s); then the system has a nontrivial (strong) solution.     

Critical Nonlinearities in Partial Differential Equations

This paper focuses on the role of critical nonlinearities within the framework of global solvability of nonlinear PDE’s. In particular, we present some new approach to blow-up issues for nonlinear problems.     

The design of composite permutations with applications to DES-like S-boxes

This paper presents an iterative construction method for building composite permutations. Its efficiency is based on the concepts of pre-computation and equivalence classes. Equivalence class representatives of permutations on four bits are pre-computed. These class representatives can serve as input to the construction method, however, the results are also of independent interest for applications in cryptography. A well-known example of a cryptosystem using composite permutations for its Substitution boxes (S-boxes) is the Data Encryption Standard (DES). Throughout the paper, DES-like S-boxes are defined as mappings satisfying all design criteria as disclosed by one of the designers of DES. All permutations on four bits with DES-like properties are identified. Starting with pre-computed representatives of classes with such permutations, two iterations of a specialized version of the algorithm are applied to obtain bounds on the minimum differential uniformity and minimum non-linear uniformity of DES-like S-boxes. It is established that the two values cannot be less than eight, and that DES-like S-boxes for which the values are both equal to 12 do exist. In addition, if the non-linear uniformity of each of the four permutations in a DES-like S-box is at most six, as in all DES S-boxes, then its non-linear uniformity cannot be less than ten and its minimum differential uniformity equals 12.     

A method for designing dynamical S-boxes based on discretized chaotic map

A method for obtaining dynamically cryptographically strong substitution boxes (S-boxes) based on discretized chaotic map is presented in this paper. The cryptographical properties such as bijection, nonlinearity, strict avalanche, output bits independence and equiprobable input/output XOR distribution of these S-boxes are analyzed in detail. The results of numerical analysis show that all the criteria for designing good S-box can be met approximately. As a result, our approach is suitable for practical application in designing block cryptosystem.     

Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is de_ned on all . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of . This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally, in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Decentralized State-Estimation of Interconnected Systems with Unknown Nonlinearities

An efficient state-estimation scheme is developed within the LMI framework for robust decentralized state estimation of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints. The procedure utilizes a general linear estimator structure, and consists of two steps, the first giving a block-diagonal Lyapunov matrix together with the robustness degree, and the second determining the filter parameters. Extension to the case of additive filter gain perturbations is established and numerical examples are provided to illustrate the applicability of the method.     

带有临界型非线性项的强阻尼波动方程

研究一类带有临界型非线性项的强阻尼波动方程.通过选择合适的状态空间,证明了算子矩阵[OA-IηAθ]的扇形性,评估了带有临界型增长指数的非线性项的临界性,并且研究了弱解的局部与整体存在性和正则性.     

具有间断非线性项的拟线性抛物型方程(英)

本文研究具有间断非线性项的拟线性抛物型方程，利用Clarke广义梯度和伪单调算子理论证明了解的存在性．     

An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps

Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes.     

On a Quasilinear Elliptic Equation with Superlinear Nonlinearities

This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of $\mathbb{R}^{N}$. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.     

Multiplicity Results of a Nonlocal Problem Involving Concave-Convex Nonlinearities

Mathematical Notes - In this work, we investigate the following fractional $$p$$ -Laplacian equation involving a concave-convex nonlinearities as follows, $${rm (P_lambda)} begin{cases}...     

带跳跃非线性项的p-Laplacian问题的结点解

研究了带跳跃非线性项的p-Laplacian方程结点解的存在性.如果该问题的非线性项跨越其对应齐次问题的Fucik谱,我们证明了该问题至少存在一个结点解.     

Multiplicity of Periodic Solutions of Duffing Equations with Jumping Nonlinearities

We provide sufficient conditions for the existence and multiplicity of subharrnonic solutions for Duffing's equations with jumping nonlinearities.     

Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

Mathematical Notes - For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for...