广Bent函数

利用了Bent函数构造了一类新的布尔函数——“广Bent函数”，并分析了广Bent函数的密码学性质，如平衡性、高的非线性度、稳定性等。还给出了广Bent函数仅在一个非零点不满足扩散准则的充要条件，并指出广Bent函数平衡且满足2n次扩散准则的充要条件，最后揭示了平衡且满足k次扩散准则的k 1元布尔函数的结构特征。     

拟Bent函数的构造

拟Bent函数在密码系统中可用作非线性组合函数和消息摘要函数,因而具有很好的密码学性质。本文通过计算布尔函数的Walsh谱,从映射的角度确定了变元个数不超过六的拟Bent函数的代数结构;提出了一般交换群上的扩展组合函数族的概念,研究了这类函数的性质,利用商群给出了扩展组合函数的下降构造,通过组合函数给出了提升构造法,从而得到了一种由扩展组合函数族构造拟Bent函数和Bent函数的递归构造法,由这种方法可以构造大量拟Bent函数和Bent函数。另外也构造了几种参数的布尔扩展组合函数。     

多输出部分Bent函数若干性质的研究

本文给出了多输出部分Bent函数的定义并论证了其存在性;得到了多输出部分Bent函数的谱特征定理和广义自相关函数的性质;讨论了多输出部分Bent函数的平衡性、相关免疫性、非线性性和扩散性等密码学性质.     

一种拟Bent函数的构造方法

本文提出了一般有限Abel群上的组合函数概念,由组合函数给出了一种拟Bent函数的递归构造方法,并给出了两类组合函数。     

Zn4上完全非线性函数的存在性和构造

给出了剩余类环Z4上的逻辑函数-4值逻辑函数是完全非线性函数的两个条件，引入了布尔函数中“类Bent函数”的概念，并用其构造了自变量个数是偶数的一类4值完全非线性函数，给出了1元4值完全非线性函数不存在性的一个简单证明。     

Z_4~n上完全非线性函数的存在性和构造

给出了剩余类环Z4上的逻辑函数-4值逻辑函数是完全非线性函数的两个条件,引入了布尔函数中"类Bent函数"的概念,并用其构造了自变量个数是偶数的一类4值完全非线性函数,给出了1元4值完全非线性函数不存在性的一个简单证明。     

广义Bent函数的稳定性及其构造

在ｐ是素数时,用ｐ次本原单位根给出广义Ｂｅｎｔ函数的谱判别条件,并由此对广义Ｂｅｎｔ函数的稳定性的概率意义进行了考察,最后,利用谱分解式研究了广义Ｂｅｎｔ函数的性质和构造,并据此给出了广义Ｂｅｎｔ函数的一种运算形式更一般的新的构造方法。     

密码函数的一类递归构造方法

首先利用递归的方法证明了结构形式更为一般的布尔函数的 Walsh谱分解式，然后利用这类布尔函数Walsh谱分解式，给出了密码学和编码学中具有重要应用价值的一些布尔函数，如弹性函数、Bent函数以及满足严格雪崩准则的布尔函数的构造方法。     

密码学中的布尔函数研究综述

概述了目前密码学中布尔函数的研究现状和重要研究方向上的新成果，并对布尔函数的研究进行了展望，指出了一些重要的研究热点问题．     

广义部分Bent函数及其自相关函数特征和谱特征

给出了环Ｚｍ＾ｎ（ｍ≥２为整数）上广义部分Ｂｅｎｔ函数的定义,讨论了广义部分Ｂｅｎｔ函数的等价条件,得到了广义部分Ｂｅｎｔ函数的自相关函数特征和Ｃｈｒｅｓｔｅｎｓｏｎ谱特征。     

Heuristic and Bent Key Exchange Secured Energy Efficient Data Transaction for Traffic Offloading in Mobile Cloud

In today’s world, smart phones offer various applications namely face detection, augmented-reality, image and video processing, video gaming and speech recognition. With the increasing demand for computing resources, these applications become more complicated. Cloud Computing (CC) environment provides access to unlimited resource pool with several features, including on demand self-service, elasticity, wide network access, resource pooling, low cost, and ease of use. Mobile Cloud Computing (MCC) aimed at overcoming drawbacks of smart phone devices. The task remains in combining CC technology to the mobile devices with improved battery life and therefore resulting in significant performance. For remote execution, recent studies suggested downloading all or part of mobile application from mobile device. On the other hand, in offloading process, mobile device energy consumption, Central Processing Unit (CPU) utilization, execution time, remaining battery life and amount of data transmission in network were related to one or more constraints by frameworks designed. To address the issues, a Heuristic and Bent Key Exchange (H-BKE) method can be considered by both ways to optimize energy consumption as well as to improve security during offloading. First, an energy efficient offloading model is designed using Reactive Heuristic Offloading algorithm where, the secondary users are allocated with the unused primary users’ spectrum. Next, a novel AES algorithm is designed that uses a Bent function and Rijndael variant with the advantage of large block size is hard to interpret and hence is said to ensure security while accessing primary users’ unused spectrum by the secondary user. Simulations are conducted for efficient offloading in mobile cloud and performance valuations are carried on the way to demonstrate that our projected technique is successful in terms of time consumption, energy consumption along with the security aspects covered during offloading in MCC.     

A New Thermodynamic Calculation Method for Binary Alloys：Part I：Statistical Calculation of Excess Functions

The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedemaˊs model for calculating the formation heat of binary alloys.A calculation method of excess thermodynamic functions for binary alloys,the formulas of intregral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed.The calculated results are in good agreement with the experimental values.     

Carbon-nanotube-based voltage-mode multiple-valued logic design

Multivalued logic has always attracted the attention of digital system and logic designers. However, the high-performance and low-power CMOS process, which has been developed over the last two decades, has traditionally assisted successful circuit implementation of binary logic. Consequently, in spite of its large potential multivalued logic design is seldom a circuit designer's choice. This paper presents a novel method of multiple-valued logic design using carbon-nanotube field-effect transistors (CNFETs). The geometry-dependent threshold voltage of CNFETs has been effectively used to design a ternary logic family. We have developed a SPICE-compatible model of ballistic CNFETs that can account for varying geometries and operating conditions. SPICE simulations have been performed on the proposed logic gates, and the transfer characteristics as well as transient behavior have been extensively studied. Finally, a comparison in terms of power and performance of the ternary logic family vis-a/spl grave/-vis traditional complementary field-effect transistor binary logic family has been presented.     

On enrichment functions in the extended finite element method

This paper presents mathematical derivation of enrichment functions in the extended finite element method for numerical modeling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by one interface across which displacement field suffers a jump. The main steps towards the derivation of enrichment functions are as follows: (1) extension of the subfields separated by the interface to the whole element domain and definition of complementary nodal variables; (2) construction of characteristic functions for describing the geometry and physical field; (3) determination of the sets of basic nodal variables; (4) domain decompositions according to Step 3 and then reproduction of the physical field in terms of characteristic functions and nodal variables; and (5) comparison of the piecewise interpolations formulated at Steps 3 and 4 with the standard extended finite element method form, which yields enrichment functions. In this process, the physical meanings of both the basic and complementary nodal variables are clarified, which helps to impose Dirichlet boundary conditions. Enrichment functions for weak discontinuities are constructed from deeper insights into the structure of the functions for strong discontinuities. Relationships between the two classes of functions are naturally established. Improvements upon basic enrichment functions for weak discontinuities are performed so as to achieve satisfactory convergence and accuracy. From numerical viewpoints, a simple and efficient treatment on the issue of blending elements is also proposed with implementation details. For validation purposes, applications of the derived functions to heterogeneous problems with imperfect interfaces are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes

The statical behaviour of a spatial bar of an elastic and isotropic material under arbitrary distributed loads having a non-circular helicoidal axis and cross-section supported elastically by single and/or continuous supports is studied by the stiffness matrix method based on the complementary functions approach. By considering the geometrical compatibility conditions together with the constitutive equations and equations of equilibrium, a set of 12 first-order differential equations having variable coefficients is obtained for spatial elements of helicoidal axes. The stiffness matrix and the element load vector of a helicoidal bar with a non-circular axis and arbitrary cross-section are obtained taking into consideration both the presence of an elastic support and the effects of the axial and shear deformations. For helicoidal staircases, the significance of both axial and shear deformations and eccentricities existing in wide and shallow sections are also investigated. The developed model has been coded in Fortran-77, which has been applied to various example problems available in the relevant literature, and the results have been compared.     

A NURBS-based Error Reproducing Kernel Method with Applications in Solid Mechanics

A novel method for derivation of mesh-free shape functions is proposed. The first step in the method is to approximate a function and its derivatives through non-uniform-rational-B-spline (NURBS) basis functions. However since NURBS functions neither reproduce polynomials of degree higher than one nor interpolate the control points (also referred to as grid or nodal points), the approximated function leads to uncontrolled errors over the domain including the nodal points. Accordingly the error function in the NURBS approximation and its derivatives are reproduced via a family of non-NURBS basis functions. The non-NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation of the function obtained in the first step. Since any desired order of continuity in the approximation can be achieved through NURBS, the proposed error reproducing kernel method (ERKM) can even approximate functions with discontinuous derivatives. Moreover, thanks to the variation diminishing property of NURBS, it has advantages in representing sharp layers without the so-called Gibbs‘ or Runge’s phenomena. Since derivatives are reproduced within polynomial spaces of appropriately reduced dimensions, differentiability requirements of the kernel functions are avoided. Any compactly supported continuous function, monotonically decreasing on either side of its maximum, may be used as the weight function (unlike other mesh free approximations). As it turns out, a target function is mainly approximated via NURBS and error functions are just supposed to add corrections, whose magnitudes are typically an order less than those of the NURBS components. The proposed method is observed to be nearly insensitive to the support size of the weight function. The proposed method is next applied to some linear and nonlinear boundary value problems of typical interest in solid mechanics. Some of these results are compared with those obtained via the standard form of RKPM. In the process, the relative numerical advantages and accuracy of the new method are brought out to an extent.