有限自动机公钥密码体制的密码分析

提出一种针对有限自动机公钥密码系统的攻击算法,它可在多项式时间内破译有限自动机公钥密码方案FAPKCO.这一算法的基本思想,原则上也可用来攻击其他有限自动机公钥密码方案,因而在设计新的有限自动机公钥密码系统时,必须讨论它是否经得住这种方法的攻击.     

基于Rabin算法的超递增背包公钥密码体制的研究与改进

超递增背包公钥密码体制是基于超递增背包问题的密码体制,它使得加密解密的过程变得相对简单.但是,由于该体制本身存在一定的弱点,不少国内外学者都提出了破解方案.在超递增背包公钥的基础上,结合了Rabin算法,使得原先的密码体制变得更为灵活.改进后的算法不但在性能上保持了高效率,而且将原先的密钥变为公钥,可以根据用户需求动态地改变公钥,实现安全性的成倍提高.     

基于单模数线性同余方程组设计的公钥密码体系

本文基于MH-KPKC体系和HILL密码体系的构建思想,提出了基于单模数线性同余方程组设计的公钥密码体系.该体制无需利用超递增序列和贪心算法恢复明文.算例说明了该体制的可行性。     

量子Grover算法及其应用

深入剖析了G rover算法,最后将其应用于经典密码学,对序列密码和分组密码等进行了攻击和分析.     

求解图着色问题的量子蚁群算法

针对经典的图着色问题,在蚁群算法的基础上结合量子计算提出一种求解图着色问题的量子蚁群算法. 将量子比特和量子逻辑门引入到蚁群算法中,较好地避免了蚁群算法搜索易陷入局部极小的缺陷,并显著加快了算法的运算速度. 通过图着色实例的大量仿真实验,表明算法对图着色问题的求解是可行的、有效的,且具有通用性.     

结绳与量子计算

古人结绳记事,延续祖先的思维,我们用绳圈来描述粒子的轨迹;记录它们的运动;进而探讨绳圈数学的应用--拓扑量子计算.     

InAs/GaAs单电子量子点量子比特的失相率

在有效质量包络函数理论近似下, 计算了InAs/GaAs量子点的参数相图,确切定义了InAs/GaAs量子点的参数的范围,使得该量子点能作为二能级量子系统用于量子计算;发现静电场能够有效延长消相干时间,当外加静电场超过20 kV/cm时,消相干时间能够达到毫秒量级. 这些结果有助于未来实现固态量子计算.     

TSP的量子蚂蚁算法求解

在分析量子算法的基本概念的基础上,提出了一种新的算法——量子蚂蚁算法。量子蚂蚁算法结合了量子计算中量子旋转门的量子信息和蚂蚁寻优的特点,为解决实际问题提供的一种新的优化方法。本文将量子蚂蚁算法应用于TSP问题的研究,通过选取国际通用的TSP实例库中多个实例进行测试,表明了新算法具有很好的精确度和鲁棒性,即使对于大规模问题,也能以很小的种群和不长的时间求得相对误差较小的满意解。     

通信密码简介(一)

<正>利用密码传送和储存信息是保证信息安全的一项最有效措施.在近代历史上,通信的保密措施,对军事和外交等方面有极端重要的意义,它直接关系到国家的安危和战争的胜负.例如,二战时期,美国密码专家用几个月时间完全破译了日本的密码紫密.在中途岛一战,美国海军以劣     

通信密码简介(三)

<正>(三)RSA公钥体制的数字签名政治、军事、外交等活动中签署文件,商业上签订契约与合同,以及日常生活中在写信,从银行中取款等事务中的签名,传统上都采用手写签名或使用印鉴.签名起到认证、核准和生效的作用.随着信息时代的来临,人们希望     

Poly-Locality in Quantum Computing

A polynomial depth quantum circuit affects, by definition, a poly-local unitary transformation of a tensor product state space. It is a reasonable belief [Fe], [L], [FKW] that, at a fine scale, these are precisely the transformations which will be available from physics to solve computational problems. The poly-locality of a discrete Fourier transform on cyclic groups is at the heart of Shor's factoring algorithm. We describe a class of poly-local transformations, which include the discrete orthogonal wavelet transforms, in the hope that these may be helpful in constructing new quantum algorithms. We also observe that even a rather mild violation of poly-locality leads to a model without one-way functions, giving further evidence that poly-locality is an essential concept. March 1, 2000. Final version received: October 23, 2001.     

Using modifications to Grover’s Search algorithm for quantum global optimization

We study the problem of finding a global optimal solution to discrete optimization problems using a heuristic based on quantum computing methods. (Knowledge of quantum computing ideas is not necessary to read this paper.) We focus on a successful quantum computing method introduced by Baritompa, Bulger, and Wood, that we refer to as the BBW algorithm, and develop two modifications. First, we modify the BBW algorithm to achieve a dramatic speedup that lets us extend the known BBW static schedule from 33 to 43 points, thereby increasing its applicability. We further modify it by converting it from a static method to a dynamic one. Experimental results show the value of this latter modification.     

在基本计算系统中实现切比雪夫多项式的算法

提出了一个仅使用基本运算加、减和移位计算切比雪夫多项式的坐标旋转算法,证明了收敛性,讨论了误差估计.算法编码占用空间很小,适合在微计算系统中使用.     

Calderón type formula in Quantum calculus

In this paper, a Calderón type reproducing formula involving finite q$q$-measures is considered in Quantum calculus.     

Phase Condition for the Grover Algorithm

For the Grover algorithm, we derive the exact formula of the norm of the amplitude in the marked state in a sine-function form and use this formula to derive the necessary and sufficient phase condition sin Δ ≤ |β| for this algorithm with arbitrary phase rotations. We show that the condition of identical rotation angles θ = φ, which is a special case of our condition, is a sufficient but not necessary phase condition.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 472–483, September, 2005.     

Quantum Symmetric Pairs and the Reflection Equation

It is shown that central elements in G. Letzter’s quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter’s approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen. We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs can be performed preserving spherical representations from the classical situation. These tools apply to the symmetric pair FII and to all symmetric pairs which correspond to an automorphism of the underlying Dynkin diagram. Hence Noumi-Sugitani-Dijkhuizen type constructions with desirable properties are possible for various symmetric pairs for exceptional Lie algebras. Presented by Susan Montgomery.     

On the Discrete Spectrum of Generalized Quantum Tubes

The spectrum (of the Dirichlet Laplacian) of non-compact, non-complete Riemannian manifolds is much less understood than their compact counterparts. In particular it is often not even known whether such a manifold has any discrete spectra. In this article, we will prove that a certain type of non-compact, non-complete manifold called the quantum tube has non-empty discrete spectrum. The quantum tube is a tubular neighborhood built about an immersed complete manifold in Euclidean space. The terminology of “quantum” implies that the geometry of the underlying complete manifold can induce discrete spectra – hence quantization. We will show how the Weyl tube invariants appear in determining the existence of discrete spectra. This is an extension and generalization, on the geometric side, of the previous work of the author on the “quantum layer.”     

计算数学与科学工程计算及其在中国的若干发展 (迎接ICM2002特约文章)

本文论述了计算数学与科学工程计算的重要性，回顾了近50年来这一学科在中国的发展，特别是冯康的杰出贡献，介绍了国家重点基础研究发展规划相关项目的研究课题。     

Quantum families of quantum group homomorphisms

The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this paper, we define a quantum family of homomorphisms of locally compact quantum groups. Roughly speaking, we show that such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras, is introduced and the algebraic counterpart of the aforementioned result is proved. Moreover, we show that a quantum family of homomorphisms of Hopf algebras is consistent with the counits and coinverses of the given Hopf algebras. We compare our concept with weak coactions introduced by Andruskiewitsch and we apply it to the analysis of adjoint coaction.