基于DNA自组装的EIGamal系统破译

自组装DNA计算在破译密码系统方面,具有传统计算机无法比拟的优势。采用DNA分子瓦编码信息,借助于分子瓦之间的粘性末端进行自组装,通过引入非确定性的指派型分子瓦,提出了用自组装DNA计算破译EIGamal公钥密码系统的非确定性算法。通过创建数以亿计的参与计算的DNA分子瓦,该算法可以并行地以高概率地破译EIGamal公钥密码系统。     

基于DNA计算自组装模型的Diffie-Hellman算法破译(英文)

DNA自组装计算模型是近年来引人关注的计算模型,已有基于自组装模型的二进制加法、乘法以及有限域中的加法和乘法的讨论．文中利用DNA自组装模型设计的模乘系统,实现了素数P的本原根g连续乘方后模p的数的排列,从而可以在线性时间内求解离散对数,为破译Diffie—Hellman密钥交换算法提供了新的生物方法．该模乘系统使用了Θ（p）种自组装类型,组装的时间复杂度为Θ（p-1）．系统最后组装结果提取出报告链后,经过PCR和凝胶电泳读取离散对数结果．该模型扩展了DNA自组装计算模型的应用,为求取离散对数提供了新思路．     

无线自组网中有效的证密钥协商方案

在Diffie-Hellman密钥交换算法和基于身份的密码体制基础上,提出一种适用于无线自组网的认证密钥协商方案。该方案利用分布的多项式秘密共享的思想,实现PKG分布化和网络中节点公私钥的生成。通过随机数认证和基于身份的签名以及DH密钥协商算法实现认证密钥协商。该方案II3E与DH算法相结合,具有基于身份的密码体制低存储量和通信量的优点,同时认证密钥协商后的通信均可采用对称密码算法来有效降低计算量,节省网络资源。理论分析证明本方案是安全的。     

NTRU公钥密码算法基于J2ME的实现

NTRU公钥密码算法所具有的密钥生成简单、加解密速度快和对资源要求低等优点使得它非常适合用于保护移动通信中的信息安全。首先描述了NTRU公钥密码算法在J2ME上的实现,然后测试了该算法在J2ME上实现的性能。     

自组装DNA计算的研究进展及展望

近年来,许多研究者已经证明二维自组装模型有通用计算能力,同时证明了自组装DNA计算具有可扩展性。随着分子生物学技术的发展,自组装DNA计算有着广阔的应用前景,在纳米科学、优化计算、密码学、医学等众多科学领域中有突破性的创新与应用。较全面地介绍了自组装DNA计算的研究现状、原理、分子结构和数学模型,以及自组装DNA计算的复杂度和误差分析,并对自组装DNA计算待研究的问题和发展前景进行了分析和展望。     

密码算法研究

密码算法是信息安全的重要保证。介绍了密码体制的数学定义，并比较了对称密码算法和非对称密码算法，比较了DES、AES对称密码算法，两者中AES具有比DES更好的安全性、效率、灵活性；分析比较了RSA、ECC、NTRU等非对称密码算法，要实现相同的安全水平NTRU所需要密钥长度最短。     

密码算法研究

密码算法是信息安全的重要保证。介绍了密码体制的数学定义,并比较了对称密码算法和非对称密码算法,比较了DES、AES对称密码算法,两者中AES具有比DES更好的安全性、效率、灵活性;分析比较了RSA、ECC、NTRU等非对称密码算法,要实现相同的安全水平NTRU所需要密钥长度最短。     

NTRU公开密钥体制算法分析与实现

介绍了一种新的公开密钥体制NTRU。NTRU逄法的安全性取决于一从一个非常大的维数格中寻找很短向量的困难性，NTRU公开密钥体制算法主要计算对象是对多项式进行加、减、乘、模等运算。用NTRU产生的密钥方法比较容易，加密、解密的速度比RSA等著名算法快得多。从安全笥和有效性方面分析，NTRU密码体制有着广阔的应用前景。     

NTRU公钥密码体制的等价密钥

NTRU公钥密码体制存在多个私钥对应同一个公钥的问题。首先分析了NTRU成功解密的条件,提出NTRU等价密钥的概念。然后给出了NTRU截尾多项式环上多项式可逆的充分必要条件和NTRU|.|∞半范数的相关性质,提出4种等价密钥的构造方法。最后分析了NTRU等价密钥对NTRU安全性的影响。分析表明,NTRU参数选择不当会导致一些特殊形式的等价密钥存在,严重威胁安全性。     

对改进的基于DNA编码和混沌的图像加密方法的安全性分析*

混沌密码系统已展现了许多非传统密码系统所具有的优良特性,基于混沌的加密算法层出不穷,同时对混沌密码系统进行安全性分析对混沌密码的发展具有重要意义。对一种改进的基于DNA编码和混沌映射的图像加密方法进行了安全性分析,该算法的核心思想是明文图像的DNA编码矩阵与混沌映射产生的随机矩阵的DNA编码矩阵求和,然后再对这个和矩阵中的元素随机求补即得密文图像。运用选择明文攻击的方法,破解了该算法中的等效密钥,从而利用等效密钥再解密出目标明文。理论分析和实验结果验证了本文选择明文攻击策略的可行性。简要讨论了提高该密码算法安全性的一些改进措施。     

基于DNA Tiles自组装的布尔逻辑运算

大量研究工作表明,DNA tiles自组装现象是分子生物计算过程中一个很重要的计算方式.分子自组装的基本特点在于由许多小分子在一定机理的作用下,自动形成更大规模的超级分子结构的过程.自组装用于计算,在于这种组装模式可以抽象成一个自动化的系统,只需根据问题的需要设计好输入,再将其输入到运算系统,经过分子自组装过程,最后能生成问题的解.文中基于这样的运算机理,在DNA tiles自组装这个计算平台上,尝试做布尔逻辑运算,针对4变量4句子的布尔逻辑问题,提出一个DNA tiles自组装自动化运算系统.     

Approximate Self-Assembly of the Sierpinski Triangle

The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the Cartesian plane with specially labeled tiles appearing at exactly the positions of points in the Sierpinski triangle. More recently, Lathrop, Lutz, and Summers proved that the Sierpinski triangle cannot self-assemble in the ??strict?? sense in which tiles are not allowed to appear at positions outside the target structure. Here we investigate the strict self-assembly of sets that approximate the Sierpinski triangle. We show that every set that does strictly self-assemble disagrees with the Sierpinski triangle on a set with fractal dimension at least that of the Sierpinski triangle (??1.585), and that no subset of the Sierpinski triangle with fractal dimension greater than 1 strictly self-assembles. We show that our bounds are tight, even when restricted to supersets of the Sierpinski triangle, by presenting a strict self-assembly that adds communication fibers to the fractal structure without disturbing it. To verify this strict self-assembly we develop a generalization of the local determinism method of Soloveichik and Winfree.     

Convergence rates of Markov chains for some self-assembly and non-saturated Ising models

Algorithms based on Markov chains are ubiquitous across scientific disciplines as they provide a method for extracting statistical information about large, complicated systems. For some self-assembly models, Markov chains can be used to predict both equilibrium and non-equilibrium dynamics. In fact, the efficiency of these self-assembly algorithms can be related to the rate at which simple chains converge to their stationary distribution. We give an overview of the theory of Markov chains and show how many natural chains, including some relevant in the context of self-assembly, undergo a phase transition as a parameter representing temperature is varied in the model. We illustrate this behavior for the non-saturated Ising model in which there are two types of tiles that prefer to be next to other tiles of the same type. Unlike the standard Ising model, we also allow empty spaces that are not occupied by either type of tile. We prove that for a local Markov chain that allows tiles to attach and detach from the lattice, the rate of convergence is fast at high temperature and slow at low temperature.     

Activatable tiles for compact robust programmable molecular assembly and other applications

Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these existing error-resilient tile systems assumed directional growth of the tiling assembly. This is a very strong assumption because experiments show that tile self-assembly does not necessarily behave in such a fashion, since they may also grow in the reverse of the intended direction. The assumption of directional growth of the tiling assembly also underlies the growth model in theoretical assembly models such as the TAM. What is needed is a means for enforce this directionality constraint, which will allow us to reduce assembly errors. In this paper we describe a protection/deprotection strategy to strictly enforce the direction of tiling assembly growth so that the assembly process is robust against errors. Initially, we start with (1) a single “activated” tile with output pads that can bind with other tiles, along with (2) a set of “deactivated” tiles, meaning that the tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to a “deactivated” tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. When these are activated in a desired order, we can enforce a directional assembly at the same scale as the original one. Such a system can be built with minimal modifications of existing DNA tile nanostructures. We propose a new type of tiles called activatable tiles and its role in compact proofreading. Activatable tiles can be thought of as a particular case of the more recent signal tile assembly model, where signals transmit binding/unbinding instructions across tiles on binding to one or more input sites. We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree’s original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We also perform detailed stepwise simulations using a DNA Tile simulator Xgrow, and show that the activatable tiles mechanism can reduce error rates in self assembly. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as (1) a novel system for concentration of molecules, and (2) a catalyst in sequentially triggered chemical reactions.     

The effect of malformed tiles on tile assemblies within the kinetic tile assembly model

Many different constructions of proofreading tile sets have been proposed in the literature to reduce the effect of deviations from ideal behaviour of the dynamics of the molecular tile self-assembly process. In this paper, we consider the effect on the tile assembly process of a different kind of non-ideality, namely, imperfections in the tiles themselves. We assume a scenario in which some small proportion of the tiles in a tile set are “malformed”. We study, through simulations, the effect of such malformed tiles on the self-assembly process within the kinetic Tile Assembly Model (kTAM). Our simulation results show that some tile set constructions show greater error-resilience in the presence of malformed tiles than others. For example, the 2- and 3-way overlay compact proofreading tile sets of Reif et al. (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) are able to handle malformed tiles quite well. On the other hand, the snaked proofreading tile set of Chen and Goel (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) fails to form even moderately sized tile assemblies when malformed tiles are present. We show how the Chen–Goel construction may be modified to yield new snaked proofreading tile sets that are resilient not only to errors intrinsic to the assembly process, but also to errors caused by malformed tiles.     

DNA自组装的可满足性问题模型

DNA自组装技术在DNA计算和纳米技术领域都发挥着极其重要的作用,许多小规模NP完全问题都可以通过自组装模型得以解决.文中以可满足问题为模型,通过构造范式中变量的特殊补链,使其与初始数据库中初始DNA链发生杂交反应,形成发夹结构,利用形成发夹结构的DNA链与没形成发夹结构的DNA链长度不同的特点,通过凝胶电泳将这些带发夹的DNA链提取出来;然后加入与这些特殊补链完全互补的DNA链,在一定温度下,通过碱基互补配对原则,发夹结构又将被重新打开.该模型充分利用了DNA分子间的自组装能力,在计算过程中只需要用到凝胶电泳操作,在一定程度上大大减少了因生物操作过多而引起的各种实验误差.     

Toward minimum size self-assembled counters

DNA self-assembly is a promising paradigm for nanotechnology. In this paper we study the problem of finding tile systems of minimum size that assemble a given shape in the Tile Assembly Model, defined by Rothemund and Winfree (Proceedings of the thirty-second annual ACM symposium on theory of computing, 2000). We present a tile system that assembles an rectangle in asymptotically optimal time. This tile system has only 7 tiles. Earlier constructions need at least 8 tiles (Chen et al. Proceedings of symposium on discrete algorithms, 2004). We managed to reduce the number of tiles without increasing the assembly time. The new tile system works at temperature 3. The new construction was found by the combination of exhaustive computerized search of the design space and manual adjustment of the search output.