NTRU算法的分析

陈克耀 谢康林

介绍了一种新的公开密钥体制NTRU算法，NTRU算法的安全性是基于数论中在一个非常大的维数格中寻找一个很短向量的数学难题。NTRU算法与RSA等算法相比具有更高的运算速度，更快的密钥生成速度和更少的存储空间，尽管在安全性方面与RSA相比有一些缺陷，但也有弥补的方法，因此NTRU算法将会有更广阔的应用前景。

NTRU公钥密码体制及其算法的优化

陈宇锋 钱森水 赵立杰

NTRU(Number Theory Research Unit)是1996年提出来的一种新的公钥密码体制，其安全性取决于从一个非常大的维数格中寻找很短向量的困难性，它很好地解决了公钥密码体制的最大瓶颈——速度问题，这使它有着非常广泛的应用前景，成为新一代最优秀的公钥密码体制，本文主要介绍了NTRU公钥密码体制并对其算法进行了优化设计，从而使NTRU能得到更好的应用．

NTRU公钥密码体制及安全性分析

NTRU Public Key Cryptosystem and Its Analysis of Security

卓泽朋[1] 魏仕民[2]

NTRU算法是一个新的公钥密码体制，它的加密使用基于多项式代数和对数P，q约化模的混合系统，而解密使用基于概率论的非混合系统．NTRU的安全性基于多项式、不同模混合运算的相互作用和从一个非常大的维数格中寻找最短向量的困难性。描述了NTRU公钥密码体制的基本算法，并分析了NTRU的安全性。[著者文摘]

NTRU is a new public key cryptosystem. The encryption procedure uses a mixing system based on polynomial algebra and reduction modulo two p and q. The deeryption procedure uses an un - mixing system whose validity depends on elementary probability theory . The security of the NTRU public key cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction modulo p and q and the difficulty in finding extremely short vectors. In this paper, the basic NTRU, s encryption algorithm is described and the security of NTRU is specially analyzed.[著者文摘]

一类用于攻击NTRU的新格

肖烨 卢伟清

NTRU算法是一个新的公钥密码算法．其安全性取决于从一个非常大的维数格中寻找最短向量的困难性．作者研究了NTRU算法的安全性．使用格约化方法对NTRU算法进行攻击．并找到了一类特殊的格．由于利用了NTRU私钥的特殊结构，该格的维(dimension)比常用的格更小．研究表明．具有某种特征的NTRU密钥特别容易被攻击，但是本文的方法可以用于攻击所有的NTRU密钥．该研究不会影响NTRU的应用．只是对NTRU格参数的选取有了更加严格的限制条件．从安全性和有效性综合考虑，NTRU公钥密码体制有着广阔的应用前景．

NTRU中多项式的逆问题

Problem of Polynomial＇s Inverse in NTRU

缪祥华[1,2] 何大可[1,2] 余位弛[1,2] 张文芳[1,2] 孙宇[1,2]

在NTRU公钥密码体制中,一个多项式是否有逆多项式是一个很重要的问题.本文介绍了NTRU公钥密码体制,给出了NTRU中多项式是否有逆的判定定理,并对所提出的定理进行了相应的证明.最后我们用例子来说明怎样运用该判定定理,给出了求解多项式逆的算法.[著者文摘]

In NTRU public key cryptosystem,it is very important whether or not a polynomial has inverse. This article puts forward to a judgement thcorem about inverse of a polynomial in NTRU public key cryptcsystem, and proves the judgement theorem. At last we illustrate how to use the judgement theorem and give the ,solve algorithm of polynomial＇s inverse.[著者文摘]

NTRU公钥密码体制的遗传算法攻击

Genetic Algorithms Attack on NTRU public-key cryptosystem

赵小龙[1] 王衍波[1] 李彬[2] 于杰山[1]

提出了一种应用遗传算法攻击NTRU公钥密码体制的方法。针对NTRU私钥的特点，该方法在编码时采取了顺序编码，交叉算子基于双亲的一组循环基因位实现，适应度定义为私钥在[-1，1]间系数个数与总系数个数之比。仿真结果表明，该攻击方法设计合理，将搜索空间缩小了2个数量级。[著者文摘]

A method to attack NTRU public-key cryptosystem utilizing a genetic algorithm to search the key space is presented. According to the NTRU private key＇s characteristics, order coding was selected as the GA＇s representation, crossover operation was implemented based on a group of circular genes in parents and the fitness was measured by the ratio of the number of the private key＇s coefficients between [-1,1 ] to the total number of its coefficients. Simulation experiments show that the solution which reduces the search space 2 orders in quantity is reasonable.[著者文摘]

NTRU中间距失败的概率分析及其影响

Probabilities analysis and affection of gap failure in NTRU

陈桂东 陈亦望 姚泽清

NTRU是一种极有发展潜力的公钥密码体制,然而它的解密机制是不完善的,可能出现合法密文无法解密的现象,这严重影响了该体制的安全性。间距失败是导致解密失败的一个重要原因,对此,在=2相关多项式均为系数为0或1的二元多项式条件下,讨论了卷积系数的弱线性相关性,在此基础上对间距失败的概率计算进行了介绍和分析,得到了相关的计算公式,并介绍了一种利用间距失败对NTRU的攻击方法。[著者文摘]

NTRU public-key cryptosystem has greatly developmental potential. But dose not provide perfect decryption. That is, some valid ciphertexts can not be decrypted. This defect seriously affect the security of NTRU system. The weak linear relation between the coefficients of the convolution is discussed when the related polynomials are binary and p=2. Probabilities analysis and the calculative formula of the gap failure are introduced. An attack on the NTRU based on gap failure is also introduced.[著者文摘]

NTRU公钥密码体制的实现与分析

端木庆峰[1] 王衍波[2] 郑学瑜[2] 赵小龙[2] 于杰山[2]

NTRU是Jeffrey Hoffstein等在1996年提出的一种新的公钥密码体制，其安全性基于大维数格中寻找最短向量的数学难题。速度上的优势使它有着非常广泛的应用前景，和椭圆曲线密码体制一起，成为新一代最优秀的公钥密码体制。主要介绍了NTRU的设计原理，对算法进行了优化设计和分析，特别地，将算法中的卷积转化为加减运算，提高了系统的性能。

NTRU数字签名体制的发展研究

李敏

本文简单叙述了NTRU数字签名体制，介绍了NTRU密码已取得的研究成果和已使用的研究方法与策略，并对NTRUSIGN与NSS进行了分析和比较，突出了不同体制之间的差异，展示了其逐步深化研究的方法和取得的成果，并列举了尚待解决的问题。[著者文摘]

A novel mutual authentication and key agreement protocol based on NTRU cryptography for wireless communications

蒋军 何晨

In this paper, the authors present a novel mutual authentication and key agreement protocol based on the Number Theory Research Unit (NTRU) public key cryptography. The symmetric encryption, hash and “challenge-response” techniques were adopted to build their protocol. To implement the mutual authentication and session key agreement, the proposed protocol contains two stages: namely initial procedure and real execution stage. Since the lightweight NTRU public key cryptography is employed, their protocol can not only overcome the security flaws of secret-key based authentication protocols such as those used in Global System for Mobile Communications (GSM) and Universal Mobile Telecommunications System (UMTS), but also provide greater security and lower computational complexity in comparison with currently well-known public key based wireless authentication schemes such as Beller-Yacobi and M.Aydos protocols.