Computing Prime Factorization And Discrete Logarithms: From Index Calculus To Xedni Calculus

The integer factorization problem (IFP), the finite field discrete logarithm problem (DLP) and the elliptic curve discrete logarithm problem (ECDLP) are essentially the only three mathematical problems that the practical public-key cryptographic systems are based on. For example, the most famous RSA cryptosystem is based on IFP, the US government's Digital Signature Standard, DSS, is based on DLP, whereas the ECC (Elliptic Curve Cryptography) and Elliptic Curve Digital Signature Algorithm (ECDSA) are based on ECDLP. The security of such cryptographic systems relies on the computational intractability of these three mathematical problems. In this paper, we shall present a survey of various methods for solving the IFP/DLP and particularly the ECDLP problems. More specifically, we shall first discuss how the index calculus as well as quantum algorithms can be used to solve IFP/DLP. Then we shall show why the index calculus cannot be used to solve ECDLP. Finally, we shall introduce a new method, xedni calculus , due to Joseph Silverman, for attack ECDLP; some open problems and new research directions, will also be addressed.     

FPGA based unified architecture for public key and private key cryptosystems

Recently, security in embedded system arises attentions because of modern electronic devices need cautiously either exchange or communicate with the sensitive data. Although security is classical research topic in worldwide communication, the researchers still face the problems of how to deal with these resource constraint devices and enhance the features of assurance and certification. Therefore, some computations of cryptographic algorithms are built on hardware platforms, such as field program gate arrays (FPGAs). The commonly used cryptographic algorithms for digital signature algorithm (DSA) are rivest-shamir-adleman (RSA) and elliptic curve cryptosystems (ECC) which based on the presumed difficulty of factoring large integers and the algebraic structure of elliptic curves over finite fields. Usually, RSA is computed over GF(p), and ECC is computed over GF(p) or GF(2 ^p ). Moreover, embedded applications need advance encryption standard (AES) algorithms to process encryption and decryption procedures. In order to reuse the hardware resources and meet the trade-off between area and performance, we proposed a new triple functional arithmetic unit for computing high radix RSA and ECC operations over GF(p) and GF(2 ^p ), which also can be extended to support AES operations. A new high radix signed digital (SD) adder has been proposed to eliminate the carry propagations over GF(p). The proposed unified design took up 28.7% less hardware resources than implementing RSA, ECC, and AES individually, and the experimental results show that our proposed architecture can achieve 141.8MHz using approximately 5.5k CLBs on Virtex-5 FPGA.     

深入浅出图说网络加密技术

计算机网络安全技术应用越来越广,对于计算机网络专业的学生,无论是中专生、大专生还是本科生,掌握一定的加密技术的概念和原理是非常有益的。本文针对高职和大专层次的学生,采用易懂的讲述方式,通俗的语言,浅显的图例,深入浅出地介绍了加密模型、加密算法、对称加密算法、非对称加密算法、数字签名、数字证书、虚拟私有网(VPN)、安全套接层(SSL)等网络安全的内容。     

RSA数字签名算法在电子病历中的应用

为解决电子病历的真实性与完整性问题,需要对电子病历进行加密。本文提出了一种数字签名算法,通过验证数字签名来确定电子病历的合法性。在此基础上,给出了RSA算法的实现策略,实现了电子病历的安全性与不可抵赖性。     

利用组合加解密方案改进SET协议的研究

文章首先对电子商务的安全体系进行了分析,针对SET协议对加解密算法的限制,提出一种采用组合加解密方案来提高SET协议的适应性和安全性,同时,又给出多证书和多数字签名的生成和认证方法。     

Identity-based Encryption: From Identity and Access Management to Enterprise Privacy Management

ABSTRACT

A scheme for establishing authenticated Diffie-Hellman based shared keys using Digital Signature Standard (DSS). A similar technique with one random variable was proposed earlier, and it was found that such system with one random variable is not well secured. Subsequently, it was pointed out that at least two random variables are required for satisfying three cryptographic properties of authenticity, security, and uniqueness of the session keys established. In this work, a new approach for establishing authenticated secret session keys using two random numbers is presented. An in-depth analysis of the proposed scheme for the three cryptographic properties of authenticity, security, and uniqueness has been done, and no such weakness has been found.     

The Elliptic Curve Digital Signature Algorithm (ECDSA)

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard and in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard and is under consideration for inclusion in some other ISO standards. Unlike the ordinary discrete logarithm problem and the integer factorization problem, no subexponential-time algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strength-per-key-bit is substantially greater in an algorithm that uses elliptic curves. This paper describes the ANSI X9.62 ECDSA, and discusses related security, implementation, and interoperability issues. Published online: 27 July 2001     

A key agreement authentication protocol using an improved parallel Pollard rho for electronic payment system

An improved protocol with a key agreement authentication using parallel Pollard rho algorithm for electronic payment system is proposed in this paper. The protocol employs a two step of key agreement and authentication with parallel Pollard rho and encryption of transaction information using Elliptic Curve Digital Signature Algorithm (ECDSA). Pollard rho was used in parallel as a key calculator that measures attack on discrete logarithm problem (DLP) of three main e-payment parties, namely customer, merchant and bank. Customers card information was used to infer the discrete logarithm problem which in turn was reused by the merchant and bank. The ECDSA was applied to encrypt information, resulting in a combination of the summation of participatory key, l. The length l serves as a diversion against intruders’ attempt to guess the DLP. The result shows that the protocol ensured higher security within a shorter period of time in comparison with others in the literature.     

公钥密码体制的现状与发展

文中对公钥密码体制的现状与发展进行了介绍,其中着重讨论了几个比较重要的公钥密码体制M-H背包算法、RSA、ECC、量子密码、NTRU密码体制和基于辫群上的密码体制。     

公钥密码体制的现状与发展

文中对公钥密码体制的现状与发展进行了介绍，其中着重讨论了几个比较重要的公钥密码体制M-H背包算法、RSA、ECC、量子密码、NTRU密码体制和基于辫群上的密码体制。     

基于智能卡的RSA数字签名算法

数字签名是目前保证网络通信安全的一种可靠而重要的技术手段.本文提出一种基于智能卡的RSA数字签名算法,利用智能卡提供的COS(Card Operaiing System)操作系统的Verify命令,并编写相关配套软件实现RSA数字签名及其验证,成功地将智能卡应用到PKI中.同时分析了应用智能卡实现RSA数字签名及验证的安全性以及相关方面的一些关键问题.     

关于椭圆曲线数字签名算法研究

椭圆曲线密码(ECC)是目前最流行的公钥密码体制,而椭圆曲线数字签名(ECDSA)是ELGamal公钥签名体制在椭圆曲线密码体制中的重要应用。该文从工程实现的角度详细介绍和讨论了椭圆曲线数字签名算法,并提出了在实现椭圆曲线签名中需要注意的几个问题。     

On the security of MQ cryptographic systems for constructing secure Internet of medical things

The Internet of Medical Things (IoMTs) are the group of medical devices connected to Internet, to perform the processes and services that support healthcare. The amount of data handled by medical devices grows exponentially, which means higher exposure of personal sensitive data. RSA, ECC and, other related public key cryptographic systems with countermeasures of power analysis and fault analysis, e.g., random masking, are often adapted by medical devices for guaranteing security and privacy. However, Shor algorithm has proven that they are not secure to quantum computer attacks. Fortunately, there exists a few quantum-resistant public key cryptographic schemes, e.g., Rainbow. To ensure end-to-end service delivery in the IoMTs under quantum attacks, there is a critical need for research into new designs and evaluation for the hardware security of new quantum-resistance cryptographic systems, e.g., rainbow, to make the medical devices more secure and reliable. Therefore, we present a physical analysis model of Rainbow by combining fault analysis and differential power analysis. The proposed model is implemented on cloud computing platform. Based on the experimental results, we successfully recover all the secret keys of Rainbow signature, which shows the importance of protecting multivariate signature with countermeasures on medical devices.     

无线传感器网络HEDSA数据聚合研究

现有普通安全方案不能满足无线传感器网络高安全性和高效率要求,为此,提出一种同态加密与数字签名算法。利用同态加密技术对加密的数据进行聚合,提高网络的数据传输效率,通过数字签名提供数据的完整性和不可否认性鉴别。理论证明和仿真实验表明,该算法具有较高的安全性和效率。     

具有防御功耗攻击性能的双域椭圆曲线密码处理器设计

提出了一种新型椭圆曲线密码处理器设计方案．采用OJW（最优联合权重）点乘调度算法加速点乘运算，该方法对椭圆曲线数字签名算法的验证运算尤为有效．通过引入双域求逆与Montgomery模乘相统一的算法和数据通路，处理器能进行任意GF（p）和GF（2^n）域上的有限域运算．同时针对简单功耗攻击和差分功耗攻击，本文提出了有效的抗攻击措施．基于SMIC 0．18CMOS工艺的实现结果表明，该设计在面积、速度、芯片抗攻击性能方面较同类设计有明显优势．     

对一种ECDSA改进算法的攻击

椭圆曲线数字签名算法ECDSA的应用越来越广。本文通过分析其中一种提高ECDSA签名效率的改进算法,指出该算法存在的安全隐患,分析其不安全的根源,并提出一种攻击方法。该攻击方法在不需要解离散对数的情况下,可以得到签名者的私钥,并且计算量不大。     

The evolution of the Advanced Encryption Standard

The National Institute of Standards and Technology (NIST) is working with industry, academia and the cryptographic community to replace the Data Encryption Standard (DES). The new algorithm will be called the Advanced Encryption Standard (AES), and the goal is to develop a Federal Information Processing Standard (FIPS) that specifies the encryption algorithm(s) capable of protecting sensitive but unclassified information well into the 21st century.¹ It is expected that the AES will be used by the US Government and, on a voluntary basis, by the private sector.¹     

基于ECC算法的PKI系统设计与实现

2008年,随着国家商用密码应用技术体系研究与数字电视密码应用示范工程课题开展,针对电视节目版权的保护越来越受到重视。采用了硬件实现ECC算法,并将该算法成功的架构到PKI系统中,实现了对原有的RSA算法的改造,提高了安全性和运算速度。     

基于椭圆曲线的多重签名

本文从椭圆曲线离散对数问题(ECELP)出发,针对现有的椭圆曲线数字签名算法(ECDSA),提出了两个基于椭圆曲线的多重签名方案,包括按序多重签名和广播多重签名,基于计算量和效率,又提出了另外一种椭圆曲线的广播多重签名。它们都满足数字签名的基本要求,并具有良好的安全性和实用性。     

Anti-counterfeiting, key distribution, and key storage in an ambient world via physical unclonable functions

Virtually all applications which provide or require a security service need a secret key. In an ambient world, where (potentially) sensitive information is continually being gathered about us, it is critical that those keys be both securely deployed and safeguarded from compromise. In this paper, we provide solutions for secure key deployment and storage of keys in sensor networks and radio frequency identification systems based on the use of Physical Unclonable Functions (PUFs). In addition, to providing an overview of different existing PUF realizations, we introduce a PUF realization aimed at ultra-low cost applications. We then show how the properties of Fuzzy Extractors or Helper Data algorithms can be used to securely deploy secret keys to a low cost wireless node. Our protocols are more efficient (round complexity) and allow for lower costs compared to previously proposed ones. We also provide an overview of PUF applications aimed at solving the counterfeiting of goods and devices.