Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R << x1; :::; xn >> in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables

From Quantum Cheating to Quantum Security

For thousands of years, code-makers and code-breakers have been competing for supremacy. Their arsenals may soon include a powerful new weapon: quantum mechanics. We give an overview of quantum cryptology as of November 2000.Comment: 14 pages, 4 figures. Originally appeared in Physics Today: . This article may be downloaded for personal use only. Any other use requires prior permission of both the author and the American Institute of Physic

INFORMATION SECURITY MANAGEMENT IN WEB-BASED PRODUCT DESIGN AND REALIZATION

There is an increasing interest in research and development in the area of information security. Areas of computer misuse include the theft of computational resources, disruption of computational services, unauthorized disclosure of computer information and unauthorized modification of computer information. In the recent past decades, there have been myriads of computer security implementations. Nevertheless, there have also been numerous computer break-ins and security breaches. This is a thesis on Information Security Management in Web-Based Product Design and Realization, which is a sub-cluster of a broader currently on-going research project called Pegasus, at the Automation and Robotics Laboratory, University of Pittsburgh. Pegasus is a proposed scalable, flexible, and efficient collaborative web-based (or Internet-oriented) product design system, which will involve continuous transfer of sensitive information across seamless and possibly, international boundaries. The thesis commences with a statement of the problem of information security and presents a comprehensive summary of previous and current related research along with applicable results and application areas. With the dawn of the 21st century upon us and use of the Internet growing exponentially, secrecy in the realm of technology has become an important issue. A managerial approach for alleviating the problem of information security or reducing it to the barest minimum is proposed in this thesis through the design and development of an Information Security Management Model (ISM Model) to monitor, enforce and manage information security. The design of the ISM Model incorporates a methodology for referencing activities in Pegasus with information security technologies

Adaptive trust and reputation system as a security service in group communications

Group communications has been facilitating many emerging applications which require packet delivery from one or more sender(s) to multiple receivers. Owing to the multicasting and broadcasting nature, group communications are susceptible to various kinds of attacks. Though a number of proposals have been reported to secure group communications, provisioning security in group communications remains a critical and challenging issue. This work first presents a survey on recent advances in security requirements and services in group communications in wireless and wired networks, and discusses challenges in designing secure group communications in these networks. Effective security services to secure group communications are then proposed. This dissertation also introduces the taxonomy of security services, which can be applied to secure group communications, and evaluates existing secure group communications schemes. This dissertation work analyzes a number of vulnerabilities against trust and reputation systems, and proposes a threat model to predict attack behaviors. This work also considers scenarios in which multiple attacking agents actively and collaboratively attack the whole network as well as a specific individual node. The behaviors may be related to both performance issues and security issues. Finally, this work extensively examines and substantiates the security of the proposed trust and reputation system. This work next discusses the proposed trust and reputation system for an anonymous network, referred to as the Adaptive Trust-based Anonymous Network (ATAN). The distributed and decentralized network management in ATAN does not require a central authority so that ATAN alleviates the problem of a single point of failure. In ATAN, the trust and reputation system aims to enhance anonymity by establishing a trust and reputation relationship between the source and the forwarding members. The trust and reputation relationship of any two nodes is adaptive to new information learned by these two nodes or recommended from other trust nodes. Therefore, packets are anonymously routed from the \u27trusted\u27 source to the destination through \u27trusted\u27 intermediate nodes, thereby improving anonymity of communications. In the performance analysis, the ratio of the ATAN header and data payload is around 0.1, which is relatively small. This dissertation offers analysis on security services on group communications. It illustrates that these security services are needed to incorporate with each other such that group communications can be secure. Furthermore, the adaptive trust and reputation system is proposed to integrate the concept of trust and reputation into communications. Although deploying the trust and reputation system incurs some overheads in terms of storage spaces, bandwidth and computation cycles, it shows a very promising performance that enhance users\u27 confidence in using group communications, and concludes that the trust and reputation system should be deployed as another layer of security services to protect group communications against malicious adversaries and attacks

Cryptanalysis of a Homomorphic Public-Key Cryptosystem

The aims of this research are to give a precise description of a new homomorphic public-key encryption scheme proposed by Grigoriev and Ponomarenko [7] in 2004 and to break Grigoriev and Ponomarenko homomorphic public-key cryptosystem. Firstly, we prove some properties of linear fractional transformations. We analyze the X_n-representation algorithm which is used in the decryption scheme of Grigoriev and Ponomarenko homomorphic public-key cryptosystem and by these properties of the linear fractional transformations, we correct and modify the X_n-representation algorithm. We implement the modified X_n-representation algorithm by programming it and we prove the correctness of the modified X_n-representation algorithm. Secondly, we find an explicit formula to compute the X(n,S)-representations of elements of the group \Lambda_n. The X(n,S)-representation algorithm is used in the decryption scheme of Grigoriev and Ponomarenko homomorphic public-key cryptosystem and we modify the X(n,S)-representation algorithm. We implement the modified X(n,S)-representation algorithm by programming it and we justify the modified X(n,S)-representation algorithm. By these two modified X_n-representation algorithm and X(n,S)-representation algorithm, we make its decryption scheme more efficient. Thirdly, by using those properties of the linear fractional transformations, we design new X_1-representation algorithms I and II and we mainly use these two X_1-representation algorithms to break Grigoriev and Ponomarenko homomorphic public-key cryptosystem. We implement the algorithms by programming them and we prove the correctness of these two algorithms. Fourthly, we analyze Grigoriev and Ponomarenko homomorphic public-key cryptosystem and we give a clear description of Grigoriev and Ponomarenko scheme with a practical example. We also consider implementation issues for its practical applications. Lastly, we show several attack methods with examples and experiments according as the attack methods and so we break Grigoriev and Ponomarenko homomorphic public-key cryptosystem