Classification of the Deletion Correcting Capabilities of Reed–Solomon Codes of Dimension Over Prime Fields

Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRSk(l,q,alpha,v), is a code of length l over GF(q) with qk codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are also capable of correcting deletions. We consider a subclass of GRS codes with dimension k=2 and q prime, and study them with respect to deletion correcting capability. We give transformations that either preserve the code or maintain its deletion correction capability. We use this to define equivalent codes; and then use exhaustive and selective computer searches to find inequivalent codes with the highest deletion correcting capabilities. We show that, for the class under consideration, up to l-3 deletions may be corrected. We also show that for lles36 there exist codes with q2 codewords such that receiving only 3 out of t transmitted symbols of a codeword is enough to recover the codeword, thus meeting the bound specified above. We also specify some nice codes which are associated with the smallest field possible for codes of a given length and deletion correcting capability. Some of the identified codes are unique, with respect to the defined equivalence

Achievable secrecy enchancement through joint encryption and privacy amplification

In this dissertation we try to achieve secrecy enhancement in communications by resorting to both cryptographic and information theoretic secrecy tools and metrics. Our objective is to unify tools and measures from cryptography community with techniques and metrics from information theory community that are utilized to provide privacy and confidentiality in communication systems. For this purpose we adopt encryption techniques accompanied with privacy amplification tools in order to achieve secrecy goals that are determined based on information theoretic and cryptographic metrics. Every secrecy scheme relies on a certain advantage for legitimate users over adversaries viewed as an asymmetry in the system to deliver the required security for data transmission. In all of the proposed schemes in this dissertation, we resort to either inherently existing asymmetry in the system or proactively created advantage for legitimate users over a passive eavesdropper to further enhance secrecy of the communications. This advantage is manipulated by means of privacy amplification and encryption tools to achieve secrecy goals for the system evaluated based on information theoretic and cryptographic metrics. In our first work discussed in Chapter 2 and the third work explained in Chapter 4, we rely on a proactively established advantage for legitimate users based on eavesdropper’s lack of knowledge about a shared source of data. Unlike these works that assume an errorfree physical channel, in the second work discussed in Chapter 3 correlated erasure wiretap channel model is considered. This work relies on a passive and internally existing advantage for legitimate users that is built upon statistical and partial independence of eavesdropper’s channel errors from the errors in the main channel. We arrive at this secrecy advantage for legitimate users by exploitation of an authenticated but insecure feedback channel. From the perspective of the utilized tools, the first work discussed in Chapter 2 considers a specific scenario where secrecy enhancement of a particular block cipher called Data Encryption standard (DES) operating in cipher feedback mode (CFB) is studied. This secrecy enhancement is achieved by means of deliberate noise injection and wiretap channel encoding as a technique for privacy amplification against a resource constrained eavesdropper. Compared to the first work, the third work considers a more general framework in terms of both metrics and secrecy tools. This work studies secrecy enhancement of a general cipher based on universal hashing as a privacy amplification technique against an unbounded adversary. In this work, we have achieved the goal of exponential secrecy where information leakage to adversary, that is assessed in terms of mutual information as an information theoretic measure and Eve’s distinguishability as a cryptographic metric, decays at an exponential rate. In the second work generally encrypted data frames are transmitted through Automatic Repeat reQuest (ARQ) protocol to generate a common random source between legitimate users that later on is transformed into information theoretically secure keys for encryption by means of privacy amplification based on universal hashing. Towards the end, future works as an extension of the accomplished research in this dissertation are outlined. Proofs of major theorems and lemmas are presented in the Appendix

Universal homophonic coding

Redundancy in plaintext is a fertile source of attack in any encryption system. Compression before encryption reduces the redundancy in the plaintext, but this does not make a cipher more secure. The cipher text is still susceptible to known-plaintext and chosen-plaintext attacks. The aim of homophonic coding is to convert a plaintext source into a random sequence by randomly mapping each source symbol into one of a set of homophones. Each homophone is then encoded by a source coder after which it can be encrypted with a cryptographic system. The security of homophonic coding falls into the class of unconditionally secure ciphers. The main advantage of homophonic coding over pure source coding is that it provides security both against known-plaintext and chosen-plaintext attacks, whereas source coding merely protects against a ciphertext-only attack. The aim of this dissertation is to investigate the implementation of an adaptive homophonic coder based on an arithmetic coder. This type of homophonic coding is termed universal, as it is not dependent on the source statistics.Computer ScienceM.Sc. (Computer Science

Security Enhanced Symmetric Key Encryption Employing an Integer Code for the Erasure Channel

An instance of the framework for cryptographic security enhancement of symmetric-key encryption employing a dedicated error correction encoding is addressed. The main components of the proposal are: (i) a dedicated error correction coding and (ii) the use of a dedicated simulator of the noisy channel. The proposed error correction coding is designed for the binary erasure channel where at most one bit is erased in each codeword byte. The proposed encryption has been evaluated in the traditional scenario where we consider the advantage of an attacker to correctly decide to which of two known messages the given ciphertext corresponds. The evaluation shows that the proposed encryption provides a reduction of the considered attacker’s advantage in comparison with the initial encryption setting. The implementation complexity of the proposed encryption is considered, and it implies a suitable trade-off between increased security and increased implementation complexity

Ein analytisches Framework zur Bewertung der Zuverlässigkeit und Security von fortschrittlichen Netzwerk Systemen

Today, anonymous networks such as The Onion Routing (Tor) have been designed to ensure anonymity, privacy and censorship prevention, which have become major concerns in modern society. Although the Tor network provides layered encryption and traffic tunneling against eavesdropping attacks, the jamming attacks and their impact on the network and network services can not be efficiently handled today. Moreover, to defy modern censorship, it is not enough just to use the Tor network to hide the client's identity and the message content as the censorship has become a type of jamming attack, which prevents users from connecting to the censored network nodes by blocking or jamming (Tor) traffic. In network security, the main tools to protect privacy and anonymity as well as integrity and service reliability against eavesdropping and jamming, respectively, are diversity, randomness, coding or encryption and over-provisioning, all less exploit in traditional networks. This thesis provides radical new network concepts to address the needs of traditional networks for privacy, anonymity, integrity, and reliability; and designs \emph{advanced network systems} based on parallel transmission, random routing, erasure coding and redundant configurations as tools to offer diversity, randomness, coding and over-provisioning. Since the network systems designed in this thesis can not be evaluated with existing analytical models due to their rather complex configurations, the main focus of this work is a development of novel analytical approaches for evaluation of network performance, reliability and security of these systems and to show their practicality. The provided analysis is based on combinatorics, probability and information theory. In contrast to current reliability models, the analysis in this thesis takes into account the sharing of network components, heterogeneity of software and hardware, and interdependence between failed components. The significant property of the new security analysis proposed is the ability to assess the level of privacy, anonymity, integrity and censorship success when multiple jamming and eavesdropping adversaries reside in the network.Derzeit werden anonyme Internet Kommunikationssysteme, wie The Onion Routing (Tor), verwendet, um die Anonymität, die Privatsphäre und die Zensurfreiheit der Internetnutzer zu schützen. Obwohl das Tor-Netzwerk einen Schutz vor Lauschangriffe (Eavesdropping) bietet, kann ein beabsichtigtes Stören (Jamming) der Übertragung und den daraus resultierenden Auswirkungen auf die Netzwerkfunktionen derzeit nicht effektiv abgewehrt werden. Auch das moderne Zensurverfahren im Internet stellt eine Art des Jammings dar. Deswegen kann das Tor Netzwerk zwar die Identität der Tor-Nutzer und die Inhalte ihrer Nachrichten geheim halten, die Internetzensur kann dadurch nicht verhindert werden. Um die Netzwerksicherheit und insbesondere Anonymität, Privatsphäre und Integrität zusammen mit der Verfügbar.- und Zuverlässigkeit von Netzwerkservices zu gewährleisten, sind Diversität, Zufallsprinzip, Codierung (auch Verschlüsselung) und eine Überversorgung, die in den konventionellen Netzwerksystemen eher sparsam angewendet werden, die wichtigsten Mittel gegen Security-Angriffe. Diese Arbeit befasst sich mit grundlegend neuen Konzepten für Kommunikationsnetze, die einen Schutz der Anonymität und der Privatsphäre im Internet bei gleichzeitiger Sicherstellung von Integrität, Verfügbarkeit und Zuverlässigkeit ermöglichen. Die dabei verwendeten Konzepte sind die parallele Datenübertragung, das Random Routing, das Erasure Coding und redundante Systemkonfigurationen. Damit sollen Diversität, Zufallsprinzip, Codierung und eine Überversorgung gewährleistet werden. Da die entwickelten Übertragungssysteme komplexe Strukturen und Konfigurationen aufweisen, können existierende analytische Modelle nicht für eine fundierte Bewertung angewendet werden. Daher ist der Schwerpunkt dieser Arbeit neue analytische Verfahren für eine Bewertung von unterschiedlichen Netzwerkleistungsparametern, Zuverlässigkeit und Security zu entwickeln und die Praxistauglichkeit der in der Arbeit aufgeführten neuen Übertragungskonzepte zu beurteilen. Im Gegensatz zu existierenden Zuverlässigkeitsmodellen berücksichtigt der analytische Ansatz dieser Arbeit die Vielfalt von beteiligten Netzwerkkomponenten, deren komplexe Zusammenhänge und Abhängigkeiten im Fall eines Ausfalls

Physical Layer Authentication

A fundamental problem in security is authentication: namely, how to verify the identity of another party. Without this verification, the ideas of privacy and integrity are moot. Modern authentication techniques use cryptographic operations that secure the system against adversaries that do not have tremendous amounts of computation and memory. However, when the abilities of the adversary increase, such authentication paradigms become more susceptible to defeat. With the greater threat of defeat, the secret authentication keys must be replaced more often. Unfortunately, the popular key replacement algorithms typically rely on either third parties or on non-trivial computational ability. In this thesis we attack these two aspects of the authentication problem by presenting novel methods for authentication and key replacement in wireless environments. We describe how to exploit the randomness of the physical layer to hide the authentication from adversaries. Typically, no effort is made to hide the authentication - it is sent in plain view of friend and foe alike. The proposed technique reveals significantly less key information than traditional authentication methods and can increase the data throughput of the system. We define metrics to quantify the performance of the proposed authentication system and use them to study the associated tradeoffs. A software radio implementation is then presented to demonstrate the feasibility of the proposed scheme. Finally, we consider how secret keys can be replaced in an efficient manner. We describe a novel method of key replacement and generation that, unlike other methods, requires no additional message exhanges after initialization and yet generates highly random keys. As an added benefit, the method is shown to be extremely lightweight in terms of computation and memory requirements