Secure Message Transmission and its Applications Stelios Erotokritou A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Computer Science University College London June 2016 2 Declaration I, Stelios Erotokritou hereby declare that the work presented in this dissertation submission entitled “Secure Message Transmission and its Applications” in partial fulfilment of the re- quirements for the degree of Doctor of Philosophy of University College London, to the best of my knowledge and belief, contains no material previously published or written by another person and is an authentic record and presentation of my own work during a period of seven and a half years from October 2007 to April 2015 under the supervision of Professor Yvo Desmedt, Department of Computer Science, University College London. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Abstract In this thesis we focus on various aspects of secure message transmission protocols. Such protocols achieve the secure transmission of a message from a sender to a receiver - where the term “secure” encapsulates the notion of privacy and reliability of message transmission. These two parties are connected using an underlying network in which a static computationally unlimited active adversary able to corrupt up to t network nodes is assumed to be present. Such protocols are important to study as they are used extensively in various cryptographic protocols and are of interest to other research areas such as ad-hoc networks, military networks amongst others. Optimal bounds for the number of phases (communication from sender to receiver or vice versa), connectivity requirements (number of node disjoint network paths connecting sender and receiver - denoted by n), communication complexity (complexity of the number of field elements sent - where F is the finite field used and jFj = q) and transmission complexity (pro- portion of communication complexity to complexity of secrets transmitted) for secure message transmission protocols have been proven in previous work. In the one-phase model it has been shown that n ≥ 3t+1 node disjoint paths are required to achieve perfect communication. In the two phase model only n ≥ 2t + 1 node disjoint paths are necessary. This connectivity is also the required bound for almost perfectly secure one-phase protocols - protocols which achieve perfect privacy but with a negligible probability may fail to achieve reliability. In such cases the receiver accepts a different message to that transmitted by the sender or does not accept any message. The main focus of recent research in secure message transmission protocols has been to present new protocols which achieve optimal transmission complexity. This has been achieved through the transmission of multiple messages. If a protocol has a communication complexity of O(n3) field elements, to achieve optimal transmission complexity O(n2) secrets will have to be communicated. This has somewhat ignored the simplification and improvement of pro- tocols which securely transmit a single secret. Such improvements include constructing more efficient protocols with regards to communication complexity, computational complexity and the number of field elements sent throughout the whole protocol. In the thesis we first consider one-phase almost perfectly secure message transmission and present two new protocols which improve on previous work. We present a polynomial time protocol of O(n2) communication complexity which at the time of writing this thesis, is computationally more efficient than any other protocol of similar communication complexity for the almost perfectly secure transmission of a single message. 4 Abstract Even though our first almost perfectly secure transmission protocol is of polynomial time, it is important to study other protocols also and improve previous work presented by other researchers. This is the idea behind the second one-phase almost perfectly secure message transmission protocol we present which requires an exponential complexity of field operations but lower (O(n)) communication complexity. This protocol also improves on previous proto- cols of similar communication complexity, requiring in the order of O(log q) less computation to complete - where q denotes the size of the finite field used. Even though this protocol is of exponential time, for small values of n (e.g. when t = 1, t = 2 or t = 3) it may be beneficial to use this protocol for almost perfectly secure communication as opposed to using the polynomial time protocol. This is because less field elements need to be transmitted over the whole net- work which connects a sender and a receiver. Furthermore, an optimal almost perfectly secure transmission protocol will be one with O(n) communication complexity and with polynomial computational complexity. We hope that in the future, other researchers will be inspired by our proposed protocol, improve on our work and ideally achieve these optimal results. We also consider multi-phase protocols. By combining various cryptographic schemes, we present a new two-phase perfectly secure single message transmission protocol. At the time of writing this thesis, the protocol is the most efficient protocol when considering communication complexity. Our protocol has a communication complexity of O(n2) compared to O(n3) of previous work thus improving on the communication complexity by an order of O(n) for the perfectly secure message transmission of a single message. This protocol is then extended to a three phase protocol where a multi-recipient broadcast end channel network setting is considered. As opposed to point to point networks where a path from a sender reaches a single receiver, this network model is new in the field of message trans- mission protocols. In this model each path from a sender reaches multiple receivers, with all receivers receiving the same information from their common network communication channel. We show how the use of this protocol upon such a network can lead to great savings in the transmission and computation carried out by a single sender. We also discuss the importance and relevance of such a multi-recipient setting to practical applications. The first protocols in the field of perfectly secure message transmission with a human re- ceiver are also presented. This is a topic proposed by my supervisor Professor Yvo Desmedt for which I constructed solutions. In such protocols, one of the communicating parties is considered to be a human who does not have access to a computational device. Because of this, solutions for such protocols need to be computationally efficient and computationally simple so that they can be executed by the human party. Experiments with human participants were carried out to assess how easily and accurately human parties used the proposed protocols. The experimental results are presented and these identify how well human participants used the protocols. In addition to the security of messages, we also consider how one can achieve anonymity of message transmission protocols. For such protocols, considering a single-receiver multi-sender scenario, the presence of a t-threshold bounded adversary and the transmission of multiple secrets (as many as the number of sender), once the protocols ends one should not be able to identify the sender of a received message. Considering a passive and active adversary new protocols are presented which achieve the secure and anonymous transmission of messages in Abstract 5 the information-theoretic security model. Our proposed solutions can also be applied (with minor alterations) to the dual problem when a single-sender multi-recipient communication setting is considered. The contributions of the thesis are primarily theoretical - thus no implementation of the proposed protocols was carried out. Despite this, we reflect on practical aspects of secure mes- sage transmission protocols. We review the feasibility of implementing secure message trans- mission protocols in general upon various networks - focusing on the Internet which can be considered as the most important communication network at this time. We also describe in the- ory how concepts of secure message transmission protocols could possibly be used in practical implementations for secure communication on various existing communication networks. Open problems that remain unsolved in the research area of the proposed protocols are also discussed and we hope that these inspire research and future solutions for the design (and implementation) of better and more efficient secure message transmission protocols. Acknowledgements Primarily I would like to thank my thesis advisor, Professor Yvo Desmedt. I am most grateful to him both on a personal and academic level. It has been an absolute pleasure for me to know him as a person, to have been his student and to learn from him. His work ethic, motivation, encouragement and demand for thoroughness has greatly im- proved me as a student and as a researcher. Through his teaching I have improved and developed essential skills required for a researcher to possess and I thank him for that. I would also like to thank him for his help during my work - helping me in the identification of errors and providing me with ideas and references to help me find better and correct solutions while at the same time helping me increase my knowledge and become more cautious with my work. Another person I would also like to thank is Dr. Paul Kearney who was my industrial contact with British Telecom (BT). He was always very helpful and was very active in the search for my primary field of research - both from a theoretical and practical viewpoint. He also helped me greatly with gaining access to various industrial contacts at BT labs - which aided me greatly with my work. I would also like to thank British Telecom which partly funded my PhD thesis and allowed me to use its resources during my research period. Special thanks must also be given to Theo Dimitrakos and Srijith Nair of BT labs with whom I worked with during my placement at BT.