Sending private messages over communication environments under surveillance is an important challenge in communication security and has attracted attentions of cryptographers through time. We believe that resources other than cryptographic keys can be used for communication privacy. We consider private message transmission (PMT) in an abstract multipath communication model between two communicants, Alice and Bob, in the presence of an eavesdropper, Eve. Alice and Bob have pre-shared keys and Eve is computationally unbounded. There are a total of $n$ paths and the three parties can have simultaneous access to at most $t_a$, $t_b$, and $t_e$ paths. The parties can switch their paths after every $λ$ bits of communication. We study perfect (P)-PMT versus asymptotically-perfect (AP)-PMT protocols. The former has zero tolerance of transmission error and leakage, whereas the latter allows for positive error and leakage that tend to zero as the message length increases. We derive the necessary and sufficient conditions under which P-PMT and AP-PMT are possible. We also introduce explicit P-PMT and AP-PMT constructions. Our results show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT is possible even in poorest condition where $t_a=t_b=1$ and $t_e=n-1$. It remains however an open question whether the derived rates can be improved by more sophisticated AP-PMT protocols. We study applications of our results to private communication over the real-life scenarios of multiple-frequency links and multiple-route networks. We show practical examples of such scenarios that can be abstracted by the multipath setting: Our results prove the possibility of keyless information-theoretic private message transmission at rates $17\%$ and $20\%$ for the two example scenarios, respectively. We discuss open problems and future work at the end.
Sending private messages over communication environments under surveillance is an important challenge in communication security and has attracted attentions of cryptographers through time. We believe that resources other than cryptographic keys can be used for communication privacy. We consider private message transmission (PMT) in an abstract multipath communication model between two communicants, Alice and Bob, in the presence of an eavesdropper, Eve. Alice and Bob have pre-shared keys and Eve is computationally unbounded. There are a total of n paths and the three parties can have simultaneous access to at most ta, tb, and te paths. The parties can switch their paths after every λ bits of communication. We study perfect (P)-PMT versus asymptotically-perfect (AP)-PMT protocols. The former has zero tolerance of transmission error and leakage, whereas the latter allows for positive error and leakage that tend to zero as the message length increases. We derive the necessary and sufficient conditions under which P-PMT and AP-PMT are possible. We also introduce explicit P-PMT and AP-PMT constructions. Our results show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT is possible even in poorest condition where ta=tb=1 and te=n−1. It remains however an open question whether the derived rates can be improved by more sophisticated AP-PMT protocols. We study applications of our results to private communication over the real-life scenarios of multiple-frequency links and multiple-route networks. We show practical examples of such scenarios that can be abstracted by the multipath setting: Our results prove the possibility of keyless information-theoretic private message transmission at rates 17% and 20% for the two example scenarios, respectively. We discuss open problems and future work at the end.
In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob. In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).
In the model that has become known as “Perfectly Secure Message Transmission” (PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve gains no information about the message while Bob is able to recover it completely. We focus on PSMT protocols that work in two transmission rounds for n = 2t + 1. We break from previous work by following a conceptually simpler blueprint. This has two consequences: first, we obtain improved efficiency, namely, we reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n3log n) to O(n2log n). Our solution also reaches optimal transmission rate for a secret of size O(n log n), thus answering the hitherto open question of attaining a threshold below O(n2log n) bits. Second, our construction can be adapted to more general scenarios relevant to Network Coding, where the adversary is given more power.
Abstract. Consider two parties Alice and Bob, who hold private inputs x and y, and wish to compute a function f(x, y) privately in the information theoretic sense; that is, each party should learn nothing beyond f(x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f(x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties ’ inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant c> 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors.
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 (proportion 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 protocols 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. 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 protocols 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 network 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 transmission 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 receiver 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 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 message transmission protocols. We review the feasibility of implementing secure message transmission 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 theory 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.
In the model that has become known as "Perfectly Secure Message Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely. In this paper, we focus on protocols that work in two transmission rounds for n= 2t+1. We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size O(n^2 log n) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of O(n log n) bits. Additionally, we show how our protocol can be adapted to a Network Coding context.
Consider two parties, Alice and Bob, who hold private inputs x and y, and wish to compute a function f (x, y) privately in the information theoretic sense; that is, each party should learn nothing beyond f (x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f (x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties' inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and errorresilience are contradictory goals. In particular, we show that for every constant c > 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors.