In Secure Message Transmission (SMT) protocol a sender S can send a message m to a receiver R in a ‘private’ and ‘reliable’ way. S and R are connected by n channels where at most t of them can be fully controlled by an adaptive adversary with unlimited computational power. In this paper, noting the similarity between the privacy goal of SMT and an encryption function, we introduce a new definition for privacy of SMT systems which is inspired by the definition of semantic security in encryption. We show the relationship between this new definition and the previously known one, and propose an efficient 1-round protocol that is secure under the new definition and insecure under the previous one. The protocol has a better transmission rate compared to all known 1-round protocols in the previous model. We discuss our results and show how it relates to known results in this area.
In Secure Message Transmission (SMT) protocol a sender S can send a message m to a receiver R in a ‘private’ and ‘reliable’ way. S and R are connected by n channels where at most t of them can be fully controlled by an adaptive adversary with unlimited computational power. In this paper, noting the similarity between the privacy goal of SMT and an encryption function, we introduce a new definition for privacy of SMT systems which is inspired by the definition of semantic security in encryption. We show the relationship between this new definition and the previously known one, and propose an efficient 1-round protocol that is secure under the new definition and insecure under the previous one. The protocol has a better transmission rate compared to all known 1-round protocols in the previous model. We discuss our results and show how it relates to known results in this area.
In the Secure Message Transmission (SMT) problem two nodes in a network want to communicate securely (both privately and reliably), given that some of the nodes in the network are corrupted by an adaptive byzantine adversary with unlimited computational power. A SMT protocol uses multiple paths between the sender S and a receiver R to guarantee privacy and reliability of the message transmission. Privacy means that the adversary learns no information about the transmitted secret, whereas reliability means that the receiver always receives the message sent by the sender. S and R are connected by n disjoint paths where a subset of which (at most t in case of a threshold adversary) can be corrupted by an adversary. Efficiency parameters of a SMT protocol are the number of rounds (number of interactions between S and R ), communication complexity, and computational complexity. An (e, δ)-SMT protocol bounds the adversary's success probability of breaking privacy and reliability to e and δ, respectively. A SMT protocol for a given number of rounds is optimal if its transmission rate (amount of communication per one bit of message) matches the lower bound for that number of rounds. Optimal protocols have been constructed for a restricted set of parameters. It has been proved that secure SMT is possible if and only if n ≥ 2t + 1, where t is the number of paths corrupted by the adversary.
This thesis describes a number of contributions to the study of SMT problem. First, we improve the system parameter of a previously introduced wire virtualization method for constructing optimal protocols using two component protocols. Using the improved wire virtualization method we present the first optimal 1-round (0, δ)-SMT protocol for higher connectivity.
Then we introduce a modular approach for constructing SMT protocols using two or more modules. Using this approach we design an optimal 1-round (0, δ)-SMT protocol for the minimum connectivity, which has higher reliability than any comparable protocol. We also design a similar protocol for higher connectivity improving the reliability of the protocol presented in the first part of this thesis.
Constructing secure and efficient (in communication) SMT protocols against a threshold adversary has been extensively researched. However less is known about SMT problem for a generalized adversary who can corrupt one out of a set of possible subsets. In this part of the thesis, we focus on 1-round (0, δ)-SMT protocols against a generalized adversary. These protocols are especially attractive because of their possible practical applications.
Finally, we introduce a new security definition by presenting an alternative privacy definition, which is based on guessing advantage of the adversary, to construct more efficient (in communication) protocols. Our motivation is that if the received message is long enough and has sufficient entropy, then it can be used as a secret key. We give the relationship between the new security definition and the known one, and revisit bounds on connectivity and transmission rates of SMT protocols under the new definition. We also give constructions for a 1-round and a 3-round protocol, secure under the new definition, that are optimal.
The contributions made in this thesis add to the research on the secure message transmission problem and show new directions for future research.
In a secure message transmission (SMT) scenario, a sender wants to send a message in a private and reliable way to a receiver. Sender and receiver are connected by n wires, t of which can be controlled by an adaptive adversary with unlimited computational resources. In Eurocrypt 2008, Garay and Ostrovsky considered an SMT scenario where sender and receiver have access to a public discussion channel and showed that secure and reliable communication is possible when n ≥ t + 1. In this paper, we will show that a secure protocol requires at least three rounds of communication and two rounds invocation of the public channel and hence give a complete answer to the open question raised by Garay and Ostrovsky. We also describe a round optimal protocol that has constant transmission rate over the public channel.
In Secure message transmission (SMT) protocols two nodes in a network want to communicate securely, given that some of the nodes in the network are corrupted by an adversary with unlimited computational power. An SMT protocol uses multiple paths between the sender and a receiver to guarantee privacy and reliability of the message transmission. An (e, δ)-SMT protocol bounds the adversary's success probability of breaking privacy and reliability to e and δ, respectively. Rate optimal SMT protocols have the smallest transmission rate (amount of communication per one bit of message). Rate optimal protocols have been constructed for a restricted set of parameters.In this paper we use wire virtualization method to construct new optimal protocols for a wide range of parameters using previously known optimal protocols. In particular, we design, for the first time, an optimal 1-round (0, δ)-SMT protocol for n = (2 + c)t, c ≥ 1/t, where n is the number of paths between the sender and the receiver, up to t of which are controlled by the adversary. We also design an optimal 2-round (0, 0)-SMT protocol for n = (2 + c)t, c ≥ 1/t, with communication cost better than the known protocols. The wire virtualization method can be used to construct other protocols with provable properties from component protocols.
The problem of secure message transmission (SMT), due to its importance in both \npractice and theory, has been studied extensively. Given a communication network in \nwhich a sender S and a receiver R are indirectly connected by unreliable and distrusted \nchannels, the aim of SMT is to enable messages to be transmitted from S to R with a \nreasonably high level of privacy and reliability. SMT must be achieved in the presence \nof a Byzantine adversary who has unlimited computational power and can corrupt the \ntransmission. In the general adversary model, the adversary is characterized by an \nadversary structure. We study two diff�erent measures of security: perfect (PSMT) and \nalmost perfect (APSMT). Moreover, reliable (but not private) message transmission (RMT) are considered as a specifi�c part of SMT. In this thesis, we study RMT, APSMT \nand PSMT in two di�fferent network settings: point-to-point and multicast. \nTo prepare the study of SMT in these two network settings, we present some ideas \nand observations on secret sharing schemes (SSSs), generalized linear codes and critical \npaths. First, we prove that the error-correcting capability of an almost perfect SSS is \nthe same as a perfect SSS. Next, we regard general access structures as linear codes, \nand introduce some new properties that allow us to construct pseudo-basis for efficient \nPSMT protocol design. In addition, we de�fine adversary structures over "critical paths", \nand observe their properties. Having these new developments, the contributions on SMT \nin the aforementioned two network settings can be presented as follows. \nThe results on SMT in point-to-point networks are obtained in three aspects. First, \nwe show a Guessing Attack on some existing PSMT protocols. This attack is critically \nimportant to the design of PSMT protocols in asymmetric networks. Second, we determine necessary and sufficient conditions for di�fferent levels of RMT and APSMT. \nIn particular, by applying the result on almost perfect SSS, we show that relaxing the \nrequirement of privacy does not weaken the minimal network connectivity. Our �final \ncontribution in the point-to-point model is to give the �first ever efficient, constant round \nPSMT protocols in the general adversary model. These protocols are designed using \nlinear codes and critical paths, and they signifi�cantly improve some previous results in \nterms of communication complexity and round complexity. \nRegarding SMT in multicast networks, we solve a problem that has been open for \nover a decade. That is, we show the necessary and sufficient conditions for all levels of \nSMT in di�fferent adversary models. First, we give an Extended Characterization of the \nnetwork graphs based on our observation on the eavesdropping and separating activities \nof the adversary. Next, we determine the necessary and sufficient conditions for SMT \nin the general adversary model with the new Extended Characterization. Finally, we \napply the results to the threshold adversary model to completely solve the problem of \nSMT in general multicast network graphs.
The existed model on information-theoretically Secure Message Transmission(SMT) assumes tn of the channels connecting Alice and Bob can be controlled by a computationally unbounded adversary,while the rest n-t channels are completely secure and no noise.However,the existence of channels without noise is only reasonable in ideal scenarios.For this reason,a model,called adversarial channel model,is introduced to study the SMT problem.The adversary,under the new model,is not only allowed to control any tn channels,but also allowed to partially affect the rest n-t channels by introducing noises at her will.The cause that general error-correcting codes may fail to recover messages is analyzed,and then by the help of information reconciliation protocol,a new SMT protocol is presented,which is efficient in both computational and communicational complexity,and optimal in round complexity.
Abstract. In Secure Message Transmission (SMT) problem, a sender S is connected to a receiver R through N node disjoint bidirectional paths in the network, t of which are controlled by an adversary with unlimited computational power. S wants to send a message m to R in a reliable and private way. It is proved that SMT is possible if and only if N ≥ 2t+1. In Reliable Message Transmission (RMT) problem, the network setting is the same and the goal is to provide reliability for communication, only. In this paper we focus on 1-round δ-RMT and (0, δ)-SMT where the chance of protocol failure (receiver cannot decode the sent message) is at most δ, and in the case of SMT, privacy is perfect. We propose a new approach to the construction of 1-round δ-RMT and (0, δ)-SMT for all connectivities N ≥ 2t + 1, using list decodable codes and message authentication codes. Our concrete constructions use folded Reed-Solomon codes and multireceiver message authentication codes. The protocols have optimal transmission rates and provide the highest reliability among all known comparable protocols. Important advantages of these constructions are, (i) they can be adapted to all connectivities, and (ii) have simple and direct security (privacy and reliability) proofs using properties of the underlying codes, and δ can be calculated from parameters of the underlying codes. We discuss our results in relation to previous work in this area and propose directions for future research. 1