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International Journal of Applied Cryptography

Unconditionally reliable and secure message transmission in undirected synchronous networks: possibility, feasibility and optimality

Arpita Patra, Ashish Choudhury, Chandrasekharan Pandu Rangan, Kannan Srinathan

Published Jan 1, 2010• 38 citations
Publisher

Abstract

We study the interplay of network connectivity and the issues related to the 'possibility', 'feasibility' and 'optimality' for unconditionally reliable message transmission (URMT) and unconditionally secure message transmission (USMT) in an undirected synchronous network, under the influence of an adaptive mixed adversary having unbounded computing power, who can corrupt some of the nodes in the network in Byzantine, omission, fail-stop and passive fashion respectively. We consider two types of adversary, namely threshold and non-threshold. One of the important conclusions we arrive at from our study is that allowing a negligible error probability significantly helps in the 'possibility', 'feasibility' and 'optimality' of both reliable and secure message transmission protocols. To design our protocols, we propose several new techniques which are of independent interest.

DOI
10.1504/ijact.2010.038309

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We study the interplay of network connectivity and the issues related to the 'possibility', 'feasibility' and 'optimality' for unconditionally reliable message transmission (URMT) and unconditionally secure message transmission (USMT) in an undirected synchronous network, under the influence of an adaptive mixed adversary having unbounded computing power, who can corrupt some of the nodes in the network in Byzantine, omission, fail-stop and passive fashion respectively. We consider two types of adversary, namely threshold and non-threshold. One of the important conclusions we arrive at from our study is that allowing a negligible error probability significantly helps in the 'possibility', 'feasibility' and 'optimality' of both reliable and secure message transmission protocols. To design our protocols, we propose several new techniques which are of independent interest.
We study the interplay of network connectivity and the issues related to the possibility, feasibility and optimality for unconditionally reliable message transmission (URMT) and unconditionally secure message transmission (USMT) in an undirected synchronous network, under the influence of an adaptive mixed adversary A (tb,to,tf,tp), who has unbounded computing power and can corrupt up to tb, to, tf and tp nodes in the network in Byzantine, omission, fail-stop and passive fashion respectively. In URMT problem, a sender S and a receiver R are part of a distributed network, where S and R are connected by intermediate nodes, of which at most tb, to, tf and tp nodes can be under the control of A (tb,to,tf,tp). S wants to send a message m which is a sequence of ℓ (ℓ ≥ 1) field elements from a finite field F to R. The challenge is to design a protocol, such that after interacting in phases1 as per the protocol, R should be able to obtain m with probability at least 1 − δ, where 0 < δ < 1 2, irrespective of any adversarial strategy of A (tb,to,tf,tp). The USMT problem has an additional requirement that A (tb,to,tf,tp) should not know anything about m in information theoretic sense. In this paper, we answer the following in context of URMT and USMT: (a) Possibility: when
The problem of unconditionally reliable message transmission (URMT) is to design a protocol which when run by players in a network enables a sender s to deliver a message to a receiver r with high probability, even when some players in the network are under the control of an unbounded adversary. Renault and Tomala [JoC2008] gave a characterization of undirected neighbour networks over which URMT tolerating Byzantine adversary is possible. In this paper, we generalize their result to the case of directed networks. 1
We study the problem of information-theoretically secure message transmission (SMT) in asynchronous directed networks. In line with the literature, the distrust and failures of the network is captured via a computationally unbounded Byzantine adversary that may corrupt some subset of nodes. We give a characterization of networks over which SMT from sender S to receiver R is possible in both the well-known settings, namely perfect SMT (PSMT) and unconditional SMT (USMT). We distinguish between two variants of USMT: one in which R can output an incorrect message (with small probability) and another in which R never outputs a wrong message, but may choose to abort (with small probability). We also provide efficient protocols for an important class of networks.
We study the problem of perfectly reliable message transmission (PRMT) and perfectly secure message transmission (PSMT) in an undirected synchronous network tolerating an all powerful threshold mobile Byzantine adversary. Specifically, we show that the mobility of the threshold adversary does not affect the possibility and optimality of PRMT and PSMT protocols. We also characterise PSMT in directed networks tolerating mobile adversary. All existing PRMT and PSMT protocols abstract the paths between the sender and the receiver as wires, neglecting the intermediate nodes in the paths, thus causing significant over estimation in the communication and round complexity of protocols. Here, we consider the underlying paths as a whole instead of abstracting them as wires and derive a tight bound on the number of rounds required to achieve reliable communication tolerating a threshold mobile adversary with arbitrary roaming speed. Finally, we briefly study PRMT and PSMT protocols in the presence of non-threshold mobile Byzantine adversary. Even though the characterisation for PRMT/PSMT is shown to be same against both threshold static and threshold mobile adversary (in this article), we show that the characterisation for PRMT/PSMT against non-threshold static and non-threshold mobile adversary are not same.
We study the problem of Perfectly Reliable Message Transmission (PRMT) and Perfectly Secure Message Transmission (PSMT) between two nodes S and R in an undirected synchronous network, a part of which is under the influence of an all powerful mobile Byzantine adversary. In ACISP’2007 Srinathan et. al. has proved that the connectivity requirement for PSMT protocols is same for both static and mobile adversary thus showing that mobility of the adversary has no effect on the possibility of PSMT (also PRMT) protocols. Similarly in CRYPTO 2004, Srinathan et. al. has shown that the lower bound on the communication complexity of any multiphase PSMT protocol is same for static and mobile adversary. The authors have also designed a O(t) phase1 protocol satisfying this bound where t is the maximum number of nodes corrupted by the Byzantine adversary. In this work, we design a three phase bit optimal PSMT protocol using a novel technique, whose communication complexity matches the lower bound proved in CRYPTO 2004 and thus significantly reducing the number of phases from O(t) to three. Further using our novel technique, we design a three phase bit optimal PRMT protocol which achieves
Abstract. In this paper we give the minimal connectivity required in a synchronous directed network, which is under the influence of a computationally unbounded Byzantine adversary that can corrupt a subset of nodes, so that Secure Message Transmission is possible between sender S and receiver R. We also show that secure communication between a pair of nodes in a given synchronous directed network is possible in both directions if and only if reliable communication is possible between them. We assume that in a network, every node is capable of computation and we model the network along the lines of [14].