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International Conference on Distributed Computing and Networking (ICDCN)

Perfectly secure message transmission over partially synchronous networks

Ravi Kishore, Anupriya Inumella, Kannan Srinathan

Published Jan 4, 2019• 1 citation
Publisher

Abstract

In a distributed network, we consider two special nodes called the sender S and the receiver R that are connected by n node-disjoint (except for S and R) bi-directional wires. Out of these n wires, the adversary can control at most t wires (of its choice) in Byzantine fashion. In this setting, our goal is to design a message transmission protocol Π that assures the following two conditions hold: (1) by the end of the protocol Π, R gets the correct message m transmitted by S without any error (perfect reliability), and (2) the adversary learns no information about m, whatsoever, in information theoretic sense (perfect secrecy). Protocols that satisfy these two conditions are known as the Perfectly Secure Message Transmission (PSMT) protocols.

DOI
10.1145/3288599.3288612

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In a distributed network, we consider two special nodes called the sender S and the receiver R that are connected by n node-disjoint (except for S and R) bi-directional wires. Out of these n wires, the adversary can control at most t wires (of its choice) in Byzantine fashion. In this setting, our goal is to design a message transmission protocol Π that assures the following two conditions hold: (1) by the end of the protocol Π, R gets the correct message m transmitted by S without any error (perfect reliability), and (2) the adversary learns no information about m, whatsoever, in information theoretic sense (perfect secrecy). Protocols that satisfy these two conditions are known as the Perfectly Secure Message Transmission (PSMT) protocols.
Consider the following problem: a sender S and a receiver R are part of a directed synchronous network and connected through intermediate nodes. Specifically, there exists n node disjoint paths, also called as wires, which are directed from S to R and u wires, which are directed from R to S. Moreover, the wires from S to R are disjoint from the wires directed from R to S. There exists a centralized, static adversary A static , who has unbounded computing power and who can control at most t wires between S and R in Byzantine fashion. S has a message m S , which we wants to send to R. The challenge is to design a protocol, such that after interacting in phases 5 as per the protocol, R should correctly output m R = m S , except with error probability 2 −(κ) , where κ is the error parameter. This problem is called as statistically reliable message transmission (SRMT). The problem of statistically secure message transmission (SSMT) has an additional requirement that at the end of the protocol, m S should be information theoretically secure from A static . Desmedt et.al [14, 55] have given the necessary and sufficientcondition for the existence of SRMT and SSMT protocols in the above settings. They also presented an SSMT protocol, satisfying their characterization. The authors in [14, 55] claimed that their protocol is efficientand has polynomial computational and communication complexity. However, we show that it is not so. That is, we specify an adversary strategy, which may cause the protocol to have exponential computational and communication complexity 6 . We then present
In the perfectly secure message transmission (PSMT) problem, two synchronized non-faulty players (or processors), the Sender S and the Receiver R are connected by n wires (each of which facilitates 2-way communication); S has a message, represented by a sequence oft elements from a finite field, that he wishes to send to R; after exchanging messages in phases R should correctly obtain S 's message, while an adversary listening on and actively controlling any set of t (or less) wires should have no information about S 's message. Similarly, in the problem of perfect reliable message transmission (PRMT), the receiver R should correctly obtain S's message, in spite of the adversary actively controlling any set oft (or less) wires.
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 consider the problem of perfect (information-theoretically) secure message transmission (PSMT) from a sender SSS to a receiver RRR in asynchronous directed networks tolerating dual adversary. The adversary can control at most tpt_ptp​ nodes in a passive fashion and at most tft_ftf​ nodes in a fail-stop fashion. We achieve PSMT in this setting with a new class of message transmission protocols called the quiescent protocols. Quiescent protocols ensure that the players eventually stop sending messages but in contrast to the usual terminating protocols, these protocols do not require the players to go into the halt state, from which they cannot take any further action. To show the significance of quiescent protocols, we first identify conditions in which it is impossible for any terminating protocol to achieve PSMT. To circumvent this impossibility, we transform the existing synchronous PSMT protocol into a quiescent protocol which accomplishes PSMT. By focusing on designing quiescent protocols rather than terminating protocols, we show that asynchrony in the network does not demand any extra connectivity over its state-of-the-art synchronous counterpart. This shows that quiescent protocols are befitted to solve PSMT in asynchronous networks with fail-stop faults.
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