Adversarial wiretap channel with public discussion

Abstract

Wyner's elegant model of wiretap channel exploits noise in the communication channel to provide perfect secrecy against a computationally unlimited eavesdropper without requiring a shared key. We consider an adversarial model of wiretap channel proposed in [18,19] where the adversary is active: it selects a fraction ρr of the transmitted codeword to eavesdrop and a fraction ρw of the codeword to corrupt by "adding" adversarial error. It was shown that this model also captures network adversaries in the setting of 1-round Secure Message Transmission [8]. It was proved that secure communication (1-round) is possible if and only if ρr + ρw < 1. In this paper we show that by allowing communicants to have access to a public discussion channel (authentic communication without secrecy) secure communication becomes possible even if ρr + ρw > 1. We formalize the model of AWTP PD protocol and for two efficiency measures, information rate and message round complexity derive tight bounds. We also construct a rate optimal protocol family with minimum number of message rounds. We show application of these results to Secure Message Transmission with Public Discussion (SMT-PD), and in particular show a new lower bound on transmission rate of these protocols together with a new construction of an optimal SMT-PD protocol.Alice and Bob are connected by N node disjoint paths, a subset of which is controlled by a computationally unlimited adversary and the goal is to provide secrecy and reliability for the communication. The adversary in AWTP channel is more general (powerful) than the widely studied threshold SMT adversary and can choose different subsets for eavesdropping and corruption.Motivation It was proved [18] that perfect secrecy and reliability for AWTP in 1round communication is possible if and only if, ρ r + ρ w < 1. We consider a scenario where in addition to the AWTP channel, a public discussion channel denoted by PD, is available to the communicants. We call this model AWTP with public discussion (or AWTP PD for short). Our goal is to see if the use of this extra resource can make secure communication possible when ρ r + ρ w > 1 (for example ρ r = ρ w = 0.9). Public discussion channels had been considered in wiretap and SMT models, both. In wiretap setting it was shown [11,2] that a public discussion channel substantially expands the range of scenarios in which secure communication is possible. In particular secure communication becomes possible even if the eavesdroper channel is less noisy than the main channel. A similar result holds for SMT. Access to a public discussion channel in SMT was considered by Garay et.al. [9] who showed that secure message tranmission will be possible when N ≥ t + 1 while without a PD , N ≥ 2t + 1. We allow communicants to interact over the PD but assume communication over the AWTP channel is one-way and from Alice to Bob. This restriction is to simplify our analysis and as we will show, will still allow us to construct protocols that are optimal.The assumption is also natural in setting...

Perfectly Secure Message Transmission Against Rational Adversaries

“…It was proved in [42,Proposition 1] that AWTP codes correspond to 1-round symmetric SMT protocols. In [43], the authors studied the public discussion model of AWTP codes and showed a similar relationship.…”

“…The coding problem over adversarial wiretap (AWTP) channels [42], [43] is closely related to SMT protocols. It was proved in [42,Proposition 1] that AWTP codes correspond to 1-round symmetric SMT protocols.…”

Secure Key Agreement over Partially Corrupted Channels

“…The question that one can ask is, if the distribution P X n Y n Z n is Xsimulatable (Y -simulatable), Adversary model. The adversarial model for physical layer adversaries was first proposed in [40]. The goal of the protocol however was to provide reliable communication.…”

“…Adversary model. The adversarial model for physical layer adversaries was first proposed in [40]. The goal of the protocol however was to provide reliable communication.…”