Adversarial Wiretap Channel with Public Discussion
This work addresses secure communication in adversarial settings, such as network security, by extending classical models with public discussion, offering incremental improvements to existing protocols.
The paper tackles the problem of secure communication over an adversarial wiretap channel where an active adversary can both eavesdrop and corrupt parts of the transmission, showing that by adding a public discussion channel, secure communication becomes possible even when the sum of eavesdropping and corruption fractions exceeds 1, with tight bounds derived for information rate and message round complexity.
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 $ρ_r$ of the transmitted codeword to eavesdrop and a fraction $ρ_w$ 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 $ρ_r + ρ_w <1$. 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 $ρ_r + ρ_w >1$. We formalize the model of \awtppd protocol and for two efficiency measures, {\em information rate } and {\em 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.