Secure Key Agreement over Partially Corrupted Channels

Key agreement (KA) is a fundamental cryptographic primitive. Assuming that Alice and Bob do not have any prior shared correlation, it has been proved that key agreement with security against a computationally unbounded adversary is impossible if communication is either over a fully public channel, or the channel is fully controlled by the adversary. In this paper we consider a setting where communication is over a partially corrupted channel, and there is no prior shared correlation. We formalize security and reliability of key agreement protocols in this setting, derive bounds on the rate of secret key agreement, and give constructions that achieve the respective bounds. Our results show that secret key agreement, and hence secret message transmission, is possible, as long as a small fraction of the transmitted symbols in each round remain untouched by the adversary. Our results can be extended to key agreement between nodes in a network, when the two nodes are connected by a set of disjoint paths, and in each round a subset of paths is eavesdropped and another subset (possibly with overlap) is tampered with. We relate our results to previous works, and discuss future directions.