Secret Keys from Channel Noise

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We study the problem of unconditionally secure Secret Key Establishment (SKE) when Alice and Bob are connected by two noisy channels that are eavesdropped by Eve. We consider the case that Alice and Bob do not have any sources of initial randomness at their disposal. We start by discussing special cases of interest where SKE is impossible and then provide a simple SKE construction over binary symmetric channels that achieves some rates of secret key. We next focus on the Secret Key (SK) capacity and provide lower and upper bounds on this capacity. We prove the lower bound by proposing a multi-round SKE protocol, called the main protocol. The main protocol consists of an initialization round and the repetition of a two-round SKE sub-protocol, called the basic protocol. We show that the two bounds coincide when channels do not leak information to the adversary. We apply the results to the case that communicants are connected by binary symmetric channels.