Secret-key generation with arbitrarily varying eavesdropper's channel

Information-theoretic secret-key generation often requires the legitimate users to know the eavesdropper's statistics, which might not always be a realistic assumption. We study secret-key generation for a channel model with unknown and arbitrarily varying channel states at the eavesdropper. We first develop an achievable secret-key rate in the case of finite alphabets. We then extend the result to multiple-input multiple-output (MIMO) channels with continuous alphabets. In this case, we show that a positive secret-key rate, optimal in terms of secure degrees of freedom, is achievable if the eavesdropper has strictly less antennas than the legitimate users.