Information-theoretic security under computational, bandwidth, and randomization constraints
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The objective of the proposed research is to develop and analyze coding schemes for information-theoretic security, which could bridge a gap between theory an practice. We focus on two fundamental models for information-theoretic security: secret-key generation for a source model and secure communication over the wire-tap channel. Many results for these models only provide existence of codes, and few attempts have been made to design practical schemes. The schemes we would like to propose should account for practical constraints. Specifically, we formulate the following constraints to avoid oversimplifying the problems. We should assume: (1) computationally bounded legitimate users and not solely rely on proofs showing existence of code with exponential complexity in the block-length; (2) a rate-limited public communication channel for the secret-key generation model, to account for bandwidth constraints; (3) a non-uniform and rate-limited source of randomness at the encoder for the wire-tap channel model, since a perfectly uniform and rate-unlimited source of randomness might be an expensive resource. Our work focuses on developing schemes for secret-key generation and the wire-tap channel that satisfy subsets of the aforementioned constraints.