| The Prisoners' Problem can be stated as follows: Two prisoners, Alice and Bob, want to communicate a secret escape plan under the surveillance of a warden, Wendy. To be indiscernable, the communication must appear to Wendy to be "innocent". If a traditional cryptographic mechanism (such as encryption) is used to protect their secret plan, Alice and Bob will be caught by Wendy because of the visible randomness of the ciphertexts. Therefore a new approach must be used in which information is hidden, not just encrypted. Information hiding, and more specifically steganography deals with such problems.; This dissertation investigates the Prisoners' Problem in a game theoretic setting in which Alice plays against Wendy. The objective of Alice is to encode her secret messages so that they are indistinguishable from innocent messages. The goal of Wendy is to distinguish Alice's messages with concealed information from innocent messages.; We study this game theoretic problem in three security models: perfect, statistical and computational security. These models correspond to three adversarial models of Wendy, namely: unbounded; polynomial number of queries; polynomial time. We show that under very general conditions, efficient and secure steganography can be achieved. In each of the three models, we give necessary and sufficient conditions for the existence of secure steganography. Our proofs yield efficient and proven secure steganographic systems. In almost all of the cases, these constructions are also optimal. We then extend these models to introduce the novel concepts of invisible steganography and steganographic secret sharing. |
