Perfect Secrecy and Adversarial Indistinguishability
نویسنده
چکیده
Claude Shannon introduced an entropy model for information, and applied it to secrecy in communications. It supposes a source of information, Alice, which chooses among a set of possible messages. There is associated with this choice a likelihood that Alice would chose a particular message. Symbols are then sent across a channel to Bob. These symbols should refine Bob’s likelihood function, emphasizing the likelihood of Alice’s chosen message. Alice and Bob share a secret key, but this key is not shared with the eavesdropper Eve. Eve sees the symbols on the channel, and understands as well the likelihood by which Alice chooses messages. However, because Eve does not share the secret key, Eve should find no use for these symbols. Her likelihood function should not be refined. Alice’s likelihood is represented as a probability distribution over a message space. The messages space M is assumed finite. A probability distribution P (M) is a map from M to [0, 1], satisfying the axioms of a probability distribution; but might be better to think of P (M) as a map from events in M , that is, subsets of M , to [0, 1]. Events are things we can learn about the message, such as “the event that the message contains a vowel”. Generally, for every message m, the event “the message
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