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We present a new information-theoretic definition and associated results,based on list decoding in a source coding setting. We begin by presentinglist-source codes, which naturally map a key length (entropy) to list size. Wethen show that such codes can be analyzed in the context of a novelinformation-theoretic metric, \epsilon-symbol secrecy, that encompasses boththe one-time pad and traditional rate-based asymptotic metrics, but, like mostcryptographic constructs, can be applied in non-asymptotic settings. We derivefundamental bounds for \epsilon-symbol secrecy and demonstrate how these boundscan be achieved with MDS codes when the source is uniformly distributed. Wediscuss applications and implementation issues of our codes.

Lists that are smaller than their parts: A coding approach to tunable secrecy