A coding approach to tunable secrecy

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, ǫsymbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in nonasymptotic settings. We derive fundamental bounds for ǫsymbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.