Lists that are smaller than their parts: 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, \epsilon-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for \epsilon-symbol 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. 
Flavio du Pin Calmon, Muriel M\'edard, Linda M. Zeger, Jo\~ao Barros,   Mark M. Christiansen, Ken. R. Duffy
cs.IT cs.CR math.IT