Quantum entropic security and approximate quantum encryption

Authors:
Simon Pierre Desrosiers;Frédéric Dupuis
Affiliations:
McGill University, Montréal, QC, Canada;Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland and Université de Montréal, Montréal, QC, Canada and McGill University, Montreal, Quebec, Canada
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

An encryption scheme is said to be entropically secure if an adversary whose min-entropy on the message is upper bounded cannot guess any function of the message. Similarly, an encryption scheme is entropically indistinguishable if the encrypted version of a message whose min-entropy is high enough is statistically indistinguishable from a fixed distribution. We present full generalizations of these two concepts to the encryption of quantum states in which the quantum conditional min-entropy, as introduced by Renner, is used to bound the adversary's prior information on the message. A proof of the equivalence between quantum entropic security and quantum entropic indistinguishability is presented. We also provide proofs of security for two different ciphers in this model and a proof for a lower bound on the key length required by any such cipher. These ciphers generalize existing schemes for approximate quantum encryption to the entropic security model.