Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing

We establish an upper bound on the rate of codes for a wiretap channel with public feedback for a fixed probability of error and secrecy parameter. As a corollary, we obtain a strong converse for the capacity of a degraded wiretap channel with public feedback. Our converse proof is based on a reduction of active hypothesis testing for discriminating between two channels to coding for wiretap channel with feedback.Comment: This paper was presented at Allerton 201

Rate-Distortion Theory for Secrecy Systems

Secrecy in communication systems is measured herein by the distortion that an adversary incurs. The transmitter and receiver share secret key, which they use to encrypt communication and ensure distortion at an adversary. A model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver, but also potentially has side information. Specifically, the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver's reconstruction sequence. The main contribution is the characterization of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. It is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff. It is also shown that measures of secrecy based on normalized equivocation are a special case of the framework.Comment: Update version, to appear in IEEE Transactions on Information Theor

Converse bounds for private communication over quantum channels

This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a "privacy test" to establish a general meta-converse bound for private communication, which has a number of applications. The meta-converse allows for proving that any quantum channel's relative entropy of entanglement is a strong converse rate for private communication. For covariant channels, the meta-converse also leads to second-order expansions of relative entropy of entanglement bounds for private communication rates. For such channels, the bounds also apply to the private communication setting in which the sender and receiver are assisted by unlimited public classical communication, and as such, they are relevant for establishing various converse bounds for quantum key distribution protocols conducted over these channels. We find precise characterizations for several channels of interest and apply the methods to establish several converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in IEEE Transactions on Information Theor

Universal Hashing for Information Theoretic Security

The information theoretic approach to security entails harnessing the correlated randomness available in nature to establish security. It uses tools from information theory and coding and yields provable security, even against an adversary with unbounded computational power. However, the feasibility of this approach in practice depends on the development of efficiently implementable schemes. In this article, we review a special class of practical schemes for information theoretic security that are based on 2-universal hash families. Specific cases of secret key agreement and wiretap coding are considered, and general themes are identified. The scheme presented for wiretap coding is modular and can be implemented easily by including an extra pre-processing layer over the existing transmission codes.Comment: Corrected an error in the proof of Lemma