The secrecy of a communication system in which both the legitimate receiver and an eavesdropper are allowed some distortion is investigated. The secrecy metric considered is the exponent of the probability that the eavesdropper estimates the source sequence successfully within an acceptable distortion level. The problem is first studied when the transmitter and the legitimate receiver do not share any key and the transmitter is not subject to a rate constraint, which corresponds to a stylized model of a side channel and reveals connections to source coding with side information. The setting is then generalized to include a shared secret key between the transmitter and the legitimate receiver and a rate constraint on the transmitter, which corresponds to the Shannon cipher system. A single-letter characterization of the highest achievable exponent is provided, and asymptotically optimal strategies for both the primary user and the eavesdropper are demonstrated.
The secrecy of a communication system in which both the legitimate receiver and an eavesdropper are allowed some distortion is investigated. The secrecy metric considered is the exponent of the probability that the eavesdropper estimates the source sequence successfully within an acceptable distortion level. The problem is first studied when the transmitter and the legitimate receiver do not share any key and the transmitter is not subject to a rate constraint, which corresponds to a stylized model of a side channel and reveals connections to source coding with side information. The setting is then generalized to include a shared secret key between the transmitter and the legitimate receiver and a rate constraint on the transmitter, which corresponds to the Shannon cipher system. A single-letter characterization of the highest achievable exponent is provided, and asymptotically optimal strategies for both the primary user and the eavesdropper are demonstrated.
A secrecy system in which both the legitimate receiver and an eavesdropper are allowed some distortion is studied. The eavesdropper is allowed to make one guess, and the considered secrecy metric is the exponent of the probability that the guess is within an acceptable distortion level. A subsequent notion of information leakage is suggested. In the absence of any shared key between the transmitter and the legitimate receiver, a single-letter characterization of the highest achievable exponent is provided. Moreover, asymptotically-optimal universal strategies for both the primary user and the eavesdropper are demonstrated, where universality means independence of the source statistics. When a secret key is shared between the transmitter and the legitimate receiver, and a rate constraint is imposed, upper and lower bounds on the optimal exponent are given. Certain sufficient conditions for the bounds to meet are provided, and examples where they apply are discussed.
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. In particular, 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.
In this work, secrecy in communication systems is measured by the distortion incurred by the worst-case adversary. The transmitter and receiver share secret key, which they use to encrypt communication and cause distortion at an adversary. In our model, we assume that an adversary not only intercepts the communication between the transmitter and receiver, but also may have access to noisy observations of the system. For example, the adversary may have causal access to a signal that is correlated with the source sequence or with the output of the receiver. Our main contribution is the solution of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. We demonstrate that side information at the adversary plays a pivotal role, and provide a number of examples that motivate and give insight into our results.
Imperfect secrecy in communication systems is investigated. Instead of using equivocation as a measure of secrecy, the distortion that an eavesdropper incurs in producing an estimate of the source sequence is examined. The communication system consists of a source and a broadcast (wiretap) channel, and lossless reproduction of the source sequence at the legitimate receiver is required. A key aspect of this model is that the eavesdropper's actions are allowed to depend on the past behavior of the system. Achievability results are obtained by studying the performance of source and channel coding operations separately, and then linking them together digitally. Although the problem addressed here has been solved when the secrecy resource is shared secret key, it is found that substituting secret key for a wiretap channel brings new insights and challenges: the notion of weak secrecy provides just as much distortion at the eavesdropper as strong secrecy, and revealing public messages freely is detrimental.
Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of 2mRLreconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity lossy equivocation, which is proved to be the minimum optimistic one-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for infinitely many blocklengths) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proved to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product, optimistic lossy source coding has also been addressed.
Recently, a secrecy measure based on list-reconstruction has been proposed [2], in which a wiretapper is allowed to produce a list of 2mRL reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity \emph{lossy-equivocation}, which is proven to be the minimum optimistic 1-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for \emph{infinitely many blocklengths}) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with \emph{noisy} wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proven to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product optimistic lossy source coding has also been addressed.