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IEEE Transactions on Information Theory

Secure Source Coding With Action-Dependent Side Information

Kittipong Kittichokechai, Tobias J. Oechtering, Mikael Skoglund, Yeow-Khiang Chia

Published Oct 6, 2015• 26 citations
Publisher

Abstract

We consider the problems of secure lossy source coding with side information in the presence of a passive eavesdropper who has access to the source description. The encoder wishes to compress the source sequence in order to satisfy a distortion criterion at the decoder, while revealing only limited knowledge about the source to the eavesdropper. The side information available to the encoder, the legitimate decoder, or the eavesdropper can be influenced by a cost-constrained action sequence. Three different settings are studied. In the first two settings, we are interested in understanding the influence of the action sequence on the rate-distortion-leakage tradeoff where the action is taken either by the decoder or by the encoder to influence side information at the decoder and eavesdropper. Next, we consider a setting where common action-dependent side information is available securely to both encoder and decoder, and thus can be used for secret key generation. We characterize the optimal rate-distortion-cost-leakage region or the corresponding inner bounds for a discrete memoryless source for above settings. The results are useful in characterizing fundamental limits for example in secure sensor networking and future cyber physical systems.

DOI
10.1109/tit.2015.2487448

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We consider the problems of secure lossy source coding with side information in the presence of a passive eavesdropper who has access to the source description. The encoder wishes to compress the source sequence in order to satisfy a distortion criterion at the decoder, while revealing only limited knowledge about the source to the eavesdropper. The side information available to the encoder, the legitimate decoder, or the eavesdropper can be influenced by a cost-constrained action sequence. Three different settings are studied. In the first two settings, we are interested in understanding the influence of the action sequence on the rate-distortion-leakage tradeoff where the action is taken either by the decoder or by the encoder to influence side information at the decoder and eavesdropper. Next, we consider a setting where common action-dependent side information is available securely to both encoder and decoder, and thus can be used for secret key generation. We characterize the optimal rate-distortion-cost-leakage region or the corresponding inner bounds for a discrete memoryless source for above settings. The results are useful in characterizing fundamental limits for example in secure sensor networking and future cyber physical systems.
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob, and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the conventional problems of secure source coding with side information at the decoders, and the wiretap channel. Inner and outer bounds on the rate-distortion-equivocation region for the case of arbitrary channels and side informations are derived. In some special cases of interest, it is shown that separation holds. By means of an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
In the secure cooperative source-coding problem that we consider, Encoder 1 and Decoder 1 observe, respectively, a pair of independent identically distributed (i.i.d.) correlated sources and wish to communicate the first source to Decoder 2 subject to a distortion constraint. Encoder 1 sends a message to both the decoders over a public nonsecure channel, and then Decoder 1-the helper-sends a message just to Decoder 2 over a secure channel. An eavesdropper, which has access to memoryless side-information that is correlated with the first source, intercepts the message sent by Encoder 1 and based on both wishes to minimize its uncertainty about the first source. The secrecy measure of the system is the equivocation of the first source at the eavesdropper. We determine the rates equivocation region for this problem assuming that conditioned on the side-information of Decoder 1 the eavesdropper's side-information is independent of the first source. To that end, we derive an inner and an outer bound that depend explicitly on the proportional rate that Encoder 1 spends in the cooperation process. Subsequently, we evaluate this region for the case of a doubly symmetric binary source and Hamming distortion.
The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.
The distributed source coding problem is extended by positing that noisy measurements of a remote source are the correlated random variables that should be reconstructed at another terminal. We consider a secure and private distributed lossy source coding problem with two encoders and one decoder such that (i) all terminals noncausally observe a noisy measurement of the remote source; (ii) a private key is available to each legitimate encoder and all private keys are available to the decoder; (iii) rate-limited noiseless communication links are available between each encoder and the decoder; (iv) the amount of information leakage to an eavesdropper about the correlated random variables is defined assecrecyleakage, andprivacyleakage is measured with respect to the remote source; and (v) two passive attack scenarios are considered, where a strong eavesdropper can access both communication links and a weak eavesdropper can choose only one of the links to access. Inner and outer bounds on the rate regions defined under secrecy, privacy, communication, and distortion constraints are derived for both passive attack scenarios. When one or both sources should be reconstructed reliably, the rate region bounds are simplified.
The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established.
We extend the problem of secure source coding by considering a remote source whose noisy measurements are correlated random variables used for secure source reconstruction. The main additions to the problem are as follows: (1) all terminals noncausally observe a noisy measurement of the remote source; (2) a private key is available to all legitimate terminals; (3) the public communication link between the encoder and decoder is rate-limited; and (4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region for the lossless case as well. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established. An achievable lossy rate region that can be numerically computed is also provided for binary-input multiple additive discrete-time Gaussian noise measurement channels.