Private Key and Decoder Side Information for Secure and Private Source Coding

Abstract

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.

The Secure CEO Problem With Physical Identifiers Under Logarithmic Loss and Quadratic Distortion Measures

“…Therefore, considering the setting where both helper data are available on Eve's side is of sufficient interest, and the current work deals with such a scenario. Slepian-Wolf type of multiterminal source coding models with a shared secret key is investigated in [29], [30]. In these models, the task of the CEO is to estimate a lossy version of the measurement observed at the encoder within a certain distortion value, which is different from our settings.…”

“…For instance, suppose that face is availed as the information source in a private remote authentication. The models in [29], [30] correspond to the case where the CEO tries to reproduce the scanned face (the noisy image of the original face), while in our model, the CEO is interested in reconstructing the original face, e.g., as a means to confirm whether the identified person is a legitimate user or not. In this sense, our settings may be more realistic.…”

“…Furthermore, to derive the outer region for Gaussian sources, the outer regions under log-loss and quadratic distortions are demonstrated by different approaches. More specifically, for log-loss distortion, we adopt a similar method used in [30], [39]- [41] for analyzing key agreement problems using physical identifiers, which is based on fixing conditional entropies to find the optimal outer region. This method is deployed because the proof can be shown via the single-letter expression (cf.…”

“…4 as the outer bound for Gaussian sources is also characterized by the same expression. For k ∈ {1, 2} and a parameter β k > 0, similar to the technique in [30], [39]- [41], let us fix…”

Information Theoretic Methods for Future Communication Systems

“…Focusing on coding theory over rings, a new weight that extends the traditional Hamming weight used for algebraic structures is proposed and its properties are analyzed in [ 8 ]. Moreover, security aspects for future communication and computation systems are considered to analyze Gaussian wiretap channels with a jammer that overhears the transmissions [ 9 ], to propose new polynomial codes that enable straggler-tolerant secure matrix multiplication [ 10 ], and to illustrate the private-key rate regimes observed when reconstructing source sequences at another node with side information under privacy and security constraints [ 11 ]. It is expected that these contributions will have a significant impact on the applications of information and coding theory to future communication and computation systems.…”