Table of Links Abstract and I. Introduction Abstract and I. Introduction II. System Model II. System Model III. Secure and Private Source Coding Regions III. Secure and Private Source Coding Regions IV. Gaussian Sources and Channels IV. Gaussian Sources and Channels V. Proof for Theorem 1 V. Proof for Theorem 1 Acknowledgment and References Acknowledgment and References V. PROOF FOR THEOREM 1 A. Achievability Proof for Theorem 1 A. Achievability Proof for Theorem 1 Proof Sketch: We leverage the output statistics of random binning (OSRB) method [16], [43], [44] for the achievability proof by following the steps described in [45, Section 1.6] Proof Sketch: Communication Rate: (58) and (60) result in a communication (storage) rate Communication Rate: Privacy Leakage Rate: Since the private key K is uniformly distributed and is independent of source and channel random variables, we can consider the following virtual scenario to calculate the leakage. We first assume for the virtual scenario that there is no private key such that the encoder output for the virtual scenario i Privacy Leakage Rate: We calculate the leakage for the virtual scenario. Then, given the mentioned properties of the private key and due to the one-time padding step in (52), we can subtract H(K) = nR0 from the leakage calculated for the virtual scenario to obtain the leakage for the original problem, which follows from the sum of (59) and (60) if ǫ → 0 when n → ∞. Thus, we have the privacy leaka B. Converse Proof for Theorem 1 B. Converse Proof for Theorem 1 Privacy Leakage Rate: We obtain Privacy Leakage Rate: n(Rℓ + δn) Secrecy Leakage Rate: We have Secrecy Leakage Rate: Cardinality Bounds: We use the support lemma [48, Lemma 15.4] for the cardinality bound proofs, which is a standard step, so we omit the proof. Cardinality Bounds: ACKNOWLEDGMENT O. Gunlu and R. F. Schaefer were supported in part by the German Federal Ministry of Education and Research (BMBF) under the Grant 16KIS1004. H. Boche was supported in part by the BMBF within the national initiative on 6G Communication Systems through the research hub 6G-life under the Grant 16KISK002 and within the national initiative on Information Theory for Post Quantum Crypto “Quantum Token Theory and Applications - QTOK” under the Grant 16KISQ037K, which has received additional funding from the German Research Foundation (DFG) within Germany’s Excellence Strategy EXC-2092 CASA-390781972. H. V. Poor was supported in part by the U.S. National Science Foundation (NSF) under the Grant CCF-1908308. REFERENCES [1] D. Slepian and J. Wolf, “Noiseless coding of correlated information sources,” IEEE Trans. Inf. Theory, vol. 19, no. 4, pp. 471–480, July 1973. [2] A. El Gamal and Y.-H. Kim, Network Information Theory. Cambridge, U.K.: Cambridge University Press, 2011. [3] A. Orlitsky and J. R. 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(1) Onur Gunlu, Chair of Communications Engineering and Security, University of Siegen and Information Coding Division, Department of Electrical Engineering, Linkoping University (onur.guenlue@uni-siegen.de);
(2) Rafael F. Schaefer, Chair of Communications Engineering and Security, University of Siegen (rafael.schaefer@uni-siegen.de);
(3) Holger Boche, Chair of Theoretical Information Technology, Technical University of Munich, CASA: Cyber Security in the Age of Large-Scale Adversaries Exzellenzcluster, Ruhr-Universitat Bochum, and BMBF Research Hub 6G-Life, Technical University of Munich (boche@tum.de);
(4) H. Vincent Poor, Department of Electrical and Computer Engineering, Princeton University (poor@princeton.edu). Authors: Authors: (1) Onur Gunlu, Chair of Communications Engineering and Security, University of Siegen and Information Coding Division, Department of Electrical Engineering, Linkoping University (onur.guenlue@uni-siegen.de); (2) Rafael F. Schaefer, Chair of Communications Engineering and Security, University of Siegen (rafael.schaefer@uni-siegen.de); (3) Holger Boche, Chair of Theoretical Information Technology, Technical University of Munich, CASA: Cyber Security in the Age of Large-Scale Adversaries Exzellenzcluster, Ruhr-Universitat Bochum, and BMBF Research Hub 6G-Life, Technical University of Munich (boche@tum.de); (4) H. Vincent Poor, Department of Electrical and Computer Engineering, Princeton University (poor@princeton.edu). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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