Umbala we-Left Abstract futhi I. Introduction II. Isakhiwo Model I-Secure and Private Source Coding Regions IV. Izinto Gaussian kanye nezindiza V. Ukubonisa I-Theorem 1 Ukubuyekezwa futhi References V. Ukubonisa I-Theorem 1 A. Ukubuyekezwa kwe-Theorem 1 Thina usebenzise izibalo lokukhipha ye-random binning (OSRB) indlela [16], [43], [44] ngenxa yokuqinisekisa ukufinyelela ngokulandelana nezinyathelo ezijwayelekile [45, Isigaba 1.6] Ukubuyekeza Sketch: (58) no (60) imiphumela ku-communication (storage) rate Communication Rate: Uma i-private key K iyahlaziywa ngokuqondile futhi iyahambisana ne-source ne-channel random variables, singathanda isinyathelo se-virtual elandelayo ukucubungula ukucubungula. Okokuqala, singathanda isinyathelo se-virtual ukuthi akukho isinyathelo se-private efana nokukhiqizwa kwe-encoder ye-virtual scenario i Privacy Leakage Rate: Ngemuva kwalokho, ngokuvamile izakhiwo ze-private key, futhi ngenxa ye-step-padding ye-one-time in (52), singakwazi ukuthatha H(K) = nR0 kusuka ku-leakage eyenziwe ku-scenario ye-virtual ukuze uthole leakage ye-problem yokuqala, okuyinto esilandelayo kusuka ku-sum of (59) and (60) if ŏ → 0 when n → ∞. Ngakho, sincoma i-privacy leaka I-Converse Proof ye-Theorem 1 Thola Privacy Leakage Rate: n(Rl + δn) Thina Secrecy Leakage Rate: Thina usebenzisa support lemma [48, Lemma 15.4] for the cardinality binding proofs, okuyinto isinyathelo esiyingqayizivele, ngakho thina siphinde i-proof. Cardinality Bounds: Ukuvumelana U-O. Gunlu no-R. F. Schaefer wahlanganiswa ngokuhambisana ne-BMBF ngaphansi kwe-Grant 16KIS1004. U-H. Boche wahlanganiswa ngokuhambisana ne-BMBF ngaphakathi kwe-National Initiative on 6G Communication Systems ngokusebenzisa i-hub research 6G-life ngaphansi kwe-Grant 16KISK002 ne-National Initiative on Information Theory for Post Quantum Crypto “Quantum Token Theory and Applications – QTOK” ngaphansi kwe-Grant 16KISQ037K, eyenziwe ngama-Grant 16KISQ037K, eyenziwe ngama-Fundament of German Research (DFG) ngaphansi kwe-Excellence Strategy yaseJalimane EXC-2092 CASA-390781972. U-H. V. Poor Imibuzo [1] D. Slepian no. J. Wolf, “I-coding ye-noise of correlated information sources,” IEEE Trans. Inf. Theory, Vol. 19, No. 4, pp. 471-480, July 1973. [2] A. El Gamal futhi Y.-H. Kim, Network Information Theory. Cambridge, UK: Cambridge University Press, 2011. [3] A. Orlitsky no. J. R. Roche, “Coding for computing,” IEEE Trans. Inf. Theory, Vol. 47, No. 3, pp. 903-917, March 2001. [4] O. Gunlu, “Function calculation under privacy, secrecy, distortion, and communication constraints,” Entropy, Vol. 24, No. 1, Juni 2022. [5] V. Prabhakaran noK. Ramchandran, “On Secure Distributed Source Coding,” in Proc. IEEE Inf. Theory Workshop, Tahoe City, CA, Septhemba 2007, iphe. 442-447. [6] D. Gunduz, E. Erkip, no-H. V. Poor, “Ukuhlukaniswa okuhlobene nokumiswa kwe-side”, ku-Proc. IEEE Inf. Theory Workshop, Porto, Portugal, ngo-May 2008, pp. 169-173 [7] R. Tandon, S. Ulukus, no. K. Ramchandran, “I-Secure source encoding nge-helper,” IEEE Trans. Inf. Theory, Vol. 59, No. 4, iphe. 2178-2187, Apr. 2013. [8] D. Gunduz, E. Erkip, futhi H. V. Poor, “Ukuhlukaniswa okuhloswe nge izinzuzo zokhuseleko,” ku Proc. IEEE Int. Symp. Inf. Theory, Toronto, ON, Canada, July 2008, pp. 111-115. [9] W. Luh noD. Kundur, “Distributed secret sharing for discrete memoryless networks,” IEEE Trans. Inf. Forensics Security, Vol. 3, No. 3, pp. 1-7, Sep 2008. [10] K. Kittichokechai, Y.-K. Chia, T. J. Oechtering, M. Skoglund, no. T. Weissman, “I-Safe Source Coding with a Public Helper”, IEEE Trans. Inf. Theory, Vol. 62, No. 7, pp. 3930-3949, July 2016. [11] S. Salimi, M. Salmasizadeh, no. M. R. Aref, “Generalized Secure Distributed Source Coding with Side Information”, IET Commun., Vol. 4, No. 18, pp. 2262-2272, Disemba 2010. [12] F. Naghibi, S. Salimi, no. M. Skoglund, “The CEO problem with secrecy constraints,” IEEE Trans. Inf. Forensics Security, Vol. 10, No. 6, pp. 1234-1249, Juni 2015. [13] H. Yamamoto, "I-Coding theorems for Shannon's encryption system with correlated source outputs, and common information", IEEE Trans. Inf. Theory, Vol. 40, No. 1, iphe. 85-95, ngoJanuwari 1994. [14] H. Ghourchian, P. A. Stavrou, T. J. Oechtering, no. M. Skoglund, “I-Secure source coding nge-side-information at decoder no-shared key at encoder and decoder,” in Proc. IEEE Inf. Theory Workshop, Kanazawa, Japan, Okthoba 2021, pp. 1-6. [15] U. M. Maurer, “I-Secret Key Agreement by Public Discussion from Common Information,” IEEE Trans. Inf. Theory, Vol. 39, No. 3, pp. 2733–2742, ngo-May 1993. [16] R. Ahlswede no-I. Csisz'ar, "Ukuhlukaniswa okuhlobene emithi yobuchwepheshe kanye ne-cryptography - I-Part I: Ukuhlobisa okuhlobene," IEEE Trans. Inf. Theory, Vol. 39, No. 4, pp. 1121-1132, ngoJul. 1993. [ 17] A. C. Yao, “I-Protocols for Secure Computations”, ku-Proc. IEEE Symp. Foundations Comp. Sci., Chicago, IL, ngoNovemba 1982, iphe. 160-164 [18] ——, “How to generate and exchange secrets,” in Proc. IEEE Symp. Foundations Comp. Sci., Toronto, ON, Canada, Okthoba 1986, amakhasi 162-167 [19] M. Bloch et al., “A Overview of Information-Theoretical Security and Privacy: Metrics, Limits and Applications,” IEEE J. Sel. Areas Inf. Theory, Vol. 2, No. 1, pp. 5-22, Mar. 2021. [20] O. Gunlu no. G. Kramer, “I-Privacy, Secrecy, and Storage with Multiple Noisy Measurements of Identifiers”, IEEE Trans. [21] O. Gunlu, M. Bloch, no. R. F. Schaefer, “Ukuhlolwa okuhlobisa okuhlobisa okuhlobisa okuhlobisa okuhlobisa okuhlobisa ku-private remote sources,” Sep. 2021, [Online]. Kutholakala: arxiv.org/abs/2106.09485. [22] T. Berger, I-Rate Distortion Theory: A Mathematical Basis for Data Compression. Englewood Cliffs, NJ: Prentice-Hall, 1971. [23] H. Permuter noT. Weissman, “I-Source Coding with a Side Information “Vending Machine”, IEEE Trans. Inf. Theory, Vol. 57, No. 7, pp. 4530-4544, July 2011. [24] T. Berger, Z. Zhang, futhi H. Viswanathan, “The CEO problem,” IEEE Trans. Inf. Theory, Vol. 42, No. 3, pp. 887-902, ngo-May 1996. [25] O. Gunlu, “Key agreement with physical unclonable functions and biometric identifiers,” Ph.D. Thesis, TU Munich, Germany, Nov. 2018, eyakhelwe ngu Dr.-Hut Verlag ngoFebruwari 2019. [26] T. Ignatenko futhi F. M. J. Willems, “I-Biometric Systems: I-Privacy and Secrecy Aspects,” IEEE Trans. Inf. I-Forensics Security, Vol. 4, No. 4, pp. 956–973, Dec. 2009. [27] L. Lai, S.-W. Ho, noH. V. Poor, “I-privacy-security trade-offs ku-biometric security systems – Part I: Single use case,” IEEE Trans. Inf. I-Forensics Security, Vol. 6, No. 1, pp. 122-139 March 2011. [28] L. Kusters, O. G ̈unl ̈u, no. F. M. Willems, “Zero secrety leakage for multiple enrollments of physical unclonable functions,” in Proc. Symp. Inf. Theory Sign. Process. Benelux, Twente, Netherlands, May-June 2018, iphe. 119-127 [29] L. Lai, S. W. Ho, futhi H. V. Poor, “I-privacy-security trade-offs ku-biometric security systems – Part II: Multiple use case,” IEEE Trans. Inf. I-Forensics Security, Vol. 6, No. 1, pp. 140-151, Mar. 2011. [30] O. Gunlu, “I-Multi-entity and multi-enrollment key agreement with correlated noise,” IEEE Trans. Inf. I-Forensics Security, Vol. 16, pp. 1190-1202, 2021. [31] W. Tu futhi L. Lai, “On function computing with privacy and secrecy constraints,” IEEE Trans. Inf. Theory, Vol. 65, no. 10, iphe. 6716-673 Okthoba 2019. [32] J. Villard noP. Piantanida, “I-Secure multiterminal source coding nge-side information at the eavesdropper,” IEEE Trans. Inf. Theory, Vol. 59, no. 6, iphe. 3668-3692, Juni 2013. [33] S. I. Bross, “I-Secure Cooperative Source-Coding ne-Side Information at the eavesdropper,” IEEE Trans. Inf. Theory, Vol. 62, No. 8, iphe. 4544-4558, Aug. 2016. [34] E. Ekrem noS. Ulukus, “I-Secure lossy source coding nge-side information”, ku Proc. Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2011, iphe. 1098-1105. [35] J. Korner noK. Marton, “Ukuhlukaniswa kwezinhlayiyana ezimbonini ezimbonini,” Topics Inf. Theory, pp. 411-423, Aug. 1977. [36] P. Bergmans, “A simple converse for broadcast channels with additive white Gaussian noise (Corresp.),” IEEE Trans. Inf. Theory, Vol. 20, No. 2, pp. 279-280, Mar. 1974. [37] O. Gunlu, R. F. Schaefer, futhi H. V. Poor, “I-Biometric and Physical Identifiers with Correlated Noise for Controllable Private Authentication,” July 2020, [Online]. I-Arxiv.org/abs/2001.00847. [38] A. D. Wyner no. J. Ziv, "I-Theorem on the entropy of certain binary sequences and applications: Part I," IEEE Trans. Inf. Theory, Vol. 19, No. 6, pp. 769-772, November 1973. [39] S. Watanabe noY. Oohama, “I-Secret Key Agreement kusuka ku-Correlated Gaussian sources by rate limited public communication”, IEICE Trans. Fundam. Electron., Commun. Comp. Sci., Vol. 93, no. 11, pp. 1976-1983, November 2010. [40] F. M. Willems futhi T. Ignatenko, “I-effects quantitative in biometric systems,” in Proc. Inf. Theory Appl. Workshop, La Jolla, CA, Feb. 2009, iphe. 372-379. [41] V. Yachongka, H. Yagi, no-Y. Oohama, “I-Secret Key-based authentication nge-passive eavesdropper for scalar Gaussian sources,” Feb. 2022, [Online]. I-Arxiv.org/abs/2202.10018. [42] T. M. Cover futhi J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2012. [43] M. H. Yassaee, M. R. Aref, no. A. Gohari, “Ukuqinisekisa ukufinyelela nge-output statistics of random binning,” IEEE Trans. Inf. Theory, Vol. 60, no. 11, iphe. 6760-6786, ngoNovemba 2014. [44] J. M. Renes no. R. Renner, “I-coding ye-channel ye-noisy nge-privacy amplification kanye ne-information reconciliation”, IEEE Trans. Inf. Theory, Vol. 57, no. 11, iphe. 7377-7385, Nov. 2011. [45] M. Bloch, Izincwadi ze-Information-Theoretic Security. Atlanta, GA: Georgia Inst. Technol., July 2018. [46] T. Holenstein futhi R. Renner, "Ngoku-randomity of independent experiments," IEEE Trans. Inf. Theory, Vol. 57, No. 4, pp. 1865-1871, Apr. 2011. [47] M. Bloch noJ. Barros, Physical-layer Ukuvikelwa. Cambridge, UK: Cambridge University Press, 2011. [48] I. Csisz'ar futhi J. K ̈orner, Information Theory: Coding Theorems for Discrete Memoryless Systems, 2nd ed. Cambridge, UK: Cambridge University Press, 2011. 
 
 
 
 
 
 Umbhali: (1) Onur Gunlu, uMongameli we-Communications Engineering and Security, i-University of Siegen kanye ne-Information Coding Division, i-Department of Electrical Engineering, i-University of Linkoping (onur.guenlue@uni-siegen.de); (2) Rafael F. Schaefer, umongameli we-Communications Engineering and Security, University of Siegen (rafael.schaefer@uni-siegen.de); (3) Holger Boche, Umbhali we-Information Technology, Technical University of Munich, CASA: Cyber Security in the Age of Large-Scale Adversaries Exzellenzcluster, Ruhr-Universitat Bochum, futhi BMBF Research Hub 6G-Life, Technical University of Munich (boche@tum.de); (4) H. Vincent Poor, I-Department of Electrical and Computer Engineering, I-Princeton University (poor@princeton.edu). Authors: (1) Onur Gunlu, uMongameli we-Communications Engineering and Security, i-University of Siegen kanye ne-Information Coding Division, i-Department of Electrical Engineering, i-University of Linkoping (onur.guenlue@uni-siegen.de); (2) Rafael F. Schaefer, umongameli we-Communications Engineering and Security, University of Siegen (rafael.schaefer@uni-siegen.de); (3) Holger Boche, Umbhali we-Information Technology, Technical University of Munich, CASA: Cyber Security in the Age of Large-Scale Adversaries Exzellenzcluster, Ruhr-Universitat Bochum, futhi BMBF Research Hub 6G-Life, Technical University of Munich (boche@tum.de); (4) H. Vincent Poor, I-Department of Electrical and Computer Engineering, I-Princeton University (poor@princeton.edu). 
 
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