Secrecy by Design With Applications to Privacy and Compression

Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The principal technical contributions are decomposition bounds that allow the representation of a random variable <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> as a deterministic function of <inline-formula> <tex-math notation="LaTeX">$({S},{Z})$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> is a given fixed random variable and <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> is constructed to be independent of <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>. Using the problems of privacy and lossless compression as examples, the utility cost of applying secrecy by design is investigated. Privacy is studied in the setting of the privacy funnel function previously introduced in the literature and new bounds for the regime of zero information leakage are derived. For the problem of lossless compression, it is shown that strong information-theoretic guarantees can be achieved using a reduced secret key size and a quantifiable penalty on the compression rate. The fundamental limits for both problems are characterized with matching lower and upper bounds when the secret <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> is a deterministic function of the information source <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>.

[1]  Hirosuke Yamamoto.  A rate-distortion problem for a communication system with a secondary decoder to be hindered , 1988, IEEE Trans. Inf. Theory.

[2]  H. Vincent Poor,et al.  Utility-Privacy Tradeoffs in Databases: An Information-Theoretic Approach , 2011, IEEE Transactions on Information Forensics and Security.

[3]  Shahab Asoodeh,et al.  Privacy Amplification of Iterative Algorithms via Contraction Coefficients , 2020, 2020 IEEE International Symposium on Information Theory (ISIT).

[4]  Alexandre V. Evfimievski,et al.  Limiting privacy breaches in privacy preserving data mining , 2003, PODS.

[5]  Tsachy Weissman,et al.  Multiterminal Source Coding Under Logarithmic Loss , 2011, IEEE Transactions on Information Theory.

[6]  J. Massey.  Guessing and entropy , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[7]  Sergio Verdú,et al.  Optimal Lossless Data Compression: Non-Asymptotics and Asymptotics , 2014, IEEE Transactions on Information Theory.

[8]  Paul Cuff,et al.  Information Theoretic Security and Privacy of Information Systems , 2016 .

[9]  Ken R. Duffy,et al.  Principal Inertia Components and Applications , 2017, IEEE Transactions on Information Theory.

[10]  Aaron Roth,et al.  The Algorithmic Foundations of Differential Privacy , 2014, Found. Trends Theor. Comput. Sci..

[11]  Vitaly Feldman,et al.  Privacy Amplification by Iteration , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

[12]  Hirosuke Yamamoto.  Coding theorems for Shannon's cipher system with correlated source outputs, and common information , 1994, IEEE Trans. Inf. Theory.

[13]  Muriel Médard,et al.  From the Information Bottleneck to the Privacy Funnel , 2014, 2014 IEEE Information Theory Workshop (ITW 2014).

[14]  S. Rajsbaum.  Foundations of Cryptography , 2014 .

[15]  Sudeep Kamath,et al.  An operational measure of information leakage , 2016, 2016 Annual Conference on Information Science and Systems (CISS).

[16]  Gábor Lugosi,et al.  Prediction, learning, and games , 2006 .

[17]  Stephen E. Fienberg,et al.  Differential Privacy and the Risk-Utility Tradeoff for Multi-dimensional Contingency Tables , 2010, Privacy in Statistical Databases.

[18]  Sofya Raskhodnikova,et al.  What Can We Learn Privately? , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[19]  Hirosuke Yamamoto,et al.  Coding Theorems for the Shannon Cipher System With a Guessing Wiretapper and Correlated Source Outputs , 2006, IEEE Transactions on Information Theory.

[20]  Igal Sason,et al.  Concentration of Measure Inequalities in Information Theory, Communications, and Coding , 2012, Found. Trends Commun. Inf. Theory.

[21]  Fady Alajaji,et al.  Estimation Efficiency Under Privacy Constraints , 2017, IEEE Transactions on Information Theory.

[22]  Sergio Verdú,et al.  A single-shot approach to lossy source coding under logarithmic loss , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[23]  Aaron B. Wagner,et al.  Measuring secrecy by the probability of a successful guess , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[24]  Fady Alajaji,et al.  Information Extraction Under Privacy Constraints , 2015, Inf..

[25]  Cynthia Dwork,et al.  Calibrating Noise to Sensitivity in Private Data Analysis , 2006, TCC.

[26]  H. Vincent Poor,et al.  Secure lossless compression , 2018, 2018 52nd Annual Conference on Information Sciences and Systems (CISS).

[27]  Pramod Viswanath,et al.  The Composition Theorem for Differential Privacy , 2013, IEEE Transactions on Information Theory.

[28]  Oliver Kosut,et al.  Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs , 2018, IEEE Transactions on Information Theory.

[29]  Ming Jin,et al.  Virtual Occupancy Sensing: Using Smart Meters to Indicate Your Presence , 2017, IEEE Transactions on Mobile Computing.

[30]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[31]  Martin J. Wainwright,et al.  Local privacy and statistical minimax rates , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[32]  Gilles Barthe,et al.  Beyond Differential Privacy: Composition Theorems and Relational Logic for f-divergences between Probabilistic Programs , 2013, ICALP.

[33]  Deniz Gündüz,et al.  On Perfect Privacy , 2017, 2018 IEEE International Symposium on Information Theory (ISIT).

[34]  Neri Merhav.  A large-deviations notion of perfect secrecy , 2003, IEEE Trans. Inf. Theory.

[35]  Moni Naor,et al.  Our Data, Ourselves: Privacy Via Distributed Noise Generation , 2006, EUROCRYPT.

[36]  Mikael Skoglund,et al.  On the Mutual Information of Two Boolean Functions, with Application to Privacy , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[37]  Paul W. Cuff,et al.  The Henchman Problem: Measuring Secrecy by the Minimum Distortion in a List , 2014, IEEE Transactions on Information Theory.

[38]  Neri Merhav,et al.  Universal Prediction , 1998, IEEE Trans. Inf. Theory.

[39]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[40]  Frans M. J. Willems,et al.  The discrete memoryless multiple-access channel with cribbing encoders , 1985, IEEE Trans. Inf. Theory.

[41]  Bruce E. Hajek,et al.  Evaluation of an achievable rate region for the broadcast channel , 1979, IEEE Trans. Inf. Theory.

[42]  Mikael Skoglund,et al.  Lossy Communication Subject to Statistical Parameter Privacy , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[43]  Sudeep Kamath,et al.  An Operational Approach to Information Leakage , 2018, IEEE Transactions on Information Theory.

[44]  Neri Merhav,et al.  The Shannon cipher system with a guessing wiretapper , 1999, IEEE Trans. Inf. Theory.

[45]  Paul W. Cuff,et al.  Rate-distortion theory for secrecy systems , 2013, 2013 IEEE International Symposium on Information Theory.

[46]  Elza Erkip,et al.  Source Coding under Secrecy Constraints , 2009 .

[47]  Paul W. Cuff,et al.  Differential Privacy as a Mutual Information Constraint , 2016, CCS.

[48]  Toby Berger,et al.  Multiterminal source encoding with encoder breakdown , 1989, IEEE Trans. Inf. Theory.