Quantifying Opacity

In this paper we propose two dual notions of quantitative information leakage in probabilistic systems, both related to opacity for non probabilistic systems. The liberal one measures the probability for an attacker observing a random execution of the system, to be able to gain information he can be sure about. We show that a null value for this measure corresponds to a secure system, in the usual sense of opacity. On the other hand, restrictive opacity is defined as the complement of the information-theoretic notion of mutual information. It measures the level of certitude in the information acquired by an attacker observing the system: we prove that a null value for this second measure corresponds to non opacity. We also show how these measures can be computed for regular secrets and observations. We finally apply them to the dining cryptographers problem and to the crowd anonymity protocol.

[1]  Michele Boreale,et al.  Quantitative Information Flow, with a View , 2011, ESORICS.

[2]  Michele Boreale,et al.  Asymptotic information leakage under one-try attacks† , 2011, Mathematical Structures in Computer Science.

[3]  Feng Lin,et al.  Opacity of discrete event systems and its applications , 2011, Autom..

[4]  Mathieu Sassolas,et al.  Quantifying Opacity , 2010, 2010 Seventh International Conference on the Quantitative Evaluation of Systems.

[5]  Mário S. Alvim,et al.  Information Flow in Interactive Systems , 2010, CONCUR.

[6]  Annabelle McIver,et al.  Compositional Closure for Bayes Risk in Probabilistic Noninterference , 2010, ICALP.

[7]  Geoffrey Smith,et al.  Computing the Leakage of Information-Hiding Systems , 2010, TACAS.

[8]  Philippe Darondeau,et al.  Supervisory Control for Opacity , 2010, IEEE Transactions on Automatic Control.

[9]  Pedro R. D'Argenio,et al.  On the Expressive Power of Schedulers in Distributed Probabilistic Systems , 2009, Electron. Notes Theor. Comput. Sci..

[10]  Alessandro Aldini,et al.  A General Framework for Nondeterministic, Probabilistic, and Stochastic Noninterference , 2009, ARSPA-WITS.

[11]  Siu Cheung Kong,et al.  An experience of teaching for learning by observation: Remote-controlled experiments on electrical circuits , 2009, Comput. Educ..

[12]  Geoffrey Smith,et al.  On the Foundations of Quantitative Information Flow , 2009, FoSSaCS.

[13]  Chia-Hung Wang,et al.  Optimal multi-level thresholding using a two-stage Otsu optimization approach , 2009, Pattern Recognit. Lett..

[14]  Heiko Mantel,et al.  Information-Theoretic Modeling and Analysis of Interrupt-Related Covert Channels , 2008, Formal Aspects in Security and Trust.

[15]  Maciej Koutny,et al.  Opacity generalised to transition systems , 2005, International Journal of Information Security.

[16]  Sven K. Esche,et al.  A Remotely Accessed Flow Rig Student Laboratory , 2008 .

[17]  Prakash Panangaden,et al.  Anonymity protocols as noisy channels , 2006, Inf. Comput..

[18]  Michele Boreale,et al.  Quantifying information leakage in process calculi , 2006, Inf. Comput..

[19]  Pavol Cerný,et al.  Preserving Secrecy Under Refinement , 2006, ICALP.

[20]  Sven K. Esche,et al.  A Virtual Laboratory On Fluid Mechanics , 2006 .

[21]  Etienne Decencière,et al.  Image filtering using morphological amoebas , 2007, Image Vis. Comput..

[22]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[23]  B. Nordstrom.  FINITE MARKOV CHAINS , 2005 .

[24]  Yassine Lakhnech,et al.  Probabilistic Opacity for a Passive Adversary and its Application to Chaum's Voting Scheme , 2005, IACR Cryptol. ePrint Arch..

[25]  Laurent Mazaré,et al.  Decidability of Opacity with Non-Atomic Keys , 2004, Formal Aspects in Security and Trust.

[26]  Gavin Lowe,et al.  Defining information flow quantity , 2004, J. Comput. Secur..

[27]  Mario Bravetti,et al.  A Process Algebraic Approach for the Analysis of Probabilistic Non-interference , 2011 .

[28]  David Chaum,et al.  The dining cryptographers problem: Unconditional sender and recipient untraceability , 1988, Journal of Cryptology.

[29]  Larry S. Davis,et al.  W4: Real-Time Surveillance of People and Their Activities , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Michael K. Reiter,et al.  Crowds: anonymity for Web transactions , 1998, TSEC.

[31]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[32]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[33]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[34]  Mihalis Yannakakis,et al.  Markov Decision Processes and Regular Events (Extended Abstract) , 1990, ICALP.

[35]  J. Todd Wittbold,et al.  Information flow in nondeterministic systems , 1990, Proceedings. 1990 IEEE Computer Society Symposium on Research in Security and Privacy.

[36]  Jonathan K. Millen,et al.  Covert Channel Capacity , 1987, 1987 IEEE Symposium on Security and Privacy.

[37]  J. Meseguer,et al.  Security Policies and Security Models , 1982, 1982 IEEE Symposium on Security and Privacy.

[38]  B. Massey,et al.  Mechanics of Fluids , 2018 .

[39]  Michele Boreale,et al.  Quantitative Information Flow, with a View , 2011, ESORICS.

[40]  Michele Boreale,et al.  Asymptotic information leakage under one-try attacks† , 2011, Mathematical Structures in Computer Science.

[41]  Feng Lin,et al.  Opacity of discrete event systems and its applications , 2011, Autom..

[42]  Mário S. Alvim,et al.  Information Flow in Interactive Systems , 2010, CONCUR.

[43]  Annabelle McIver,et al.  Compositional Closure for Bayes Risk in Probabilistic Noninterference , 2010, ICALP.

[44]  Geoffrey Smith,et al.  Computing the Leakage of Information-Hiding Systems , 2010, TACAS.

[45]  Philippe Darondeau,et al.  Supervisory Control for Opacity , 2010, IEEE Transactions on Automatic Control.

[46]  Pedro R. D'Argenio,et al.  On the Expressive Power of Schedulers in Distributed Probabilistic Systems , 2009, Electron. Notes Theor. Comput. Sci..

[47]  Alessandro Aldini,et al.  A General Framework for Nondeterministic, Probabilistic, and Stochastic Noninterference , 2009, ARSPA-WITS.

[48]  Geoffrey Smith,et al.  On the Foundations of Quantitative Information Flow , 2009, FoSSaCS.

[49]  Heiko Mantel,et al.  Information-Theoretic Modeling and Analysis of Interrupt-Related Covert Channels , 2008, Formal Aspects in Security and Trust.

[50]  Maciej Koutny,et al.  Opacity generalised to transition systems , 2005, International Journal of Information Security.

[51]  Prakash Panangaden,et al.  Anonymity protocols as noisy channels , 2006, Inf. Comput..

[52]  Pavol Cerný,et al.  Preserving Secrecy Under Refinement , 2006, ICALP.

[53]  Michele Boreale,et al.  Quantifying information leakage in process calculi , 2006, Inf. Comput..

[54]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[55]  B. Nordstrom.  FINITE MARKOV CHAINS , 2005 .

[56]  Yassine Lakhnech,et al.  Probabilistic Opacity for a Passive Adversary and its Application to Chaum's Voting Scheme , 2005, IACR Cryptol. ePrint Arch..

[57]  Laurent Mazaré,et al.  Decidability of Opacity with Non-Atomic Keys , 2004, Formal Aspects in Security and Trust.

[58]  Gavin Lowe,et al.  Defining information flow quantity , 2004, J. Comput. Secur..

[59]  Mario Bravetti,et al.  A Process Algebraic Approach for the Analysis of Probabilistic Non-interference , 2011 .

[60]  David Chaum,et al.  The dining cryptographers problem: Unconditional sender and recipient untraceability , 1988, Journal of Cryptology.

[61]  Michael K. Reiter,et al.  Crowds: anonymity for Web transactions , 1998, TSEC.

[62]  Markov decision processes and regular events , 1998, IEEE Trans. Autom. Control..

[63]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[64]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[65]  J. Todd Wittbold,et al.  Information flow in nondeterministic systems , 1990, Proceedings. 1990 IEEE Computer Society Symposium on Research in Security and Privacy.

[66]  Jonathan K. Millen,et al.  Covert Channel Capacity , 1987, 1987 IEEE Symposium on Security and Privacy.

[67]  J. Meseguer,et al.  Security Policies and Security Models , 1982, 1982 IEEE Symposium on Security and Privacy.