1. Security of Numerical Sensors in Finite Automata Zhe Dang Dmitry Dementyev Thomas R. Fischer William J. Hutton, III Washington State University – Pullman, WA USA

2. Overview IntroductionIntroduction Mathematical foundation for computer securityMathematical foundation for computer security The “CIA” triadThe “CIA” triad Covert channelsCovert channels Our theorems (with examples)Our theorems (with examples) ConclusionConclusion

3. Introduction

4. Mathematical foundation for computer security Ad hoc experiences are not science!

5. The CIA triad Confidentiality Confidentiality Integrity Integrity Availability Availability

6. Confidentiality “ Confidentiality is the concealment of information or resources.”

7. Covert channels “A covert channel is a path of communication that was not designed to be used for communication.” -- Matt Bishop (Covert communication can be implicit!)

8. A simple covert writer as a finite automata

9. A simple covert reader as a finite automata

10. Our theorems Theorem 2. I(G) = log M

11. Maximal mutual information Graph theoryGraph theory Nodes, edgesNodes, edges Graphs, bipartite graphs, multi-bipartite graphsGraphs, bipartite graphs, multi-bipartite graphs Matching, maximal matchingMatching, maximal matching Information theoryInformation theory Mutual informationMutual information EntropyEntropy

12. Graph Theory Nodes, edges, and connectedness

13. Graph Theory Nodes left Nodes right

14. Graph Theory Nodes left Nodes right

15. Secure Numerical Sensing in Automata C Multicounter Automata M 7654321076543210 10 9 8 7 6 5 4 3 2 1 0 321321 01232100123210 V Reversal-Bounded Counters V1V1 V2V2 V.. VkVk high(C) low(V)

16. Secure Numerical Sensing in Automata C Multicounter Automata M 7654321076543210 10 9 8 7 6 5 4 3 2 1 0 321321 01232100123210 V Reversal-Bounded Counters V1V1 V2V2 V.. VkVk high(C) = { C n,,{7, 10, 3, 0}} low(V) = 20

17. Theorems 3-6 3.The information rate of a regular language is computable [5]. 4.A suffix-closed regular language is converging. 5.For a semilinear set V, [V] is a converging regular language. 6.For numerical sensors ‘low’ and ‘high’, when their set of measurements is effectively a semilinear set, the mutual information rate I(low, high) is computable.

18. Theorems 7-10 7.For integer numerical sensors ‘low’ and ‘high’, when their measurements set is Presburger definable, the mutual information rate I(low, high) is computable. 8.Suppose that ‘low’ and ‘high’ are linear numerical sensors in a reversal-bounded NPCM M. Then the mutual information rate I(low, high) is computable. 9.For a 2-tape NFA M, its mutual information rate I(low, high) is computable… 10. For a k-tape NFA M augmented with reversal-bounded counters its mutual information rate I(low, high) is computable…

19. Conclusion

20. Computability The mutual information rate between two sensors is computable for some computational models.The mutual information rate between two sensors is computable for some computational models. Nondeterministic pushdown automata augmented with reversal-bounded countersNondeterministic pushdown automata augmented with reversal-bounded counters Discrete timed automataDiscrete timed automata

21. Analysis The computed mutual information rate can be used to determine if there is no information flow between sensors.The computed mutual information rate can be used to determine if there is no information flow between sensors. This provides a method to quantitatively and algorithmically analyze some types of covert channels.This provides a method to quantitatively and algorithmically analyze some types of covert channels.

22. Thank You william.hutton@wsu.edu