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

Overview
• Introduction
• Mathematical foundation for computer security
• The “CIA” triad
• Covert channels
• Our theorems (with examples)
• Conclusion

Introduction

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

The CIA triad
• Confidentiality
• Integrity
• Availability

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

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!)

A simple covert writer as a finite automata

A simple covert reader as a finite automata

Our theorems
Theorem 1. With high probability (i.e. the probability goes to 1 as the value min( N left
, N right
)
® ¥
)
Theorem 2. I(G) = log M

Maximal mutual information
• Graph theory
• Nodes, edges
• Graphs, bipartite graphs, multi-bipartite graphs
• Matching, maximal matching
• Information theory
• Mutual information
• Entropy

Graph Theory
Nodes, edges, and connectedness

Graph Theory
Nodes left
Nodes right

Graph Theory
Nodes left
Nodes right

Secure Numerical
Sensing in Automata
Multicounter Automata M
C high(C)
1
0
3
2
5
4
7
6
V
1
V Reversal-Bounded Counters
5
4
3
7
6
10
9
8
2
1
0
V
2
V
3
2
1
..
V k
1
0
3
2
0
1
2 k
i
=
0 low(V)
V i

Secure Numerical
Sensing in Automata
Multicounter Automata M
C high(C) =
{ C n,
,{7, 10, 3, 0}}
1
0
3
2
5
4
7
6
V
1
V Reversal-Bounded Counters
5
4
3
7
6
10
9
8
2
1
0
V
2
V
3
2
1
..
V k
1
0
3
2
0
1
2 k
i
=
0
V i low(V) =
20

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.

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…

Conclusion

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

Analysis
• 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.

Thank You william.hutton@wsu.edu