Obfuscation of Abstract Data-Types - Rowan

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We study abstract data-types (consisting of a local state accessible only
by declared operations) and define obfuscations for the whole data-type. In
other words, we obfuscate the state of the data-type under the assumption that
the only way it is being accessed is via the operations of the type. Different
operations (on a given state) may require different obfuscations.
To date, obfuscation has been an area largely untouched by the formal
method approach to program correctness. We regard obfuscation as data refinement
allowing us to produce equations for proving correctness. We model
the data-type operations as functional programs. That enables us to establish
correctness easily as well as providing us with an elegant style in which to write
definitions of our operations. Two benefits of using abstract data-types are that
we can specify obfuscations which exploit structural properties inherent in the
data-type; and the ability to create random obfuscations. We also provide a
new definition of obfuscation that avoids the impossibility problem considered
by Barak et al. [6] and is appropriate for our data-type approach.
Structure of the thesis
The thesis is structured as follows:
• In Chapters 1 and 2 we consider the current view of obfuscation. In
Chapter 1 we discuss the need for obfuscation and summarise some of the
obfuscations from [10]. Also we evaluate the definitions for obfuscation
given in [6, 10]. In Chapter 2 we look at the .NET Intermediate Language
[23] and discuss joint work with Oege de Moor and Ganesh Sittampalam
that allows us to write some specifications of obfuscations for Intermediate
Language.
• In Chapter 3 we give an alternative view of obfuscation by concentrating
on abstract data-types. We use data refinement and functional programming
to produce a framework that allows us to prove the correctness of
obfuscations (or even to derive them) and we give a definition of obfuscation
pertinent to our approach.
• In Chapter 4 we use our approach to generalise an obfuscation called array
splitting and we show how to split more general data-types.
• The next three chapters concentrate on specific case studies for different
data-types. In Chapters 5 and 6 we use the results on data-type splitting
to show how to construct obfuscations for sets and matrices. In Chapter
7 we give a transformation suitable for obfuscating binary trees.
• Finally, in Chapter 8, we summarise our results and discuss possible areas
for future work.
Contributions
The thesis provides the following contributions.
Using established work on refinement, abstract data-types and functional
programming, a new approach to obfuscation is developed. This approach has
the following benefits: