In this work, we introduce patchable obfuscation: our notion
adapts the notion of indistinguishability obfuscation (iO) to a very general setting where
obfuscated software evolves over time. We model this broadly by considering
software patches P as arbitrary Turing Machines that take as input the description of a
Turing Machine M, and output a new Turing Machine description M' = P(M).
Thus, a short patch P can cause changes everywhere in the description of M and
can even cause the description length of the machine to increase by an arbitrary polynomial amount.
We further consider the setting where a patch is applied not just to a single
machine M, but to an unbounded set of machines (M_1, \dots, M_t) to
yield (P(M_1), \dots, P(M_t). We call this multi-program patchable obfuscation.
We consider both patchable obfuscation and multi-program patchable obfuscation
in a setting where there are an unbounded number of patches that can be adaptively
chosen by an adversary.
We show that sub-exponentially secure iO for circuits and sub-exponentially secure one-way functions imply patchable obfuscation; and we show that
sub-exponentially secure iO for circuits, sub-exponentially secure one-way functions,
and sub-exponentially secure DDH imply multi-program patchable obfuscation.
Finally, we exhibit some simple applications
of multi-program patchable obfuscation, to demonstrate how these concepts
can be applied.
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