Patchable indistinguishability obfuscation: IO for evolving software

Abstract

In this work, we introduce patchable indistinguishability 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 Mʹ = 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 considermulti-program patchable indistinguishability obfuscation where a patch is applied not just to a single machine M, but to an unbounded set of machines M1,…, Mn to yield P(M1),…, P (Mn). We consider both single-program and multi-program patchable indistinguishability 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 re-randomizable encryption schemes (Re-randomizable encryption schemes can be instantiated under standard assumptions such as DDH, LWE.) imply single-program patchable indistinguishability obfuscation; and we show that sub-exponentially secure iO for circuits and sub-exponentially secure DDH imply multi-program patchable indistinguishability obfuscation. At the our heart of results is a new notion of splittable iO that allows us to transform any iO scheme into a patchable one. Finally, we exhibit some simple applications of patchable indistinguishability obfuscation, to demonstrate how these concepts can be applied.