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Foundations of Cryptography: Basic Tools
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On the (Im)possibility of Obfuscating Programs
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Towards Realizing Random Oracles: Hash Functions That Hide All Partial Information
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How to Go Beyond the Black-Box Simulation Barrier
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Foundations of Cryptography: Volume 2, Basic Applications
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A semantics-based approach to malware detection
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Towards a Theory of Extractable Functions
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Multi-stage binary code obfuscation using improved virtual machine
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On the (im)possibility of obfuscating programs
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Secure obfuscation for encrypted signatures
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Barak et al. formalized the notion of obfuscation, and showed that there exist (contrived) classes of functions that cannot be obfuscated. In contrast, Canetti and Wee showed how to obfuscate point functions, under various complexity assumptions. Thus, it would seem possible that most programs of interest can be obfuscated even though in principle general purpose obfuscators do not exist. We show that this is unlikely to be the case. In particular, we consider the notion of obfuscation w.r.t. auxiliary input, which corresponds to the setting where the adversary, which is given the obfuscated circuit, may have some additional a priori information. This is essentially the case of interest in any usage of obfuscation we can imagine. We prove that there exist many natural classes of functions that cannot be obfuscated w.r.t. auxiliary input, both when the auxiliary input is dependent of the function being obfuscated and even when the auxiliary input is independent of the function being obfuscated. We also give a positive result. In particular, we show that any obfuscator for the class of point functions is also an obfuscator w.r.t. independent auxiliary input.