### On the (Im)possibility of Obfuscating Programs

Boaz Barak, Oded Goldreich, Russell Impagliazzo, Steven Rudich, Amit Sahai, Salil Vadhan, and Ke Yang

##### Abstract

Informally, an {\em obfuscator} $O$ is an (efficient, probabilistic) compiler'' that takes as input a program (or circuit) $P$ and produces a new program $O(P)$ that has the same functionality as $P$ yet is unintelligible'' in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic and complexity-theoretic applications, ranging from software protection to homomorphic encryption to complexity-theoretic analogues of Rice's theorem. Most of these applications are based on an interpretation of the unintelligibility'' condition in obfuscation as meaning that $O(P)$ is a virtual black box,'' in the sense that anything one can efficiently compute given $O(P)$, one could also efficiently compute given oracle access to $P$. In this work, we initiate a theoretical investigation of obfuscation. Our main result is that, even under very weak formalizations of the above intuition, obfuscation is impossible. We prove this by constructing a family of functions $F$ that are {\em \inherently unobfuscatable} in the following sense: there is a property $\pi : F \rightarrow \{0,1\}$ such that (a) given {\em any program} that computes a function $f\in F$, the value $\pi(f)$ can be efficiently computed, yet (b) given {\em oracle access} to a (randomly selected) function $f\in F$, no efficient algorithm can compute $\pi(f)$ much better than random guessing. We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only {\em approximately} preserve the functionality, and (c) only need to work for very restricted models of computation ($TC_0$). We also rule out several potential applications of obfuscators, by constructing unobfuscatable'' signature schemes, encryption schemes, and pseudorandom function families.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Extended abstract in CRYPTO 2001. Also posted on Electronic Colloquium on Computational Complexity.
Keywords
complexity theorysoftware protectionhomomorphic encryptionRice's Theoremsoftware watermarkingpseudorandom functionsstatistical zero knowledge
Contact author(s)
boaz @ wisdom weizmann ac il
History
Short URL
https://ia.cr/2001/069

CC BY

BibTeX

@misc{cryptoeprint:2001/069,
author = {Boaz Barak and Oded Goldreich and Russell Impagliazzo and Steven Rudich and Amit Sahai and Salil Vadhan and Ke Yang},
title = {On the (Im)possibility of Obfuscating Programs},
howpublished = {Cryptology ePrint Archive, Paper 2001/069},
year = {2001},
note = {\url{https://eprint.iacr.org/2001/069}},
url = {https://eprint.iacr.org/2001/069}
}

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