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Sloan Foundation","doi-asserted-by":"publisher","award":["0205594, 0312809, 0456717, 0627781, 07163890830803, 0916574, 1065276, 1118096, and 1136174"],"award-info":[{"award-number":["0205594, 0312809, 0456717, 0627781, 07163890830803, 0916574, 1065276, 1118096, and 1136174"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2012,4]]},"abstract":"\n Informally, an\n obfuscator<\/jats:italic>\n O<\/jats:italic>\n is an (efficient, probabilistic) \u201ccompiler\u201d that takes as input a program (or circuit)\n P<\/jats:italic>\n and produces a new program\n O<\/jats:italic>\n (\n P<\/jats:italic>\n ) that has the same functionality as\n P<\/jats:italic>\n yet is \u201cunintelligible\u201d 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 \u201cunintelligibility\u201d condition in obfuscation as meaning that\n O<\/jats:italic>\n (\n P<\/jats:italic>\n ) is a \u201cvirtual black box,\u201d in the sense that anything one can efficiently compute given\n O<\/jats:italic>\n (\n P<\/jats:italic>\n ), one could also efficiently compute given oracle access to\n P<\/jats:italic>\n .\n <\/jats:p>\n \n 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 efficient programs\n P<\/jats:italic>\n that are\n unobfuscatable<\/jats:italic>\n in the sense that (a) given\n any<\/jats:italic>\n efficient program\n P<\/jats:italic>\n ' that computes the same function as a program\n P<\/jats:italic>\n \u2208\n p<\/jats:italic>\n , the \u201csource code\u201d\n P<\/jats:italic>\n can be efficiently reconstructed, yet (b) given\n oracle access<\/jats:italic>\n to a (randomly selected) program\n P<\/jats:italic>\n \u2208\n p<\/jats:italic>\n , no efficient algorithm can reconstruct\n P<\/jats:italic>\n (or even distinguish a certain bit in the code from random) except with negligible probability.\n <\/jats:p>\n \n We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only approximately preserve the functionality, and (c) only need to work for very restricted models of computation (\n \n TC\n 0<\/jats:sup>\n <\/jats:bold>\n ). We also rule out several potential applications of obfuscators, by constructing \u201cunobfuscatable\u201d signature schemes, encryption schemes, and pseudorandom function families.\n <\/jats:p>","DOI":"10.1145\/2160158.2160159","type":"journal-article","created":{"date-parts":[[2012,5,1]],"date-time":"2012-05-01T13:43:38Z","timestamp":1335879818000},"page":"1-48","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":339,"title":["On the (im)possibility of obfuscating programs"],"prefix":"10.1145","volume":"59","author":[{"given":"Boaz","family":"Barak","sequence":"first","affiliation":[{"name":"Microsoft Research New England, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oded","family":"Goldreich","sequence":"additional","affiliation":[{"name":"Weizmann Institute of Science, Rehovot, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Russell","family":"Impagliazzo","sequence":"additional","affiliation":[{"name":"University of California, San Diego, La Jolla, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven","family":"Rudich","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amit","family":"Sahai","sequence":"additional","affiliation":[{"name":"UCLA, University of California, Los Angeles, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salil","family":"Vadhan","sequence":"additional","affiliation":[{"name":"Harvard Universit, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ke","family":"Yang","sequence":"additional","affiliation":[{"name":"Google Inc., Mountain View, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2012,5,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/874063.875552"},{"key":"e_1_2_2_2_1","unstructured":"Barak B. 2002. 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