The Impossibility of Obfuscation with Auxiliary Input or a Universal Simulator

In this paper we show that the existence of general indistinguishability obfuscators conjectured in a few recent works implies, somewhat counterintuitively, strong impossibility results for virtual black box obfuscation. In particular, we show that indistinguishability obfuscation for all circuits implies: • The impossibility of average-case virtual black box obfuscation with auxiliary input for any circuit family with super-polynomial pseudo-entropy. Such circuit families include all pseudo-random function families, and all families of encryption algorithms and randomized digital signatures that generate their required coin flips pseudo-randomly. Impossibility holds even when the auxiliary input depends only on the public circuit family, and not the specific circuit in the family being obfuscated. • The impossibility of average-case virtual black box obfuscation with a universal simulator (with or without any auxiliary input) for any circuit family with super-polynomial pseudo-entropy. These bounds significantly strengthen the impossibility results of Goldwasser and Kalai (STOC 2005). ∗Tel Aviv University, [email protected]. Supported by an IBM Ph.D. Fellowship, and the Check Point Institute for Information Security. †Boston University and Tel Aviv University, [email protected]. Supported by the Check Point Institute for Information Security, an NSF EAGER grant, and an NSF Algorithmic Foundations grant 1218461. ‡Microsoft Research, One Memorial Drive, Cambridge, MA 02142, [email protected]. §MIT and the Weizmann Institute of Science, [email protected]. ¶Microsoft Research, One Memorial Drive, Cambridge, MA 02142, [email protected]. ‖Boston University, [email protected]. Supported by the Simons award for graduate students in theoretical computer science and an NSF Algorithmic foundations grant 1218461. ∗∗Efi Arazi School of Computer Science, IDC Herzliya, Israel, [email protected]. Supported by ISF grant no. 1255/12 and by the ERC under the EU’s Seventh Framework Programme (FP/2007-2013) ERC Grant Agreement n. 307952. ar X iv :1 40 1. 03 48 v3 [ cs .C R ] 1 3 Fe b 20 14