**More on the Impossibility of Virtual-Black-Box Obfuscation with Auxiliary Input**

*Nir Bitansky and Ran Canetti and Omer Paneth and Alon Rosen*

**Abstract: **We show that if there exist indistinguishability obfuscators for a certain class C of circuits then there do not exist independent-auxiliary-input virtual-black-box (VBB) obfuscators for any family of circuits that compute a pseudo-entropic function. A function f_k is pseudo-entropic if it is hard, given oracle access to f_k but without asking explicitly on a value x, to distinguish f_k(x) from a random variable with some real entropy.

This strengthens the bound of Goldwasser and Kalai [FOCS `05, ePrint `13] that rules out dependent-auxiliary-input VBB obfuscation for the same set of circuit families, assuming inditinguishability obfuscators for another class, C', of circuits. That is, while they only rule out the case where the adversary and the simulator obtain auxiliary information that depends on the actual (secret) obfuscated function, we rule out even the case where the auxiliary input depends only on the (public) family of programs.

**Category / Keywords: **

**Date: **received 27 Oct 2013, last revised 18 Feb 2014

**Contact author: **omerpa at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20140218:134641 (All versions of this report)

**Short URL: **ia.cr/2013/701

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