**Candidate Differing-Inputs Obfuscation from Indistinguishability Obfuscation and Auxiliary-Input Point Obfuscation**

*Pan Dongxue and Li Hongda and Ni Peifang*

**Abstract: **Differing-inputs obfuscation (diO), first proposed by Barak et. al. [4], provides stronger security than that provided by indistinguishability obfuscation (iO). An iO scheme provides indistinguishability between the obfuscations of two programs that are equivalent and have the same length of description. A diO scheme ensures that the obfuscations of two efficiently generated programs with the same description length are indistinguishable if it is hard to find an input on which their outputs differ. Ananth et. al. [1] showed the definition of diO with respect to arbitrary auxiliary inputs. However, Garg et al. [19] showed that the existence of this kind of diO contradicts a certain “special-purpose obfuscation” conjecture. Ishai, Pandey and Sahai [23] suggested a diO variant called public-coin diO, which requires the auxiliary input to be a public random string and given as input to all relevant algorithms. They gave a construction of public-coin diO by assuming the existence of public-coin differing-inputs obfuscator for NC^1 circuits.
In this paper, we use a slightly different definition, called public-coin-dependent diO. It allows the obfuscation algorithm to additionally take as input the random coins used to sample the circuit pair (including the circuit to be obfuscated) and thus the obfuscation algorithm can use the property of the circuit pair. We first construct a public-coin differing-inputs obfuscator for a class of new defined function with iO and point obfuscation with auxiliary input (AIPO). And then we use it to complete the public-coin-dependent diO for any pair of circuits that are hard to be found an input on which their outputs differ. The constructions are based on secure iO schemes for NC^1, fully homomorphic encryption scheme, and the existence of AIPO. Besides, we show the applications of our constructions.

**Category / Keywords: **foundations /

**Date: **received 31 Oct 2018, last revised 15 Nov 2018

**Contact author: **pandongxue at iie ac cn

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

**Version: **20181115:071036 (All versions of this report)

**Short URL: **ia.cr/2018/1055

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