### Using Indistinguishability Obfuscation via UCEs

Chris Brzuska and Arno Mittelbach

##### Abstract

We provide the first standard model construction for a powerful class of Universal Computational Extractors (UCEs; Bellare et al. Crypto 2013) based on indistinguishability obfuscation. Our construction suffices to instantiate correlation-secure hash functions and universal one-way functions. For many cryptographic primitives and in particular for correlation-secure hash functions all known constructions are in the random-oracle model. Indeed, recent negative results by Wichs (ITCS 2013) rule out a large class of techniques to prove the security of correlation-secure hash functions in the standard model. Our construction is based on puncturable PRFs (Sahai und Waters; STOC 2014) and indistinguishability obfuscation. However, our proof also relies on point obfuscation under auxiliary inputs (AIPO). This is crucial in light of Wichs' impossibility result. Namely, Wichs proves that it is often hard to reduce two-stage games (such as UCEs) to a "one-stage assumption" such as DDH. In contrast, AIPOs and their underlying assumptions are inherently two-stage and, thus, allow us to circumvent Wichs' impossibility result. Our positive result is also noteworthy insofar as Brzuska, Farshim and Mittelbach (Crypto 2014) have shown recently, that iO and some variants of UCEs are mutually exclusive. Our results, hence, validate some of the new UCE notions that emerged as a response to the iO-attack.

Available format(s)
Category
Foundations
Publication info
A minor revision of an IACR publication in ASIACRYPT 2014
Keywords
correlation-secure hash functionshardcore functionsindistinguishability obfuscationdiffering-inputs obfuscationpoint-function obfuscationauxiliary-input obfuscationuniversal computational extractors (UCEs)
Contact author(s)
arno mittelbach @ cased de
History
2015-06-11: revised
See all versions
Short URL
https://ia.cr/2014/381

CC BY

BibTeX

@misc{cryptoeprint:2014/381,
author = {Chris Brzuska and Arno Mittelbach},
title = {Using Indistinguishability Obfuscation via UCEs},
howpublished = {Cryptology ePrint Archive, Paper 2014/381},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/381}},
url = {https://eprint.iacr.org/2014/381}
}

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