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.Category / Keywords: foundations / correlation-secure hash functions, hardcore functions, indistinguishability obfuscation, differing-inputs obfuscation, point-function obfuscation, auxiliary-input obfuscation, universal computational extractors (UCEs) Date: received 28 May 2014, last revised 28 May 2014 Contact author: arno mittelbach at cased de Available format(s): PDF | BibTeX Citation Version: 20140528:164103 (All versions of this report) Discussion forum: Show discussion | Start new discussion