Cryptology ePrint Archive: Report 2013/873

Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation

Mihir Bellare and Igors Stepanovs and Stefano Tessaro

Abstract: We show how to extract an arbitrary polynomial number of simultaneously hardcore bits from any one-way function. In the case the one-way function is injective or has polynomially-bounded pre-image size, we assume the existence of indistinguishability obfuscation (iO). In the general case, we assume the existence of differing-input obfuscation (diO), but of a form weaker than full auxiliary-input diO. Our construction for injective one-way functions extends to extract hardcore bits on multiple, correlated inputs, yielding new D-PKE schemes. Of independent interest is a definitional framework for differing-inputs obfuscation in which security is parameterized by circuit-sampler classes.

Category / Keywords: foundations / Hardcore predicates, indistinguishability obfuscation, one-way functions.

Original Publication (with minor differences): IACR-ASIACRYPT-2014

Date: received 27 Dec 2013, last revised 14 Sep 2014

Contact author: mihir at eng ucsd edu

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Version: 20140915:003039 (All versions of this report)

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