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 construc- tion for injective one-way functions extends to extract hardcore bits on multiple, correlated inputs, yielding new D-PKE schemes. Of indepen- dent interest is a definitional framework for differing-inputs obfuscation in which security is parameterized by circuit-sampler classes.
['Mihir Bellare', 'Igors Stepanovs', 'Stefano Tessaro']
Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation