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.
CITATION STYLE
Bellare, M., Stepanovs, I., & Tessaro, S. (2014). Poly-many hardcore bits for any one-way function and a framework for differing-inputs obfuscation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8874, pp. 102–121). Springer Verlag. https://doi.org/10.1007/978-3-662-45608-8_6
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