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.
↧