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Indistinguishability Obfuscation vs. Auxiliary-Input Extractable Functions: One Must Fall

We show that if there exist indistinguishability obfuscators for all circuits then there do not exist auxiliary-input extractable one-way functions. In particular, the knowledge of exponent assumption with respect to adversaries with auxiliary input is false in any group where computing discrete logarithms is intractable. The proof uses the “punctured programs” technique of [Sahai-Waters 2013].