Indistinguishability Obfuscation for All Circuits from Secret-Key Functional Encryption

We show that indistinguishability obfuscation (IO) for all circuits can be constructed solely from secret-key functional encryption (SKFE). In the construction, SKFE need to be able to issue a-priori unbounded number of functional keys, that is, collusion-resistant. Our strategy is to replace public-key functional encryption (PKFE) in the construction of IO proposed by Bitansky and Vaikuntanathan (FOCS 2015) with puncturable SKFE. Bitansky and Vaikuntanathan introduced the notion of puncturable SKFE and observed that the strategy works. However, it has not been clear whether we can construct puncturable SKFE without assuming PKFE. In particular, it has not been known whether puncturable SKFE is constructed from ordinary SKFE. In this work, we show that a relaxed variant of puncturable SKFE can be constructed from collusion-resistant SKFE. Moreover, we show that the relaxed variant of puncturable SKFE is sufficient for constructing IO.

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