Pseudorandom Obfuscation and Applications

We introduce the notion of pseudorandom obfuscation, a way to obfuscate (keyed) pseudorandom functions $f_K$ in an average-case sense. We study several variants of pseudorandom obfuscation and show a number of applications.

1. Applications in the iO World: Our weakest variant of pseudorandom obfuscation, named obfuscation for identical pseudorandom functions (iPRO), is weaker than indistinguishability obfuscation (iO): rather than obfuscating arbitrary circuits as in iO, iPRO only obfuscates circuits computing pseudorandom functions. We show that iPRO already enables several applications of iO, such as unleveled fully homomorphic encryption (without assuming circular security) and succinct randomized encodings.

2. From iPRO to iO: Despite being a weaker notion than iO, we show two transformations from iPRO to iO. Our first (and main) construction builds iO from iPRO plus standard assumptions on cryptographic bilinear maps. Our second construction builds iO, and even ideal obfuscation, from iPRO alone in the pseudorandom oracle model (Jain, Lin, Luo and Wichs, CRYPTO 2023).

We also formulate stronger variants of pseudorandom obfuscation that help us go beyond the applications of indistinguishability obfuscation.

3. Applications outside the iO World: We show how to construct a succinct witness encryption scheme from a strong version of PRO, where the size of the ciphertext is independent of the witness size. Such a witness encryption scheme is not known to exist even assuming iO.

4. Construction: We show a heuristic construction of the strongest version of PRO, secure under the sub-exponential hardness of the learning with errors (LWE) problem, and the private-coin evasive LWE heuristic (Wee, EUROCRYPT 2022; Tsabary, CRYPTO 2022).

Finally, we highlight some barriers in achieving the strongest version of pseudorandom obfuscation.