Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits
This addresses a fundamental limitation in cryptography for researchers seeking secure obfuscation methods, showing that quantum approaches do not circumvent classical impossibility results, making it incremental by extending prior work.
The paper tackles the problem of quantum virtual black-box obfuscation of classical circuits, showing that under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant is generally impossible, and it also proves impossibility for classical point functions with dependent classical auxiliary input.
Virtual black-box obfuscation is a strong cryptographic primitive: it encrypts a circuit while maintaining its full input/output functionality. A remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator that obfuscates classical circuits into classical circuits cannot exist. A promising direction that circumvents this impossibility result is to obfuscate classical circuits into quantum states, which would potentially be better capable of hiding information about the obfuscated circuit. We show that, under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant of virtual black-box obfuscation of classical circuits is generally impossible. On the way, we show that under the presence of dependent classical auxiliary input, even the small class of classical point functions cannot be quantum virtual black-box obfuscated.