Black-Box Crypto is Useless for Pseudorandom Codes

A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant rate of random errors cannot be based on black-box reductions to almost any generic cryptographic primitive: for instance, anything that can be built from random oracles, generic multilinear groups, and virtual black-box obfuscation. Our result is optimal, as Ghentiyala and Guruswami (2024) observed that pseudorandom codes tolerating any sub-constant rate of random errors exist using a black-box reduction from one-way functions.