International Association
for Cryptologic Research

Pseudorandom codes (PRCs) are error-correcting codes with the distinguishing feature that their codewords are computationally indistin- guishable from random strings. Introduced by Christ and Gunn (CRYPTO 2024), PRCs have found applications in areas such as AI watermarking, where both robustness and pseudorandomness are essential. All known constructions of PRCs rely on coding-theoretic hardness assumptions. In this work, we study how inherent the use of coding-theoretic hardness is in the construction of pseudorandom codes. We show that there is no black-box construction of PRCs with binary alpha- bets capable of decoding from a constant fraction of Bernoulli noise from a class of oracles we call local oracles. The class of local oracles includes random oracles and trapdoor permutation oracles, and can be interpreted as a meaningful notion of oracles that are not resilient against noise. Our separation result is cast in the Impagliazzo-Rudich framework and crucially relies on the Bonami-Beckner hypercontractivity theorem on the Boolean hypercube. As a complementary result, we show that PRCs with large alphabets that can tolerate high error rates can indeed be constructed in a black-box man- ner from one-way functions.