Paper 2026/1184

Public-Key Pseudorandom Codes from Distorted McEliece Assumptions

Abstract

Pseudorandom codes (PRCs), introduced at Crypto 2024 by Christ and Gunn, are encryption schemes with pseudorandom ciphertexts and error-correction guarantees. PRCs are useful as a tool to obtain watermarking for generative models, in particular ensuring that a watermark is hard to remove against an attacker that can modify up to a given fraction of the watermarked output (a.k.a. the robustness property). A PRC is public-key if the encoding procedure is public (whereas detection requires the corresponding secret key). In this paper, we provide the first construction of public-key PRCs for the binary alphabet satisfying robustness in the presence of a constant fraction of substitutions ($1/6 - \varepsilon$, for arbitrary $\varepsilon > 0$) and at the same time achieving pseudorandomness against sub-exponential-time distinguishers. The pseudorandomness property relies on a new family of distorted McEliece assumptions that we introduce, instantiated with a class of expanded subcodes of Reed-Solomon codes, called Raw Reed-Solomon codes, for which we provide heuristic evidence of (plausible) sub-exponential hardness. Our construction is obtained by revisiting the original blueprint by Christ and Gunn to obtain public-key PRCs based on McEliece assumptions. Along the way, we also uncover that their blueprint does not work directly with Raw Reed-Solomon codes. In particular, we show that a generating matrix of a permuted Raw Reed-Solomon code is distinguishable in polynomial time from a uniformly random generating matrix. To circumvent that difficulty, we propose to distort the public key by multiplication with a sparse invertible matrix of constant row Hamming weight.

Note: Adding multi-bit construction