High-Rate Public-Key Pseudorandom Codes for Edit Errors

TL;DR

This paper introduces high-rate public-key pseudorandom codes resilient to edit errors, advancing error correction in small alphabets and establishing new theoretical links between substitution and edit error robustness.

Contribution

It provides the first high-rate public-key binary PRC constructions for edit channels and a reduction from substitution-error PRCs to edit-error PRCs.

Findings

Constructed public-key PRCs with rate close to 1 over large alphabets.

Achieved rate close to 1/2 over binary alphabet.

Attained the Singleton bound for insertion-deletion channels with poly(λ)-sized alphabets.

Abstract

Pseudorandom codes (PRCs), introduced by Christ and Gunn (CRYPTO '2024), are error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings, while still being decodable by someone holding the key. They provide a natural primitive for robust and undetectable watermarking, particularly in applications to AI-generated content. Although recent works have obtained strong results for substitution errors, the edit-error setting remains much less understood, especially in the high-rate regime and over small alphabets. We study public-key pseudorandom codes against edit errors. First, we give a new reduction showing that binary zero-bit PRCs robust against a constant fraction of substitution errors can be transformed into binary zero-bit PRCs robust against edit errors. Consequently, under any assumption that yields zero-bit Hamming-robust PRCs, one also obtains zero-bit PRCs for edit channels, albeit only for the weaker class of sublinear polynomial edit channels, namely channels with edit error rate $1/n^{\gamma}$ for any constant $\gamma>0$. In the high-rate regime, we construct public-key PRCs with rate arbitrarily close to $1$ over sufficiently large constant alphabets, and with rate arbitrarily close to $1/2$ over the binary alphabet. Moreover, if we allow the alphabet size to be $\mathrm{poly}(\lambda)$, where $\lambda$ is the security parameter, then our public-key PRCs can attain the Singleton bound for insertion-deletion channels. Taken together, these results yield the first high-rate public-key binary PRC constructions for edit channels, under the same assumption that yields zero-bit Hamming-robust PRCs.