High-Rate Public-Key Pseudorandom Codes for Edit Errors

2026-05-19

AI Summary

Existing pseudorandom codes struggle to withstand edit errors (insertions and deletions) under high-rate and small-alphabet regimes. This work proposes a novel reduction technique that transforms substitution-error-resilient zero-bit pseudorandom codes into ones resilient to edit errors, yielding the first high-rate binary public-key pseudorandom code. The construction approaches the Singleton bound over polynomial-sized alphabets, achieves rates approaching 1/2 in the binary setting and nearly 1 for large alphabets, and tolerates a sublinear fraction of edit errors—specifically, up to $1/n^\gamma$ for some constant $\gamma > 0$. Under standard cryptographic assumptions, this scheme constitutes the first high-rate public-key pseudorandom code secure against edit errors.

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 $1/n^γ$ for any constant $γ>0$. 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 $\mathrm{poly}(λ)$, where $λ$ 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.

Problem

• pseudorandom codes
• edit errors
• public-key
• high-rate
• error-correcting codes

Innovation

• pseudorandom codes
• edit errors
• public-key cryptography
• high-rate coding
• insertion-deletion channels