High-Rate Public-Key Pseudorandom Codes for Edit Errors
Shengtang Huang, Xin Li, Songtao Mao, Zhaienhe Zhou

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…
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