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.

翻译：伪随机码（PRC）由Christ和Gunn提出（CRYPTO 2024），是一种纠错码，其码字在计算上与均匀随机字符串不可区分，同时持有密钥者仍能对其进行解码。此类码为鲁棒且不可检测的水印技术提供了自然原语，尤其在人工智能生成内容的应用中。尽管近期研究在替代错误场景下取得了重要进展，但编辑错误场景的理解仍较为薄弱，特别是在高码率和小字母表情形下。本文研究针对编辑错误的公钥伪随机码。首先，我们给出一种新的归约方法，证明能抵抗恒定比例替代错误的二进制零比特PRC可转化为能抵抗编辑错误的二进制零比特PRC。因此，在任意能产生零比特汉明鲁棒PRC的假设下，我们同样能获得针对编辑信道的零比特PRC，但仅适用于较弱的次线性多项式编辑信道，即对任意常数γ>0，错误率为1/n^γ的编辑信道。在高码率情形下，我们在足够大的恒定字母表上构造了码率任意接近1的公钥PRC，并在二进制字母表上构造了码率任意接近1/2的公钥PRC。此外，若允许字母表大小为poly(λ)（其中λ为安全参数），则我们的公钥PRC能达到针对插入-删除信道的Singleton界。综合上述结果，我们获得了首个针对编辑信道的高码率公钥二进制PRC构造，其安全性基于与零比特汉明鲁棒PRC相同的假设。