伪随机纠错码
Pseudorandom Error-Correcting Codes
AI总结：
本文构造基于 LPN 等标准假设的伪随机纠错码，可容忍替换与删除，并据此提出抗恒定错误率的不可检测语言模型水印及可证明安全的无状态隐写方案。
摘要：
我们构造了伪随机纠错码（或简称伪随机码），这类纠错码具有如下性质：任意多项式数量的码字，对于任何计算能力受限的敌手而言都是伪随机的。借助解码密钥，可以高效解码被损坏的码字。\n我们构建了对替换错误和删除错误具有鲁棒性的伪随机码，其中伪随机性建立在标准密码学假设之上。具体而言，伪随机性基于 LPN 的 $2^{O(\sqrt{n})}$-困难性，或者基于 LPN 的多项式困难性以及低密度下的植入 XOR 问题。\n作为伪随机码的主要应用，我们提出了一种用于语言模型输出的不可检测水印方案，该方案对裁剪以及恒定速率的随机替换和删除具有鲁棒性。该水印是不可检测的，即任意数量的带水印文本样本，都与原始模型输出的文本在计算上不可区分。这是首个能够容忍恒定速率错误的不可检测水印方案。\n我们的第二个应用是隐写术，即将秘密消息隐藏在看似无害的内容中。我们提出了一种恒定速率的无状态隐写方案，对恒定速率的替换具有鲁棒性。我们的方案是首个具备可证明隐写安全性且对错误具有任意鲁棒性的无状态隐写方案。
英文摘要：
We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient decoding of corrupted codewords is possible with the help of a decoding key. We build pseudorandom codes that are robust to substitution and deletion errors, where pseudorandomness rests on standard cryptographic assumptions. Specifically, pseudorandomness is based on either $2^{O(\sqrt{n})}$-hardness of LPN, or polynomial hardness of LPN and the planted XOR problem at low density. As our primary application of pseudorandom codes, we present an undetectable watermarking scheme for outputs of language models that is robust to cropping and a constant rate of random substitutions and deletions. The watermark is undetectable in the sense that any number of samples of watermarked text are computationally indistinguishable from text output by the original model. This is the first undetectable watermarking scheme that can tolerate a constant rate of errors. Our second application is to steganography, where a secret message is hidden in innocent-looking content. We present a constant-rate stateless steganography scheme with robustness to a constant rate of substitutions. Ours is the first stateless steganography scheme with provable steganographic security and any robustness to errors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
