RMCW: A Deletion-Robust Watermark Based on Reed--Muller Codes for Language Models

Abstract:Large Language Model (LLM) watermarking provides a lightweight mechanism for identifying text generated by a specific model, but its robustness remains fragile under post-processing attacks. Deletion attacks are particularly challenging because they shift token positions and break the alignment between observed tokens and their original watermark positions. We propose Reed--Muller Code Watermarking (RMCW), an LLM watermarking method based on Reed--Muller codes. In contrast to global codeword recovery, RMCW searches for surviving local algebraic structure, leveraging the Reed--Solomon consistency induced by affine-line restrictions of Reed--Muller codewords. During generation, RMCW injects a Reed--Muller structure into the sequence via a secret-keyed vocabulary partition. During detection, it maps the given text to keyed vocabulary bins and tests local subsequences for low-degree Reed--Solomon consistency using Berlekamp--Welch tests. Experiments on C4 and ELI5 datasets with OPT-1.3B and Llama-3.1-8B-Instruct show that RMCW preserves strong clean-text detectability and outperforms or matches the baseline methods under several deletion and rewriting attacks. Our code is available at this https URL.

Cryptography and Security (cs.CR); Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2610.02817 [cs.CR]

(or arXiv:2610.02817v1 [cs.CR] for this version)

https://doi.org/10.48550/arXiv.2610.02817 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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