Stealing Watermarks of Large Language Models via Mixed Integer Programming

The Large Language Model (LLM) watermark is a newly emerging technique that shows promise in addressing concerns surrounding LLM copyright, monitoring AI-generated text, and preventing its misuse. The LLM watermark scheme commonly includes generating secret keys to partition the vocabulary into green and red lists, applying a perturbation to the logits of tokens in the green list to increase their sampling likelihood, thus facilitating watermark detection to identify AI-generated text if the proportion of green tokens exceeds a threshold. However, recent research indicates that watermarking methods using numerous keys are susceptible to removal attacks, such as token editing, synonym substitution, and paraphrasing, with robustness declining as the number of keys increases. Therefore, the state-of-the-art watermark schemes that employ fewer or single keys have been demonstrated to be more robust against text editing and paraphrasing. In this paper, we propose a novel green list stealing attack against the state-of-the-art LLM watermark scheme and systematically examine its vulnerability to this attack. We formalize the attack as a mixed integer programming problem with constraints. We evaluate our attack under a comprehensive threat model, including an extreme scenario where the attacker has no prior knowledge, lacks access to the watermark detector API, and possesses no information about the LLM’s parameter settings or watermark injection/detection scheme. Extensive experiments on LLMs, such as OPT and LLaMA, demonstrate that our attack can successfully steal the green list and remove the watermark across all settings.