LLM-Text Watermarking based on Lagrange Interpolation

2025-05-09

AI Summary

Existing text watermarking methods struggle to reliably attribute large language model (LLM)-generated content—especially under strong adversarial edits such as rewriting or aggressive truncation. To address this, we propose a novel text watermarking scheme based on Lagrange interpolation, the first to leverage this mathematical framework for textual watermarking. Our method embeds a sequence of collinear points into the text, enabling unique recovery of the author identifier from as few as three residual points. It integrates pseudorandom sequences (LFSR/NFSR), implicit text-level coordinate encoding, and a tamper-resilient decoding mechanism to significantly enhance robustness. Experiments demonstrate near-perfect author identification accuracy (>99%) even when 90% of the watermarked text is maliciously altered or deleted—substantially outperforming state-of-the-art approaches. This work provides an efficient, reliable solution for copyright protection and provenance tracing of LLM-generated content.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

The rapid advancement of LLMs (Large Language Models) has established them as a foundational technology for many AI and ML powered human computer interactions. A critical challenge in this context is the attribution of LLM-generated text, either to the specific language model used or to the individual user who generated it. This is essential for combating misinformation, fake news, misinterpretation, and plagiarism. One of the key techniques for addressing this issue is watermarking. This work presents a watermarking scheme for LLM-generated text based on Lagrange interpolation, which enables the recovery of a secret author identity even when the text has been heavily redacted by an adversary. The core idea is to embed a continuous sequence of points (x, f(x)) that lie on a single straight line. The x-coordinates are generated pseudorandomly using either an LFSR (when security is not a priority) or a cryptographically secure NFSR for high-security applications. The scheme efficiency and resilience to adversarial modifications are analysed. Experimental results show that the proposed method is highly effective, allowing the recovery of the author identity when as few as three points survive adversarial manipulation.

Problem

• Attribution of LLM-generated text to specific models or users
• Combating misinformation and plagiarism via watermarking
• Recovering secret author identity from heavily redacted text

Innovation

• Uses Lagrange interpolation for watermarking
• Embeds secret identity via straight line points
• Supports LFSR or NFSR for coordinate generation