# Reading Between the Lines: Towards Reliable Black-box LLM Fingerprinting via Zeroth-order Gradient Estimation

arXiv: https://arxiv.org/abs/2510.06605 · HTML: https://mlsanity.com/paper/2510.06605/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2025.

## Abstract (arXiv)

The substantial investment required to develop Large Language Models (LLMs) makes them valuable intellectual property, raising significant concerns about copyright protection. LLM fingerprinting has emerged as a key technique to address this, which aims to verify a model's origin by extracting an intrinsic, unique signature (a "fingerprint") and comparing it to that of a source model to identify illicit copies. However, existing black-box fingerprinting methods often fail to generate distinctive LLM fingerprints. This ineffectiveness arises because black-box methods typically rely on model outputs, which lose critical information about the model's unique parameters due to the usage of non-linear functions. To address this, we first leverage Fisher Information Theory to formally demonstrate that the gradient of the model's input is a more informative feature for fingerprinting than the output. Based on this insight, we propose ZeroPrint, a novel method that approximates these information-rich gradients in a black-box setting using zeroth-order estimation. ZeroPrint overcomes the challenge of applying this to discrete text by simulating input perturbations via semantic-preserving word substitutions. This operation allows ZeroPrint to estimate the model's Jacobian matrix as a unique fingerprint. Experiments on the standard benchmark show ZeroPrint achieves a state-of-the-art effectiveness and robustness, significantly outperforming existing black-box methods.