As deep neural networks become fundamental in various fields, protecting these models as valuable assets has become increasingly crucial To achieve this, various neural network fingerprint methods have been proposed. However, the existing approaches often have deficiencies in terms of efficiency, stealthiness, and discriminability. To address these issues, we present GanFinger, which constructs network fingerprints based on network behavior, characterized by the outputs of pairs of original examples and conferrable adversarial examples. Specifically, GanFinger leverages generative adversarial networks (GANs) to effectively generate conferrable adversarial examples with imperceptible perturbations. These examples produce identical outputs on copyrighted networks while yielding different results on irrelevant networks. Moreover, to enhance the accuracy of verification, the network similarity is computed based on the accuracy-robustness distance of fingerprint outputs. To evaluate the performance of GanFinger, we construct a comprehensive benchmark consisting of 186 networks with five network structures and four popular network post-processing techniques. Experiments show that GanFinger significantly outperforms the state-of-the-art in efficiency, stealthiness, and discriminability. It achieves 6.57 times faster fingerprint generation and improves the area under the uniqueness curve by 0.175, resulting in a relative improvement of approximately 26%.