  In the seller-buyer setting on machine learning models, the seller generates
different copies based on the original model and distributes them to different
buyers, such that adversarial samples generated on one buyer's copy would
likely not work on other copies. A known approach achieves this using
attractor-based rewriter which injects different attractors to different
copies. This induces different adversarial regions in different copies, making
adversarial samples generated on one copy not replicable on others. In this
paper, we focus on a scenario where multiple malicious buyers collude to
attack. We first give two formulations and conduct empirical studies to analyze
effectiveness of collusion attack under different assumptions on the attacker's
capabilities and properties of the attractors. We observe that existing
attractor-based methods do not effectively mislead the colluders in the sense
that adversarial samples found are influenced more by the original model
instead of the attractors as number of colluders increases. Based on this
observation, we propose using adaptive attractors whose weight is guided by a
U-shape curve to cover the shortfalls. Experimentation results show that when
using our approach, the attack success rate of a collusion attack converges to
around 15% even when lots of copies are applied for collusion. In contrast,
when using the existing attractor-based rewriter with fixed weight, the attack
success rate increases linearly with the number of copies used for collusion.
