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Contrastive learning pre-trains an image encoder using a large amount of unlabeled data such that the image encoder can be used as a general-purpose feature extractor for various downstream tasks. In this work, we propose PoisonedEncoder, a data poisoning attack to contrastive learning. In particular, an attacker injects carefully crafted poisoning inputs into the unlabeled pre-training data, such that the downstream classifiers built based on the poisoned encoder for multiple target downstream tasks simultaneously classify attacker-chosen, arbitrary clean inputs as attacker-chosen, arbitrary classes. We formulate our data poisoning attack as a bilevel optimization problem, whose solution is the set of poisoning inputs; and we propose a contrastive-learning-tailored method to approximately solve it. Our evaluation on multiple datasets shows that PoisonedEncoder achieves high attack success rates while maintaining the testing accuracy of the downstream classifiers built upon the poisoned encoder for non-attacker-chosen inputs. We also evaluate five defenses against PoisonedEncoder, including one pre-processing, three in-processing, and one post-processing defenses. Our results show that these defenses can decrease the attack success rate of PoisonedEncoder, but they also sacrifice the utility of the encoder or require a large clean pre-training dataset.