Title: An Equivalence Between Data Poisoning and Byzantine Gradient Attacks. Abstract: To address the resilience of distributed learning, the ``Byzantine" literature considers a strong threat model where workers can report arbitrary gradients to the parameter server. While this model helped generate several fundamental results, it has however sometimes been considered unrealistic, when the workers are mostly trustworthy machines. In this paper, we show a surprising equivalence between this model and data poisoning, a threat considered much more realistic. More specifically, we prove that any gradient attack can be reduced to data poisoning in a personalized federated learning system that provides PAC guarantees (which we show are both desirable and realistic in various personalized federated learning contexts such as linear regression and classification). Maybe most importantly, we derive a simple and practical attack that may be constructed against classical personalized federated learning models, and we show both theoretically and empirically the effectiveness of this attack.