Abstract: We consider vertical logistic regression (VLR) trained with mini-batch gradient descent -- a setting which has attracted growing interest among industries and proven to be useful in a wide range of applications including finance and medical research. We provide a comprehensive and rigorous privacy analysis of VLR in a class of open-source Federated Learning frameworks, where the protocols might differ between one another, yet a procedure of obtaining local gradients is implicitly shared. We first consider the honest-but-curious threat model, in which the detailed implementation of protocol is neglected and only the shared procedure is assumed, which we abstract as an oracle. We find that even under this general setting, single-dimension feature and label can still be recovered from the other party under suitable constraints of batch size, thus demonstrating the potential vulnerability of all frameworks following the same philosophy. Then we look into a popular instantiation of the protocol based on Homomorphic Encryption (HE).