  Federated learning allows multiple participants to conduct joint modeling
without disclosing their local data. Vertical federated learning (VFL) handles
the situation where participants share the same ID space and different feature
spaces. In most VFL frameworks, to protect the security and privacy of the
participants' local data, a third party is needed to generate homomorphic
encryption key pairs and perform decryption operations. In this way, the third
party is granted the right to decrypt information related to model parameters.
However, it isn't easy to find such a credible entity in the real world.
Existing methods for solving this problem are either communication-intensive or
unsuitable for multi-party scenarios. By combining secret sharing and
homomorphic encryption, we propose a novel VFL framework without a third party
called EFMVFL, which supports flexible expansion to multiple participants with
low communication overhead and is applicable to generalized linear models. We
give instantiations of our framework under logistic regression and Poisson
regression. Theoretical analysis and experiments show that our framework is
secure, more efficient, and easy to be extended to multiple participants.
