  Secure model aggregation across many users is a key component of federated
learning systems. The state-of-the-art protocols for secure model aggregation,
which are based on additive masking, require all users to quantize their model
updates to the same level of quantization. This severely degrades their
performance due to lack of adaptation to available bandwidth at different
users. We propose three schemes that allow secure model aggregation while using
heterogeneous quantization. This enables the users to adjust their quantization
proportional to their available bandwidth, which can provide a substantially
better trade-off between the accuracy of training and the communication time.
The proposed schemes are based on a grouping strategy by partitioning the
network into groups, and partitioning the local model updates of users into
segments. Instead of applying aggregation protocol to the entire local model
update vector, it is applied on segments with specific coordination between
users. We theoretically evaluate the quantization error for our schemes, and
also demonstrate how our schemes can be utilized to overcome Byzantine users.
