  In federated learning (FL), a set of participants share updates computed on
their local data with an aggregator server that combines updates into a global
model. However, reconciling accuracy with privacy and security is a challenge
to FL. On the one hand, good updates sent by honest participants may reveal
their private local information, whereas poisoned updates sent by malicious
participants may compromise the model's availability and/or integrity. On the
other hand, enhancing privacy via update distortion damages accuracy, whereas
doing so via update aggregation damages security because it does not allow the
server to filter out individual poisoned updates. To tackle the
accuracy-privacy-security conflict, we propose {\em fragmented federated
learning} (FFL), in which participants randomly exchange and mix fragments of
their updates before sending them to the server. To achieve privacy, we design
a lightweight protocol that allows participants to privately exchange and mix
encrypted fragments of their updates so that the server can neither obtain
individual updates nor link them to their originators. To achieve security, we
design a reputation-based defense tailored for FFL that builds trust in
participants and their mixed updates based on the quality of the fragments they
exchange and the mixed updates they send. Since the exchanged fragments'
parameters keep their original coordinates and attackers can be neutralized,
the server can correctly reconstruct a global model from the received mixed
updates without accuracy loss. Experiments on four real data sets show that FFL
can prevent semi-honest servers from mounting privacy attacks, can effectively
counter poisoning attacks and can keep the accuracy of the global model.
