It probably doesn't help you, because it requires complex deployment and
is not open-source, but I thought that it might be interesting to know
that there is a multi-prime RSA based technology that is actively used in
practice.
It is used for mobile authentication and digital signatures and has ~2.7M
active users.
Keys are generated in a distributed manner and no secrets are shared
between the parties during the process. Signature creation is also an
interactive process that implements several additional protection measures
to pass the Common Criteria evaluation at EAL4+ level.
In EU this technology can be used to create qualified digital signatures.
There is a whitepaper available at
https://cyber.ee/products/digital-identity/materials/splitkey-whitepaper.pdf
Arne
