distributed secret key

[Arne Ansper]

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