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Cooperative RSA signing

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Is there someway to modify the key shards to work with hardware tokens that expect CRT parameters or primes? Or are there hardware tokens that can operate on the (n,e,d)...

Is there any danger of private shards leaking their (non-prime) d values in the signed output?

help wanted

There are lots of papers on using oblivious transfer or other mechanisms to generate the private key so that it never lives in one place. An example protocol: https://medium.com/@benny.pinkas/fast-distributed-rsa-key-generation-against-malicious-adversaries-faaaab96821d >...

enhancement
help wanted