I read the paper on threshold signatures and I thought it would be a fun project -- and immense challenge, since I'm not an expert programmer or cryptographer! -- to try to write a Python module to implement it.

However, one aspect required is deriving shares of a random number (the K value, and also the initial private key) without ever having or revealing the fully constructed value.  They mention this is possible but don't show the protocol for it.

Instead, they reference the paper "A robust threshold elliptic curve digital signature providing a new verifiable secret sharing scheme" by the authors M.H. Ibrahim, I. Ali, I. Ibrahim, and A. El-sawi.  This paper supposedly includes the protocol for JRSS

I cannot find a copy of that paper online, and I was hoping somebody else might be able to find it, or already have it, or simply know the protocol for generating shares of a random value without anybody knowing the random value (aka JRSS).