Too many FROST types called shares

[nickfarrow]

I think we need clearer distinction between:

• Keygen shares
• Long lived secret shares

And possibly later,

• Shamir secret shares of keygen shares (for issuing new signers with cooperation from just t participants instead of N)

[LLFourn]

They are all shares. Just prefix with keychain_shares. signing_shares.

[nickfarrow]

Current thoughts:

Keygen Share - commitment polynomial evaluations shared during keygen to form a Secret Keyshare. Secret Keyshare or Secret Share - long lived secret share of the FROST key, a point on the joint polynomial at some participant index. Partial signature - partial signatures that need to be combined in order to form a complete Schnorr signature.

Keyshare Fragment (not implemented) - Shamir secret shares of a Secret Keyshare. Core Shares -> Public Polynomial Defining Points (not implemented) - A set of T points which define the image of the joint polynomial.

[nickfarrow]

See discussion: https://github.com/BlockstreamResearch/bip-frost-dkg/pull/23