Compare Rabin and Pederesen DKG and assess how much they differ

[AnomalRoil]

We currently have 2 different folders in our shares/dkg directory:

• pedersen
• rabin

However Rabin is supposed to be implemented the version of Pedersen that was "fixed" in the paper called "Secure Distributed Key Generation for Discrete-Log Based Cryptosystems", but I suspect the Pedersen folder (that was actually ported back from the drand/kyber fork) might be implementing the same scheme.

So, to-do:

• Write some example that use Pedersen
• Write some example that uses Rabin
• Change these to be fully deterministic
• Check if they are somewhat interoperable
• Check if they produce the same values or not
• Compare both codebase to confirm whether or not they are redundant
• If redundant, remove the rabin folder from the codebase

[thehoul]

At first glance, it seems that the dkg/pedersen implements the original DKG implementation proposed by Pedersen and not the revised version published by Rabin.

Based on my research so far, the main difference between Pedersen's original DKG and Rabin's version is the VSS used. Pedersen uses Feldman and Rabin uses a VSS proposed by Pedersen. The implementation in the codebase seems to be using Feldman-VSS suggesting that it is different from the implementation of dkg/rabin.

I want to mention that the implementation of Pedersen in the codebase seems overly complicated. It is over 1000 lines whereas Rabin's is about half of that. There is probably something that could be done about it but I don't know if it is worth the time.