notes.md

Core Algorithm:

1. Each participant initiates key generation:
   • keygen_begin
     • Calls generate_shares internally
     • Calls generate_dkg_challenge internally
2. Participants exchange commitments and validate peers:
   • keygen_receive_commitments_and_validate_peers
     • Calls generate_dkg_challenge internally
     • Calls is_valid_zkp internally
3. Participants finalize their keys:
   • keygen_finalize
     • Calls verify_share internally for each received share

So the complete call sequence for a participant would be:

1. keygen_begin → generate_shares → generate_dkg_challenge
2. keygen_receive_commitments_and_validate_peers → is_valid_zkp → generate_dkg_challenge
3. keygen_finalize → verify_share

• First, implement the low-level primitives:
  • generateDkgChallenge (fundamental for proofs)
  • Helper functions for scalar operations
  • Helper functions for polynomial evaluation
• Next, implement the key share generation core:
  • generateShares (builds on polynomial operations)
  • verifyShare (relies on share generation logic)
• Then build the proof validation:
  • isValidZkp (needed for commitment verification)
• Implement the main protocol functions in this order:
  • keygenBegin (initiates the DKG process)
  • keygenReceiveCommitmentsAndValidatePeers (handles verification)
  • keygenFinalize (completes the process)
• Finally, implement the optional dealer-based function:
  • keygenWithDealer (uses components from above)