New Semaphore v4 circuits

[cedoor]

Description

This PR updates the Semaphore circuit based on the findings from the analysis and research period described in the research repository. The main changes include:

• The identity trapdoor and identity nullifier have been replaced with a single value, the private key, from which an EdDSA public key is derived. The Poseidon hash of the public key is the new identity commitment.
• Some input and output names in the circuits have been changed.
  • External Nullifier → Scope
  • SignalHash → Message
  • NullifierHash → Nullifier
  • Siblings → Tree Siblings
  • Path Indices → Tree Indices
• The new circuit uses Anonymous Components to make the code clearer and more concise (24 lines of code without comments, rather than 90).
• The circuit used to calculate the Merkle tree root is now part of an external package (@zk-kit/circuits - BinaryMerkleRoot) and supports dynamic depths.

Related Issue

#357

Does this introduce a breaking change?

• Yes
• No