`ift:2025q2-zerokit:semaphore-parts-bench` Tracking issue

[Ben-PH]

Roadmap Reference

task text

### Description

Semaphore is a zero-knowledge protocol
that allows users to prove membership in a group without revealing their identity.
This enables anonymous messaging, voting, and other privacy-preserving applications.
In this task, we aim to evaluate whether replacing the current zero-knowledge proof system makes sense.
To begin, we will focus on two areas of research:

1. Compare the light-poseidon library
   with our current Poseidon hash implementation

   • Verify whether the parameters used are the same
   • Prepare performance benchmarks

2. Evaluate the efficiency of the lean-imt Merkle tree
   versus our current Merkle tree implementation

   • Focus on tree initialization, leaf insertion, proof generation, and proof verification

3. Compare the zero-knowledge proof systems themselves

• Once we understand the relative performance of Poseidon and Merkle tree implementations,
  evaluate the zk-proof construction step
• Assess the performance and complexity of generating and verifying proofs
  using the current system versus potential alternatives

For context, see our previous investigation into Semaphore usage in Zerokit:
Semaphore README in Zerokit branch

Deliverables

Submit either a pull request or a comment on this issue
in the Zerokit repository that includes:

• Benchmark results for both the Poseidon hash and the Merkle tree implementations
• A summary of findings, including whether it makes sense to proceed
  with evaluating alternative zk-proof systems based on the current efficiency data

• Benchmark PR: Benchmark current internal impl of poseidon + external available impls #305
• evaluate efficiency of lean-imt Merkle tree
• compare the zk proof systems themselves

Benchmark report can be found as a comment in issue #17

benchmarks can be found at #305 (cargo bench --bench poseidon_benchmark) and #308 (cargo bench --bench imt_benchy)