feat: integrate semaphore circuit

[khayss]

Description

This PR implements a zero-knowledge proof circuit for Semaphore using the BabyJubjub curve.

Changes Made

• Added base Semaphore circuit template with configurable Merkle tree depth
• Implemented secret validation against BabyJubjub curve order
• Added identity commitment generation using Poseidon hash
• Integrated BabyJubjub point generation from secret
• Added Merkle proof verification
• Implemented nullifier generation for unique proofs

Related Issues

Closes #16

[khayss]

@evgongora Kindly review. This is what I came up with. I'll be waiting for your review and suggestions.

[evgongora]

Hey @khayss part of what we need right now is to adjust the circuit to be handled in bls12_381, we understand there might need to be some changes on the companion curve so this won't work for now, mind if we leave research instead with a separate issue?

[evgongora]

Awesme job from your part!

[khayss]

Hey @khayss part of what we need right now is to adjust the circuit to be handled in bls12_381, we understand there might need to be some changes on the companion curve so this won't work for now, mind if we leave research instead with a separate issue?

Sure. A separate issue can be created for the research. I tried spotting as many areas that won't work with stellar but later agreed as well that it should be a separate issue with lot of consideration so I went with this basic one.
Thank you

[khayss]

@evgongora Is there anything else you'll like me to add so this PR can be ready for review and possible merge.

[evgongora]

Hey @khayss here is the issue for the doc. Will leave this as a draft
ZencypherSolutions/semaphore-stellar-docs#15

[khayss]

Should I apply for the docs issue? Also, will this be a draft pending the completion of the docs issue?

[evgongora]

Should I apply for the docs issue? Also, will this be a draft pending the completion of the docs issue?

We need to be sure how this is going to be leveraged so let's work on the docs issue for now, go ahead and apply if you want to continue with the issue :)

[khayss]

Okay. Thank you for the update