mini-SNARK is a simple implementation of zk-SNARK protocol. It's implemented in Python and the only external dependency is py-ecc from the Ethereum foundation. I wanted something simpler and easier to understand than the babySNARK. And the goal is to keep the code as simple as possible.

• field.py: Implementation of finite field arithmetic and polynomial.
• bls12.py: A symmetric adaptation of the BLS12-381 curve.

The BLS12 code is from the babySNARK repo. Also, I took the field.py partially from the stark101 tutorial repo with some modifications.

KZG is one PCS that is commonly used. I've implemented two versions.

• kzg-simple.py: A simplified KZG PCS implementation.
• kzg.py: A reusable implementation of KZG PCS.

The detailed explanation of their implementation is in docs/kzg.md.

Complete examples combining PCS with a simple circuit:

• example-single-op.py: A single operation circuit example.
• example-single-op-optimized.py: An optimized version of the example above.

The detailed explanation of their implementation is in docs/example.md.

• ZK Whiteboard lectures by Dan Boneh (2022 Aug)
• "Why and how zk-SNARK works" (2019) by Maksym Petkus (2019)