mukeshtiwari/SigmaProtocol ? reverse-engineered prompt

Build me this Rocq project for formalizing Schnorr style sigma protocols and related crypto proofs.

I want a codebase that can verify the main zero knowledge proof examples, including the basic sigma protocol, AND, OR, parallel sigma, equality proof, encryption proof, and the ElGamal and approval voting examples. It should compile with dune, and I should be able to run the demo executables from the command line and see the proofs and verification results printed out like in the README.

Please keep the formal proofs working in Rocq, and make sure the examples build cleanly. If you need to, look up current Rocq or dune docs online. If there are long proof steps that make the build too slow, keep the project usable and let me know the fastest way to compile the demos.