Add zk-discrete-log-Proof example over secp256k1 using noir_bigcurve

[cypriansakwa]

Hi @critesjosh

Proposal to Add Example: zk-discrete-log-Proof over secp256k1

Summary:

I propose adding a new example to this repository demonstrating a zero-knowledge proof of knowledge of a discrete logarithm over the secp256k1 elliptic curve using noir_bigcurve. The circuit proves knowledge of a secret scalar ( k ) such that a public point ( Q = k \cdot G ), without revealing ( k ). This showcases Noir's ability to perform real-world elliptic curve operations in zero knowledge using the noir_bigcurve library.

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Why This Is Useful

• Demonstrates a core cryptographic primitive: Zero-knowledge discrete log proof
• Learning resource: Helps developers building privacy-preserving authentication systems
• Bridges Noir with widely-used ECC curves: secp256k1 is used in Bitcoin, Ethereum, etc.

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What the Example Includes

• Noir circuit that:

  • Takes ( G ), ( Q ) as public inputs, and ( k ) as a private input
  • Verifies ( Q = k \cdot G ) on secp256k1

• Unit tests: For both correct and incorrect proofs

• A README.md: Explaining the example, its cryptographic context, and how to run it

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