Ring Proof Specification

This document describes a cryptographic scheme based on SNARKs (Succinct Non-Interactive Arguments of Knowledge) that enables a prover to demonstrate knowledge of a secret scalar $t$ and a secret index $k$ within a group of public keys, where each public key is a point on an elliptic curve. The scheme ensures that, when combined with a public elliptic curve point $H$, the relation $R = PK_k + t·H$ is satisfied. It leverages elliptic curve operations, a polynomial commitment scheme, and the Fiat-Shamir heuristic to achieve non-interactivity and zero-knowledge properties.

Acknowledgements

This specification is primarily derived from Sergey Vasilyev's original writeup and reference implementation, as cited in the references.

References

• These notes on hackmd: https://hackmd.io/@davxy/r1SVPqQc0.
• Sergey Vasilyev original writeup: https://hackmd.io/ulW5nFFpTwClHsD0kusJAA
• W3F reference implementation: https://github.com/w3f/ring-proof