Home > Sigma Proofs
Sigma Proofs¶
Proofs expressed directly as algebraic relations over a group: commitment schemes, Sigma protocols and their composition. This is the proof family behind BBS/CL/PS anonymous credentials. Commit-and-prove constructions bridge Sigma proofs and circuit-based proofs.
Contents¶
| Note | Description |
|---|---|
| Pedersen Commitments | Hiding and binding commitment scheme based on discrete log (1991) |
| Camenisch-Michels Safe Primes | Efficient proofs of knowledge over RSA-group elements (1999) |
| Proof Systems for DL | Camenisch/Stadler framework for discrete-log-based proofs (1997) |
| Sigma Protocols (Damgard) | Formal treatment of 3-move honest-verifier ZK proofs (2010) |
| Sigma Protocols (Proposal) | Krenn et al. compositional sigma-protocol proposal (2021) |
| ZKAttest | ZK attestation using ECDSA / secp256k1 (2022) |
| LegoGroth16 | Commit-and-prove Groth16 (LegoSNARK): bridges committed values between Sigma proofs and circuits |
| Docknetwork | Rust crypto library; includes BBS+ signatures and ZK credential primitives |
Commit-and-prove: bridging Sigma proofs and circuits¶
A commit-and-prove construction lets a Sigma proof and a circuit proof share a witness through a commitment, so each part is proven with the system that suits it (ZK-Proof-Taxonomy). Examples: LegoGroth16 (CFQW19-LegoSNARK), proving Sigma statements inside circuits cheaply (KMN23-Sigmabus), moving expensive operations out of the circuit (OKMZ25-Beyond-Circuit), and linking a BBS credential to an ECDSA device signature (Holder-Binding). The IRTF draft IRTF-CFRG-Sigma-Protocols standardises the Sigma-protocol layer.