Home > ZKPs
Zero-Knowledge Proofs¶
A zero-knowledge proof lets a prover convince a verifier that a statement is true without revealing anything beyond its truth: that they know a secret key, that a hidden value lies in a range, or that a program ran correctly on private inputs. Since the first definitions in the 1980s, ZKPs have gone from a theoretical curiosity to practical systems, driven by succinct proofs (SNARKs and STARKs) and their use in blockchains. Today they are used for private payments (Zcash, Monero), blockchain scaling (zk-rollups, zkEVMs), verifiable computation, and privacy-preserving identity — for example to show that a credential carries a valid issuer signature and its holder is over 18, without showing the credential.
This tab goes from the theory to concrete proof systems and tools, and then to their use for anonymous credentials in e-ID.
Foundations¶
The theory behind zero-knowledge proofs, in Foundations: the interactive proof model and the papers that defined zero knowledge (GMR85, NIZK, Fiat–Shamir); complexity results (IP = PSPACE, PCP, IOP); the tools modern SNARKs are built from (Schwartz–Zippel, Kilian, Merkle and BCS, MPC-in-the-head); and pairing-friendly curves. ZK Families Overview compares SNARKs, STARKs, Bulletproofs and others, including trusted setup and security assumptions.
ZKP Families¶
Proof systems fall into three families, by how the statement is expressed (ZK-Proof-Taxonomy). The next three sections cover one family each.
| Family | Statement expressed as… | Typical use |
|---|---|---|
| Sigma proofs | Algebraic relations over a group (discrete log, commitments) | BBS / CL / PS anonymous credentials |
| Circuit-based proofs | Arithmetic circuit / constraint system | Proofs over existing ECDSA credentials (Longfellow, Crescent, our Spartan backend) |
| zkVMs | Execution trace of an arbitrary program | General verifiable computation |
Sigma Proofs¶
Proofs written directly as algebraic relations, in Sigma Proofs: Pedersen commitments, Sigma protocols and their standardisation, proofs about discrete logarithms and committed integers, and ZKAttest for proofs about ECDSA keys. Commit-and-prove constructions such as LegoGroth16 bridge Sigma proofs and circuits. Docknetwork is the library we used for BBS-based credentials.
Circuit-Based Proofs¶
General-purpose proofs over arithmetic circuits, in three parts. Proof Systems goes from early SNARKs (Pinocchio, Groth16) through the PLONK family and transparent systems (FRI, zk-STARKs, Bulletproofs, Ligero, Spartan) to the ECDSA-credential systems Crescent and Longfellow. Intermediate Representations explains what circuits compile to: R1CS, AIR, PLONKish, CCS and Noir's ACIR. Circuit Tooling covers the languages and libraries to write them: Noir, Circom, gnark, Halo2, Barretenberg and others.
zkVMs¶
zkVMs prove the execution of ordinary programs compiled to an instruction set such as RISC-V, instead of hand-written circuits. The concept note compares them with circuit DSLs; entries cover RISC Zero, SP1, OpenVM, Pico, Valida and Powdr. Many target verifiable computation and are not zero-knowledge by default.
Anonymous Credentials¶
How to use these proofs for e-ID, in Anonymous Credentials, based on the Bormann–Lehmann SoK: the two families (multi-message signatures with Sigma proofs vs. general-purpose ZKPs over ECDSA) and the features they enable. Notes cover selective disclosure, unlinkable credentials, pairing-free credentials, holder binding, predicate proofs, revocation with signed lists and PIR, performance on phones and post-quantum security.
Choosing, Auditing and Reading¶
Practical guides across all families. The Framework Decision Guide compares Noir, Circom, gnark, RISC Zero, Docknetwork, Ligero, Halo2 and Spartan for e-ID credential proofs, and lists what to check in any candidate. Soundness Bugs and Audits covers what goes wrong in practice — under-constrained circuits, Fiat–Shamir mistakes, the Longfellow review findings — and links our external security review. ZKP Papers ranks the vault's ZKP papers by citations into foundation, relevant and other papers.