index.md

What is a zero-knowledge proof?

• A New Approach To Protecting Secrets Is Discovered - The New York Times, February 17th, 1987
• Zero Knowledge Proofs: An illustrated primer
• What are zk-SNARKs?
• "The Functionality of zk-SNARK" challenge set in "The Hunting of the SNARK".
• "Probabilistic Proof Systems" course notes
• Vitalik Buterin's introduction to SNARKs, part 1, 2, and 3; and STARKs, part 1, 2, and 3.

Zero-knowledge proving systems

• Invention of zero-knowledge
  • ZKP[GMR85]
  • [NIZK[BFM88]]
  • Succinct ZK[K92]
• [GGPR13]
  • Pinocchio [PGHR13]
  • [BCGTV13]
  • Geppetto [CFHKKNPZ14]
  • [BCTV14a]
• [BCTV14b]
  • Coda [MS18]
• [CTV15]
• ZKBoo [GMO16]
• [Groth16]
  • [GM17]
  • [BG18]
• [BCCGP16]
  • Bulletproofs [BBBPWM17]
• Hybrid Interactive ZK [CCM16]
• ZKB++ / Picnic [CDGORRSZ17]
• Ligero [AHIV17]
• Hyrax [WTSTW17]
• zk-STARKs [BBHR18]
• Updatable Universal CRSs [GKMMM18]
• Hybrid NIZK [ACM18]

Implementations of proving systems

• libsnark - C++ library for zk-SNARK proofs
  • [GGPR13] (implements [BCTV14a] approach)
  • [BCTV14b]
  • [CTV15]
• bellman - Rust library for zk-SNARK proofs
  • [Groth16]
• ZKBoo
• ZKB++
• [BCC+16]
  • BulletProofLib - Java implementation (implements Bulletproofs [BBBPWM17] approach)
  • secp256k1-zkp (experimental) - C implementation on secp256k1 (implements Bulletproofs [BBBPWM17] approach)
  • dalek-cryptography/bulletproofs - Rust implementation using Ristretto on Curve25519 (implements Bulletproofs [BBBPWM17] approach) (notes)
  • adjoint-io/bulletproofs - Haskell implementation on secp256k1 (implements Bulletproofs [BBBPWM17] approach)
• Picnic
  • Reference implementation
  • Optimized implementation
• libSTARK
  • zk-STARKs [BBHR18]
• emmy
  • ZKP primitives for Camenisch-Lysyanskaya anonymous credentials
  • Camenisch-Lysyanskaya anonymous credentials (work in progress)
  • client-server (prover-verifier) communication based on Protobuffers and gRPC
• VC implementation accompanying the Pinocchio [PGHR13] and Geppetto [CFHKKNPZ14] papers

Generating structured reference strings

Some proving systems require a structured reference string (SRS). The following works discuss secure SRS generation.

• [BCGTV15] - MPC for generating the SRS for [PGHR13]/[BCGTV13]
• [BGG17] - improved MPC for generating the SRS for [PGHR13]/[BCGTV13]
• [BGM18] - "Powers of Tau" protocol for scalable generation of structured reference string for [Groth16]

Low-level libraries/languages for writing circuits

• libsnark's gadgetlib1 and gadgetlib2 - C++ libraries for for building circuits for preprocessing zk-SNARKs
• jsnark - Java library for building circuits for preprocessing zk-SNARKs, backed by libsnark
• ZoKrates - Toolbox for zk-SNARKs on Ethereum, backed by libsnark
• Snarky - OCaml front-end for writing R1CS SNARKs, currently backed by libsnark

General-purpose compilers from high-level languages

• ZKPDL [MEKHL10]
  • Cashlib - C++ implementation
• Pinocchio [PGHR13]
  • Pinocchio toolchain - Python implementation
• Pantry [BFRSBW13]
• Geppetto [CFHKKNPZ14]
• TinyRAM [BCGTV13], vnTinyRAM [BCTV14a] and scalable TinyRAM [BCTV14b]
• Buffet [WSRBW15]
• C0C0 [KZMQCPPSS15]
• Pequin - Toolchain to verifiably execute programs expressed in (a large subset of) C, backed by libsnark.
  • Relevant publications
• Snårkl [SML17] - Haskell embedded DSL for verifiable computing
  • Implementation backed by libsnark
• xJsnark [KPS18]

Example circuits

• Zcash Sprout
  • Based on Zerocash [BCGGMTV14]
  • C++ implementation over BN128 using libsnark
  • Rust implementation over BLS12-381 using bellman
• ANONIZE [HMP15]
  • Mobile applications (closed-source)
• [KM18]
• Zcash Sapling
  • Rust implementation over BLS12-381 using bellman

Standardization efforts

• Zero Knowledge Proof Standardization and 1st Workshop
• Letter to NIST on standardizing new cryptographic standards

So are they fast yet?

Stay tuned! 😁

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