## State of ZK Proof Systems

<details>
<summary>State of ZK Proof Systems</summary>

The seeds for general-compute in zero-knowledge have been planted over the decades of the 90s and 00s under the academic umbrella of the [interactive](https://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Proof%20Systems/The_Knowledge_Complexity_Of_Interactive_Proof_Systems.pdf) [proofs](https://dl.acm.org/doi/10.1145/116825.116852) [research](https://dl.acm.org/doi/abs/10.1145/146585.146609) generally and [PCP specifically](https://dl.acm.org/doi/10.1145/273865.273901). But these noble seeds lacked sufficient conditions to grow: prohibitive proof size and prover/verifier time.

This began to change since early 2010s with innovations in [cryptographic primitives](https://link.springer.com/chapter/10.1007/978-3-642-17373-8_19) and [arithmetization](https://link.springer.com/chapter/10.1007/978-3-642-38348-9_37) of sufficiently-generic computations. More [breakthroughs](https://link.springer.com/chapter/10.1007/978-3-662-49896-5_11) followed and shoots began sprouting out, leading to the first non-trivial [implementation](https://github.com/zkcrypto/groth16) of a zkSNARK proof system in 2016: Groth16.

[More](https://github.com/zcash/libsnark), [more](https://zokrates.github.io), and [more](https://github.com/zkcrypto/bellman) shoots [sprouted](https://docs.circom.io) in years to follow, but not without hitting fundamental obstacles: (a) the tooling still too close to the metal for the average developer to build zkDapps, or the average system developer to build large systems with baked-in ZK, and (b) inefficiency and rigidity of R1CS arithmetization imposed a ceiling on what can practically be built in terms of size and performance.

More innovation followed. [PLONK](https://eprint.iacr.org/2019/953) (2019) brought flexibility and universal updatable trusted setup for zkSNARKs. Meanwhile, [older ideas](https://link.springer.com/chapter/10.1007/978-3-642-40084-1_6) began to be realized in live hash-based SNARK production systems. The 2021-22 years witnessesed an increase in large zkS{N,T}AR systems being developed, chief among which are zkRollups tethered to Ethereum. There has also being many advances in primitives such as [lookups](https://docs.google.com/presentation/d/16VgtpzbENvHlNbbG_UPu9PM6s_eJqsU41FezCNXd1NA/edit#slide=id.g2c8b6b841a5_0_1357), commitments schemes, and [incrementally verifiable computations](https://github.com/privacy-scaling-explorations/sonobe?tab=readme-ov-file#schemes-implemented) (IVC).

- > **TODO**:
- key developments in 2023-2024:
- [Blaz](https://eprint.iacr.org/2024/1609), Basefold, STIR, [Arc](https://eprint.iacr.org/2024/1731)[2](https://x.com/benediktbuenz/status/1849825189678248159)
- [WHIR](https://eprint.iacr.org/2024/1586,ARC) "serves as a direct replacement for protocols like FRI, STIR, BaseFold, and others"
- Binary fields (binius)
- Rediscovery of gkr+sumcheck
- Folding iterations
- Learnings of flexibility<>complexity in arithmetizations

</details>