LambdaWorks

From the heights of these towers of fields, forty centuries of mathematics look down on us. The library for kids who wanna learn how to do STARKs, SNARKs and learn other cryptographic stuff too.

Zero-Knowledge and Validity Proofs have gained a lot of attention over the last few years. We strongly believe in this potential and that is why we decided to start working in this challenging ecosystem, where math, cryptography and distributed systems meet. The main barrier in the beginning was not the cryptography or math but the lack of good libraries which are performant and developer friendly. There are some exceptions, though, like gnark or halo2. Some have nice APIs and are easy to work with, but they are not written in Rust, and some are written in Rust but have poor programming and engineering practices. Most of them don't have support for CUDA, Metal and WebGPU or distributed FFT calculation using schedulers like Dask.

So, we decided to build our library, focusing on performance, with clear documentation and developer-focused. Our core team is a group of passionate people from different backgrounds and different strengths; we think that the whole is greater than just the addition of the parts. We don't want to be a compilation of every research result in the ZK space. We want this to be a library that can be used in production, not just in academic research. We want to offer developers the main building blocks and proof systems so that they can build their applications on top of this library.

Provers and Polynomial Commitment Schemes using LambdaWorks

All provers are being migrated to Lambdaworks library

Right now Plonk prover is in this repo, you can find the others here:

Main crates

Crypto

Finite Field crate fully supports no-std with no-default-features

Both Math and Crypto support wasm with target wasm32-unknown-unknown by default, with std feature.

Exercises and Challenges

Lambdaworks exercises and challenges

If you use Lambdaworks libraries in your research projects, please cite them using the following template:

@software{Lambdaworks,
  author={Lambdaworks contributors},
  title={Lambdaworks},
  url={https://github.com/lambdaclass/lambdaworks},
  year={2023}
}

Gadgets

Fuzzers

Run a specific fuzzer from the ones contained in fuzz/fuzz_targets/ folder withcargo, for example to run the one for the target field_from_hex:

make run-fuzzer FUZZER=field_from_hex

Documentation

To serve the documentation locally, first install both mdbook and the Katex preprocessor to render LaTeX, then run

make docs

📊 Benchmarks

Benchmark results are hosted here.

These are the results of execution of the benchmarks for finite field arithmetic using the STARK field prime (p = 3618502788666131213697322783095070105623107215331596699973092056135872020481).

Differences of 3% are common for some measurements, so small differences are not statistically relevant.

ARM - M1

Operation	N	Arkworks	Lambdaworks
`mul`	10k	112 μs	115 μs
`add`	1M	8.5 ms	7.0 ms
`sub`	1M	7.53 ms	7.12 ms
`pow`	10k	11.2 ms	12.4 ms
`invert`	10k	30.0 ms	27.2 ms

x86 - AMD Ryzen 7 PRO

Operation	N	Arkworks (ASM)*	Lambdaworks
`mul`	10k	118.9 us	95.7 us
`add`	1M	6.8 ms	5.4 ms
`sub`	1M	6.6 ms	5.2 ms
`pow`	10k	10.6 ms	9.4 ms
`invert`	10k	34.2 ms	35.74 ms

*assembly feature was enabled manually for that bench, and is not activated by default when running criterion

To run them locally, you will need cargo-criterion and cargo-flamegraph. Install it with:

cargo install cargo-criterion

Run the complete benchmark suite with:

make benchmarks

Run a specific benchmark suite with cargo, for example to run the one for field:

make benchmark BENCH=field

You can check the generated HTML report in target/criterion/reports/index.html

Lambdaworks Plonk Prover

A fast implementation of the Plonk zk-protocol written in Rust. This is part of the Lambdaworks zero-knowledge framework. It includes a high-level API to seamlessly build your own circuits.

This prover is still in development and may contain bugs. It is not intended to be used in production yet.

Building a circuit

The following code creates a circuit with two public inputs x, y and asserts x * e = y:

let system = &mut ConstraintSystem::<FrField>::new();
let x = system.new_public_input();
let y = system.new_public_input();
let e = system.new_variable();

let z = system.mul(&x, &e);    
system.assert_eq(&y, &z);;

Generating a proof

Setup

A setup is needed in order to generate a proof for a new circuit. The following code generates a verifying key that will be used by both the prover and the verifier:

let common = CommonPreprocessedInput::from_constraint_system(&system, &ORDER_R_MINUS_1_ROOT_UNITY);
let srs = test_srs(common.n);
let kzg = KZG::new(srs); // The commitment scheme for plonk.
let verifying_key = setup(&common, &kzg);

Prover

First, we fix values for x and e and solve the constraint system:

let inputs = HashMap::from([(x, FieldElement::from(4)), (e, FieldElement::from(3))]);
let assignments = system.solve(inputs).unwrap();

Finally, we call the prover:

let witness = Witness::new(assignments, &system);
let public_inputs = system.public_input_values(&assignments);
let prover = Prover::new(kzg.clone(), TestRandomFieldGenerator {});
let proof = prover.prove(&witness, &public_inputs, &common, &verifying_key);

Verifying a proof

Just call the verifier:

let verifier = Verifier::new(kzg);
assert!(verifier.verify(&proof, &public_inputs, &common, &verifying_key));

More info

You can find more info in the documentation.

📚 References

The following links, repos and projects have been important in the development of this library and we want to thank and acknowledge them.

About

The library for kids who wanna learn how to do SNARKs and learn other cryptographic stuff too

https://lambdaclass.github.io/lambdaworks/

Apache License 2.0

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