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 SNARKs and learn other cryptographic stuff too.

References:

• arkworks-rs
• gnark

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}
}

Building blocks

• Finite Field Algebra
• Elliptic curve models
• Elliptic curve operations
• Arithmetization schemes
• Polynomial commitment schemes
• PIOP
• Cryptographic tools
• Advanced tools: agreggation, recursion, accumulation
• Protocols
• Gadgets

Blocks

Finite Field Algebra

• Big integer representation
• Basic algebra: addition, multiplication, subtraction, inversion, square root (Tonelli–Shanks)
• Field extensions
• Number theoretic transform
• Polynomial operations
• Fast Fourier Transform
• Montgomery and Barrett

Elliptic curve models

• BLS12-381 (H)
• BLS12-377 (H)
• secp256k1 (H)
• Ed25519 (H)
• Jubjub (M)
• BN254 (M)
• Pasta: Pallas and Vesta (L)
• Forms:

1. Affine (H)
2. Projective (H)
3. Montgomery (M)
4. Twisted Edwards (H)
5. Jacobi (L)

Elliptic curve operations

• Add, double, scalar multiplication.
• Multiscalar multiplication (Pippenger)
• Weyl, Tate and Ate pairings.

Arithmetization

• R1CS - gadgets (H)
• AIR (M)
• Plonkish (H)
• ACIR (L)

Polynomial commitment schemes

• KZG and variants
• Hashing
• Inner product arguments
• Dory (L)

PIOP/PCS

• Groth16
• Plonk
• Marlin
• FRI

Crypto primitives

• Pseudorandom generator
• Hashes
• Blake2
• Keccak
• Poseidon
• Pedersen
• Encryption schemes
• AES
• ChaCha20
• Rescue
• ElGamal

Protocol

• Fiat-Shamir

Gadgets