gmh5225 / zksync_era_precompiles

Yul precompile library to speedup elliptic curves operations.

zkSync Era Precompiles

DISCLAIMER: This implementation is still being developed and has not been reviewed or audited. Use at your own risk.

This is a precompile library implemented in Yul to speedup arithmetic operations of elliptic curves. In the next weeks we will add more optimizations and benchmarks.

Current Status

Precompile	MVP	Optimized
ecAdd	✅	✅
ecMul	✅	✅
ecPairing	🏗️	❌
modexp	✅	🏗️

Summary

• ecAdd is optimized with finite field arithmetic in Montgomery form and optimized modular inverse with a modification of the binary extended Euclidean algorithm that skips the Montgomery reduction step for inverting. There is not much more room for optimizations, maybe we could think of Montgomery squaring (SOS) to improve the finite field squaring.

• ecMul is optimized with finite field arithmetic in Montgomery form, optimized modular inverse with a modification of the binary extended Euclidean algorithm that skips the Montgomery reduction step for inverting, and the elliptic curve point arithmetic is being done in homogeneous projective coordinates. There are some other possible optimizations to implement, one is the one discussed in the Slack channel (endomorphism: GLV or wGLV), the windowed method, the sliding-window method, wNAF (windowed non-adjacent form) to improve the elliptic curve point arithmetic, and Montgomery squaring (SOS) to improve the finite field squaring, Jacobian projective coordiantes (this would have similar performance and gas costs as working with the homogeneous projective coordinates but it would be free to add it since we need this representation for ecPairing).

• modexp status is detailed in this Slack message

  https://lambdaclass.slack.com/archives/C03GS78HS02/p1692141200550299

• ecPairing will be implemented as it is detailed in this document. We currently have the towered field extensions working and started working on the line functions for the addition and the double step of the miller loop.

Used algorithms

	Unoptimized			Optimized
Operation	ecAdd	ecMul	modexp	ecAdd	ecMul	modexp
Modular Addition	addmod	addmod	addmod	addmod + Montgomery form	addmod + Montgomery form	addmod + Montgomery form
Modular Subtraction	addmod	addmod	addmod	addmod + Montgomery form	addmod + Montgomery form	addmod + Montgomery form
Modular Multiplication	mulmod	mulmod	mulmod	Montgomery multiplication	Montgomery multiplication	Montgomery multiplication
Modular Exponentiation	Binary exponentiation	Binary exponentiation	Binary exponentiation	Binary exponentiation + Montgomery form	Binary exponentiation + Montgomery form	Binary exponentiation + Montgomery form
Modular Inversion	Fermat’s little theorem	Fermat’s little theorem	None	Binary Extended GCD + Montgomery form	Binary Extended GCD + Montgomery form

Resources

• EVM precompiles list
• EIP-196: Precompiled contracts for addition and scalar multiplication on the elliptic curve alt_bn128
• EIP-197: Precompiled contracts for optimal ate pairing check on the elliptic curve alt_bn128
• EIP-198: Big integer modular exponentiation
• EIP-1108: Reduce alt_bn128 precompile gas costs
• EIP-2565: ModExp Gas Cost

Development

Follow the instructions below to setup the repo and run a development L2 node.

Setup the repo

make setup

Update the submodules (if needed)

make update

Run a development L2 node

make run

Run the tests

If you want to run all the tests:

make test

If you want to run a specific test:

make test PRECOMPILE=<precompile_name>