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=nil; is building an Ethereum L2 powered by zkSharding. This page features both completed and in-progress research. We welcome your feedback.

# Completed Research

## ZKPs & zkEMVM
* [Lookup argument and its tweaks](https://hackmd.io/kpn5x5O3RKqR9yLZy0PB4Q)
    * This document contains techniques that we implemented as a part of Placeholder proof system. All these algorithms were originally developed for SHA-256 PLONK component design and now they provide an important tool that is actively used in zkEVM circuits for zkSharding.
* [On Distributed FRI-based Proof Generation](https://hackmd.io/@nil-research/rJ_NVyiRA)
    * Many efficient protocols for distributed SNARK generation rely on additively homomorphic cryptographic mechanisms, which allows them to achieve low communication costs. The FRI protocol is based on hash functions which do not support homomorphic operations on data.
In this note, we discuss distributed proof generation using
FRI-based SNARKs. We show that despite many limitations, this is quite possible in practice and allows for significant efficiency gains in proof generation.

# In-progress Research

## Sharded UX

* [Refunds in Async Transactions](https://hackmd.io/7vX4yEaYRr-ZM83Ccsd30g)
    * In zkSharding, cross-shard transactions are non-atomic. This means that sometimes a transaction may fail on the destination shard. If the transaction has tokens attached, the tokens need to be returned to the sender. In this document, we’re trying to figure out how to achieve that.


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**Links**
[Website](https://nil.foundation/)
[Documentation](https://docs.nil.foundation/)

**Connect**
Email: [research@nil.foundation](mailto:research@nil.foundation?subject=HackMD_Test)
Twitter: [@nil_foundation](https://x.com/nil_foundation)

