# Efficient non-native SNARK recursion using bivariate polynomial testing

- Speakers: [Ivo Kubjas](https://streameth.org/speakers/ivo-kubjas)
- Channel: [Devcon 7 SEA](https://streameth.org/devcon_7_sea)
- Date: 2024-11-13
- Duration: 25:10
- Watch: https://streameth.org/watch/67343a9c9dbb7a90e193e070

## Description

Efficient SNARK recursion requires switching between pairing friendly elliptic curves. In most optimal approaches these curves would construct a cycle, but there are no such known cycles. Instead, we use non-native arithmetic to brute force the pairing computation at the cycle cut-off.
We describe an approach for combining direct field extension with polynomial-based non-native arithmetic. This reduces pairing computation to bivariate polynomial identity testing using Schwartz-Zippel lemma.

## About the speakers

### Ivo Kubjas

Ivo is a ZK-circuit engineer at Linea, co-maintaining the SNARK library gnark which is used for proof aggregation and compression to BN254.