Скачать или смотреть ZK13: EC Plonkish: Plonk-like proofs over the elliptic curve coordinate ring - Syed Hosseini

This was recorded at the ZK13 - Zero Knowledge Summit 13 on May 13th, 2025 in Toronto, Canada.

https://www.zksummit.com/

Title: Trustworthy ZKP Parameter Generation
Speaker: Syed Hosseini
Project: Web3 Foundation, Polkadot

Description:
Joint work with Alistair Stewart

The overwhelming majority of proof systems rely on polynomial arithmetics performed by Fast Fourier Transform (FFT). However, FFT is only efficient when the underlying field contains a $p^{k}$'th root of unity for relatively small $p$ and large $k$. Both ECFFT and Circle STARK overcome this restriction by mapping the field to a group that contains such an element and back to the field to implement a fast FRI proof system over those fields. This approach however is not sufficient to implement a PLONK proof system as that requires the field of arithmetization to contain a cyclic group of order $p^k$.

To overcome this obstacle, in this talk, we propose EC Plonkish proof system to make PLONK-like proof systems possible over such fields. We utilize the isogeny approach proposed by ECFFT to transform the problem to the coordinate ring of an elliptic curve which contains such a subgroup and we arithmetize the problem over that ring. We explain all changes we need to apply to the PLONK proof system to work in this ring.

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