fflonk: a Fast-Fourier inspired verifier efficient version of PlonK

Ariel Gabizon; Zachary J.  Williamson

Paper 2021/1167

fflonk: a Fast-Fourier inspired verifier efficient version of PlonK

Ariel Gabizon and Zachary J. Williamson

Abstract

We present a variant of the Kate, Zaverucha and Goldberg polynomial commitment scheme [KZG] where $d$ polynomials can be opened at a point that is a $d$ 'th power, such that the amount of verifier group operations does not depend on $d$ . Our method works by reducing opening multiple polynomials at a single point $x$ , to opening a single polynomial at many points via an ``FFT-like identity''. As an application we present a version of the PlonK zk-SNARK[GWC] with significantly improved verifier performance, at the cost roughly tripling the prover time. Specifically, in addition to the two pairings, the verifier only performs five scalar multiplications, rather than 16 or 18 as in the versions presented in [GWC].

Note: typos

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint. MINOR revision.
Keywords: zk-SNARKs Polynomial Commitment Schemes
Contact author(s): ariel gabizon @ gmail com
History: 2021-11-01: last of 4 revisions; 2021-09-14: received; See all versions
Short URL: https://ia.cr/2021/1167
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1167,
      author = {Ariel Gabizon and Zachary J.  Williamson},
      title = {fflonk: a Fast-Fourier inspired verifier efficient version of {PlonK}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1167},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1167}
}