---
OA_place: repository
OA_type: green
_id: '21323'
abstract:
- lang: eng
  text: We present a unifying framework for proving the knowledge-soundness of KZG-like
    polynomial commitment schemes, encompassing both univariate and multivariate variants.
    By conceptualizing the proof technique of Lipmaa, Parisella, and Siim for the
    univariate KZG scheme (EUROCRYPT 2024), we present tools and falsifiable hardness
    assumptions that permit black-box extraction of the multivariate KZG scheme. Central
    to our approach is the notion of a canonical Proof-of-Knowledge of a Polynomial
    (PoKoP) of a polynomial commitment scheme, which we use to capture the extractability
    notion required in constructions of practical zk-SNARKs. We further present an
    explicit polynomial decomposition lemma for multivariate polynomials, enabling
    a more direct analysis of interpolating extractors and bridging the gap between
    univariate and multivariate commitments. Our results provide the first standard-model
    proofs of extractability for the multivariate KZG scheme and many of its variants
    under falsifiable assumptions.
acknowledgement: Juraj Belohorec, Pavel Hubáček, and Kristýna Mašková were partially
  supported by the Academy of Sciences of the Czech Republic (RVO 67985840), Czech
  Science Foundation GAČR grant No. 25-16311S, and by Zircuit. Pavel Dvořák was supported
  by Czech Science Foundation GAČR grant No. 22-14872O. Juraj Belohorec and Kristýna
  Mašková were supported by the grant SVV–2025–260822.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Juraj
  full_name: Belohorec, Juraj
  last_name: Belohorec
- first_name: Pavel
  full_name: Dvořák, Pavel
  last_name: Dvořák
- first_name: Charlotte
  full_name: Hoffmann, Charlotte
  id: 0f78d746-dc7d-11ea-9b2f-83f92091afe7
  last_name: Hoffmann
  orcid: 0000-0003-2027-5549
- first_name: Pavel
  full_name: Hubáček, Pavel
  last_name: Hubáček
- first_name: Kristýna
  full_name: Mašková, Kristýna
  last_name: Mašková
- first_name: Martin
  full_name: Pastyřík, Martin
  last_name: Pastyřík
citation:
  ama: 'Belohorec J, Dvořák P, Hoffmann C, Hubáček P, Mašková K, Pastyřík M. On extractability
    of the KZG family of polynomial commitment schemes. In: <i>45th Annual International
    Cryptology Conference</i>. Vol 16005. Springer Nature; 2025:584-616. doi:<a href="https://doi.org/10.1007/978-3-032-01887-8_19">10.1007/978-3-032-01887-8_19</a>'
  apa: 'Belohorec, J., Dvořák, P., Hoffmann, C., Hubáček, P., Mašková, K., &#38; Pastyřík,
    M. (2025). On extractability of the KZG family of polynomial commitment schemes.
    In <i>45th Annual International Cryptology Conference</i> (Vol. 16005, pp. 584–616).
    Santa Barbara, CA, United States: Springer Nature. <a href="https://doi.org/10.1007/978-3-032-01887-8_19">https://doi.org/10.1007/978-3-032-01887-8_19</a>'
  chicago: Belohorec, Juraj, Pavel Dvořák, Charlotte Hoffmann, Pavel Hubáček, Kristýna
    Mašková, and Martin Pastyřík. “On Extractability of the KZG Family of Polynomial
    Commitment Schemes.” In <i>45th Annual International Cryptology Conference</i>,
    16005:584–616. Springer Nature, 2025. <a href="https://doi.org/10.1007/978-3-032-01887-8_19">https://doi.org/10.1007/978-3-032-01887-8_19</a>.
  ieee: J. Belohorec, P. Dvořák, C. Hoffmann, P. Hubáček, K. Mašková, and M. Pastyřík,
    “On extractability of the KZG family of polynomial commitment schemes,” in <i>45th
    Annual International Cryptology Conference</i>, Santa Barbara, CA, United States,
    2025, vol. 16005, pp. 584–616.
  ista: 'Belohorec J, Dvořák P, Hoffmann C, Hubáček P, Mašková K, Pastyřík M. 2025.
    On extractability of the KZG family of polynomial commitment schemes. 45th Annual
    International Cryptology Conference. CRYPTO: International Cryptology Conference,
    LNCS, vol. 16005, 584–616.'
  mla: Belohorec, Juraj, et al. “On Extractability of the KZG Family of Polynomial
    Commitment Schemes.” <i>45th Annual International Cryptology Conference</i>, vol.
    16005, Springer Nature, 2025, pp. 584–616, doi:<a href="https://doi.org/10.1007/978-3-032-01887-8_19">10.1007/978-3-032-01887-8_19</a>.
  short: J. Belohorec, P. Dvořák, C. Hoffmann, P. Hubáček, K. Mašková, M. Pastyřík,
    in:, 45th Annual International Cryptology Conference, Springer Nature, 2025, pp.
    584–616.
conference:
  end_date: 2025-08-221
  location: Santa Barbara, CA, United States
  name: 'CRYPTO: International Cryptology Conference'
  start_date: 2025-08-17
date_created: 2026-02-18T10:59:58Z
date_published: 2025-08-17T00:00:00Z
date_updated: 2026-02-19T07:50:33Z
day: '17'
department:
- _id: KrPi
doi: 10.1007/978-3-032-01887-8_19
intvolume: '     16005'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://eprint.iacr.org/2025/514
month: '08'
oa: 1
oa_version: Preprint
page: 584-616
publication: 45th Annual International Cryptology Conference
publication_identifier:
  eisbn:
  - '9783032018878'
  eissn:
  - 1611-3349
  isbn:
  - '9783032018861'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On extractability of the KZG family of polynomial commitment schemes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16005
year: '2025'
...