{"quality_controlled":"1","status":"public","date_published":"2025-08-17T00:00:00Z","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.","OA_place":"repository","OA_type":"green","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."}],"language":[{"iso":"eng"}],"title":"On extractability of the KZG family of polynomial commitment schemes","month":"08","oa":1,"_id":"21323","citation":{"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.","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.","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>","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.","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>.","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>","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>."},"page":"584-616","main_file_link":[{"url":"https://eprint.iacr.org/2025/514","open_access":"1"}],"alternative_title":["LNCS"],"year":"2025","publisher":"Springer Nature","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"     16005","day":"17","author":[{"last_name":"Belohorec","first_name":"Juraj","full_name":"Belohorec, Juraj"},{"last_name":"Dvořák","first_name":"Pavel","full_name":"Dvořák, Pavel"},{"full_name":"Hoffmann, Charlotte","last_name":"Hoffmann","first_name":"Charlotte","orcid":"0000-0003-2027-5549","id":"0f78d746-dc7d-11ea-9b2f-83f92091afe7"},{"last_name":"Hubáček","first_name":"Pavel","full_name":"Hubáček, Pavel"},{"last_name":"Mašková","first_name":"Kristýna","full_name":"Mašková, Kristýna"},{"full_name":"Pastyřík, Martin","first_name":"Martin","last_name":"Pastyřík"}],"type":"conference","doi":"10.1007/978-3-032-01887-8_19","publication":"45th Annual International Cryptology Conference","article_processing_charge":"No","date_created":"2026-02-18T10:59:58Z","conference":{"name":"CRYPTO: International Cryptology Conference","location":"Santa Barbara, CA, United States","start_date":"2025-08-17","end_date":"2025-08-221"},"date_updated":"2026-02-19T07:50:33Z","department":[{"_id":"KrPi"}],"volume":16005,"publication_status":"published","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783032018861"],"eisbn":["9783032018878"]}}