{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T13:01:17Z","timestamp":1784638877388,"version":"3.55.0"},"publisher-location":"Cham","reference-count":42,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032325594","type":"print"},{"value":"9783032325600","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T00:00:00Z","timestamp":1784678400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T00:00:00Z","timestamp":1784678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2027]]},"DOI":"10.1007\/978-3-032-32560-0_12","type":"book-chapter","created":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T12:03:58Z","timestamp":1784635438000},"page":"327-350","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Practical Subvector Commitments with\u00a0Optimal Opening Complexity"],"prefix":"10.1007","author":[{"given":"Matteo","family":"Campanelli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,22]]},"reference":[{"key":"12_CR1","doi-asserted-by":"publisher","unstructured":"Ateniese, G., Baldimtsi, F., Campanelli, M., Francati, D., Karantaidou, I.: Advancing scalability in decentralized storage: a novel approach to proof-of-replication via polynomial evaluation. In: Reyzin, L., Stebila, D. (eds.) CRYPTO\u00a02024, Part\u00a0II, vol. 14921. LNCS, pp. 3\u201339, Santa Barbara, CA, USA, August\u00a018\u201322, 2024. Springer, Cham, Switzerland (2024). https:\/\/doi.org\/10.1007\/978-3-031-68379-4_1","DOI":"10.1007\/978-3-031-68379-4_1"},{"key":"12_CR2","unstructured":"ALEO trusted setup (2021). https:\/\/setup.aleo.org\/"},{"key":"12_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1007\/978-3-030-64840-4_28","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"S Agrawal","year":"2020","unstructured":"Agrawal, S., Raghuraman, S.: KVaC: key-value commitments for blockchains and beyond. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 839\u2013869. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64840-4_28"},{"key":"12_CR4","unstructured":"Arkworks contributors: arkworks ZKSNARK ecosystem (2022). https:\/\/arkworks.rs"},{"key":"12_CR5","unstructured":"Axiom trusted ceremony (2025). https:\/\/web.archive.org\/web\/20250120135649\/https:\/\/docs.axiom.xyz\/docs\/transparency-and-security\/kzg-trusted-setup"},{"key":"12_CR6","doi-asserted-by":"publisher","unstructured":"Boneh, D., Boyen, X.: Efficient selective-ID secure identity based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT\u00a02004, vol. 3027. LNCS, pp. 223\u2013238, Interlaken, Switzerland, May\u00a02\u20136, 2004. Springer Berlin Heidelberg, Germany (2004). https:\/\/doi.org\/10.1007\/978-3-540-24676-3_14","DOI":"10.1007\/978-3-540-24676-3_14"},{"key":"12_CR7","unstructured":"Botta, V., Bottoni, S., Campanelli, M., Ragnoli, E., Trombetta, A.: QEDB: expressive and modular verifiable databases (without SNARKs). Cryptology ePrint Archive, Report 2025\/1408 (2025)"},{"key":"12_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1007\/978-3-030-26948-7_20","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"D Boneh","year":"2019","unstructured":"Boneh, D., B\u00fcnz, B., Fisch, B.: Batching techniques for accumulators with applications to IOPs and stateless blockchains. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 561\u2013586. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26948-7_20"},{"issue":"4","key":"12_CR9","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1007\/s00145-016-9241-9","volume":"30","author":"N Bitansky","year":"2017","unstructured":"Bitansky, N., et al.: The hunting of the SNARK. J. Cryptol. 30(4), 989\u20131066 (2017)","journal-title":"J. Cryptol."},{"key":"12_CR10","unstructured":"Buterin, V., Feist, D., Ballet, G., Merriam, P., Herold, G.: EIP-6800: Ethereum state using VERKLE trees (2024). https:\/\/eips.ethereum.org\/EIPS\/eip-6800"},{"key":"12_CR11","unstructured":"Buterin, V., et al.: EIP-4844: shard blob transactions. Ethereum Improvement Proposals, February (2022). Deployed on Ethereum mainnet March 13, 2024 (Dencun upgrade)"},{"key":"12_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-642-22792-9_7","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"S Benabbas","year":"2011","unstructured":"Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable delegation of computation over large datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111\u2013131. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22792-9_7"},{"key":"12_CR13","unstructured":"Campanelli, M.: Practical subvector commitments with optimal opening complexity. Cryptology ePrint Archive, Paper 2026\/118 (2026)"},{"key":"12_CR14","doi-asserted-by":"publisher","unstructured":"Campanelli, M., Engelmann, F., Orlandi, C.: Zero-knowledge for homomorphic key-value commitments with applications to privacy-preserving ledgers. In: Galdi, C., Jarecki, S. (eds.) SCN 22, vol. 13409. LNCS, pp. 761\u2013784, Amalfi, Italy, September\u00a012\u201314, 2022. Springer, Cham, Switzerland (2022). https:\/\/doi.org\/10.1007\/978-3-031-14791-3_33","DOI":"10.1007\/978-3-031-14791-3_33"},{"key":"12_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/978-3-642-36362-7_5","volume-title":"Public-Key Cryptography \u2013 PKC 2013","author":"D Catalano","year":"2013","unstructured":"Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55\u201372. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-36362-7_5"},{"key":"12_CR16","doi-asserted-by":"publisher","unstructured":"Campanelli, M., Faonio, A., Fiore, D., Querol, A., Rodr\u00edguez, H.: Lunar: a toolbox for more efficient universal and updatable zkSNARKs and commit-and-prove extensions. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT\u00a02021, Part\u00a0III, vol. 13092. LNCS, pp. 3\u201333, Singapore, December\u00a06\u201310, 2021. Springer, Cham, Switzerland (2021). https:\/\/doi.org\/10.1007\/978-3-030-92078-4_1","DOI":"10.1007\/978-3-030-92078-4_1"},{"key":"12_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-64834-3_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"M Campanelli","year":"2020","unstructured":"Campanelli, M., Fiore, D., Greco, N., Kolonelos, D., Nizzardo, L.: Incrementally aggregatable vector commitments and applications to verifiable decentralized storage. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 3\u201335. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_1"},{"key":"12_CR18","unstructured":"Campanelli, M., Hall-Andersen, M., Kamp, S.H.: Curve trees: practical and transparent zero-knowledge accumulators. In: Calandrino, J.A., Troncoso, C. (eds.) USENIX Security 2023, pp. 4391\u20134408, Anaheim, CA, USA, August\u00a09\u201311, 2023 (2023) USENIX Association"},{"key":"12_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1007\/978-3-030-45721-1_26","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"A Chiesa","year":"2020","unstructured":"Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.: Marlin: preprocessing zkSNARKs with universal and updatable SRS. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 738\u2013768. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_26"},{"key":"12_CR20","doi-asserted-by":"publisher","unstructured":"Campanelli, M., Nitulescu, A., R\u00e0fols, C., Zacharakis, A., Zapico, A.: Linear-map vector commitments and their practical applications. In: Agrawal, S., Lin, D. (eds.) ASIACRYPT\u00a02022, Part\u00a0IV, vol. 13794. LNCS, pages 189\u2013219, Taipei, Taiwan, December\u00a05\u20139, 2022. Springer, Cham, Switzerland (2022). https:\/\/doi.org\/10.1007\/978-3-031-22972-5_7","DOI":"10.1007\/978-3-031-22972-5_7"},{"key":"12_CR21","unstructured":"Ethereum KZG ceremony (2023). https:\/\/github.com\/ethereum\/kzg-ceremony"},{"key":"12_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/978-3-030-17656-3_12","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"B Fisch","year":"2019","unstructured":"Fisch, B.: Tight proofs of space and replication. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 324\u2013348. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17656-3_12"},{"key":"12_CR23","unstructured":"Feist, D., Khovratovich, D.: Fast amortized KZG proofs. Cryptology ePrint Archive, Report 2023\/033 (2023)"},{"key":"12_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-3-319-96881-0_2","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"G Fuchsbauer","year":"2018","unstructured":"Fuchsbauer, G., Kiltz, E., Loss, J.: The algebraic group model and its applications. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 33\u201362. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_2"},{"key":"12_CR25","doi-asserted-by":"publisher","unstructured":"Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to zk-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO\u00a02018, Part\u00a0III, vol. 10993. LNCS, pp. 698\u2013728, Santa Barbara, CA, USA, August\u00a019\u201323, 2018. Springer, Cham, Switzerland (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_24","DOI":"10.1007\/978-3-319-96878-0_24"},{"key":"12_CR26","unstructured":"Golovnev, A., Lee, J., Setty, S.T., Thaler, J. and Wahby, R.S.: Brakedown: linear-time and post-quantum SNARKs for R1CS. Cryptology ePrint Archive, Report 2021\/1043 (2021)"},{"key":"12_CR27","doi-asserted-by":"crossref","unstructured":"Gorbunov, S., Reyzin, L., Wee, H. and Zhang, Z.: PointProofs: aggregating proofs for multiple vector commitments. In: Ligatti, J., Ou, X., Katz, J., Vigna, G. (eds.) ACM CCS 2020, pp. 2007\u20132023, Virtual Event, USA, November\u00a09\u201313 (2020). ACM Press","DOI":"10.1145\/3372297.3417244"},{"key":"12_CR28","unstructured":"Gabizon, A., Williamson, Z.J., Ciobotaru, O.: PLONK: permutations over Lagrange-bases for oecumenical noninteractive arguments of knowledge. Cryptology ePrint Archive, Report 2019\/953 (2019)"},{"key":"12_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/978-3-642-17373-8_11","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"A Kate","year":"2010","unstructured":"Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177\u2013194. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-17373-8_11"},{"key":"12_CR30","doi-asserted-by":"crossref","unstructured":"Luo, Z., Jia, Y., Gracia, A.V.O., Kate, A.: CauchyProofs: batch-updatable vector commitment with easy aggregation and application to stateless blockchains. In: Blanton, M., Enck, W., Nita-Rotaru, C., (eds.) 2025 IEEE Symposium on Security and Privacy, pp. 1947\u20131963, San Francisco, CA, USA, May\u00a012\u201315 (2025). IEEE Computer Society Press","DOI":"10.1109\/SP61157.2025.00247"},{"key":"12_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1007\/978-3-030-26948-7_19","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"RWF Lai","year":"2019","unstructured":"Lai, R.W.F., Malavolta, G.: Subvector commitments with application to succinct arguments. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 530\u2013560. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26948-7_19"},{"key":"12_CR32","doi-asserted-by":"publisher","unstructured":"Libert, B., Passel\u00e8gue, A., Riahinia, M.: PointProofs, revisited. In: Agrawal, S., Lin, D. (eds). ASIACRYPT\u00a02022, Part\u00a0IV, vol. 13794. LNCS, pp. 220\u2013246, Taipei, Taiwan, December\u00a05\u20139, 2022. Springer, Cham, Switzerland. https:\/\/doi.org\/10.1007\/978-3-031-22972-5_8","DOI":"10.1007\/978-3-031-22972-5_8"},{"key":"12_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1007\/978-3-642-32009-5_34","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"B Libert","year":"2012","unstructured":"Libert, B., Peters, T., Yung, M.: Group signatures with almost-for-free revocation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 571\u2013589. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_34"},{"key":"12_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/978-3-642-11799-2_30","volume-title":"Theory of Cryptography","author":"B Libert","year":"2010","unstructured":"Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 499\u2013517. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-11799-2_30"},{"key":"12_CR35","unstructured":"Nitulescu, A.: SOK: vector commitments (2021). https:\/\/www.di.ens.fr\/nitulesc\/files\/vc-sok"},{"key":"12_CR36","unstructured":"Pathak, V., Ruj, S., van\u00a0der Meyden, R.: Vector commitment design, analysis, and applications: a survey. Cryptology ePrint Archive, Report 2025\/667 (2025)"},{"key":"12_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1007\/978-3-642-36594-2_13","volume-title":"Theory of Cryptography","author":"C Papamanthou","year":"2013","unstructured":"Papamanthou, C., Shi, E., Tamassia, R.: Signatures of correct computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 222\u2013242. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-36594-2_13"},{"key":"12_CR38","unstructured":"Srinivasan, S., Chepurnoy, A., Papamanthou, C., Tomescu, A., Zhang, Y.: Hyperproofs: aggregating and maintaining proofs in vector commitments. In: Kevin R.B., Kurt Thomas, B. (eds.) USENIX Security 2022, pp. 3001\u20133018, Boston, MA, USA, August\u00a010\u201312, 2022. USENIX Association (2022)"},{"key":"12_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-3-030-57990-6_3","volume-title":"Security and Cryptography for Networks","author":"A Tomescu","year":"2020","unstructured":"Tomescu, A., Abraham, I., Buterin, V., Drake, J., Feist, D., Khovratovich, D.: Aggregatable subvector commitments for stateless cryptocurrencies. In: Galdi, C., Kolesnikov, V. (eds.) SCN 2020. LNCS, vol. 12238, pp. 45\u201364. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-57990-6_3"},{"key":"12_CR40","unstructured":"Nusret Tas, E., Boneh, D.: Vector commitments with efficient updates. In: 5th Conference on Advances in Financial Technologies (2023)"},{"key":"12_CR41","doi-asserted-by":"publisher","unstructured":"Wee, H., Wu, D.J.: Succinct vector, polynomial, and functional commitments from lattices. In: Hazay, C., Stam, M. (eds) Advances in Cryptology \u2013 EUROCRYPT 2023. EUROCRYPT 2023, Part\u00a0III. LNCS, vol. 14006. pp. 385\u2013416, Lyon, France, April\u00a023\u201327. Springer, Cham, Switzerland (2023). https:\/\/doi.org\/10.1007\/978-3-031-30620-4_13","DOI":"10.1007\/978-3-031-30620-4_13"},{"key":"12_CR42","unstructured":"Wagner, B., Zapico, A.: A documentation of Ethereum\u2019s PeerDAS. Cryptology ePrint Archive, Paper 2024\/1362 (2024)"}],"container-title":["Lecture Notes in Computer Science","Applied Cryptography and Network Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-32560-0_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T12:04:07Z","timestamp":1784635447000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-32560-0_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,22]]},"ISBN":["9783032325594","9783032325600"],"references-count":42,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-32560-0_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,22]]},"assertion":[{"value":"22 July 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ACNS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Applied Cryptography and Network Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Stony Brook, WI","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 June 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 June 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"acns2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/acns2026.github.io\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}