{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T17:09:50Z","timestamp":1779469790536,"version":"3.53.1"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032267337","type":"print"},{"value":"9783032267344","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-26734-4_14","type":"book-chapter","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T16:24:40Z","timestamp":1779467080000},"page":"424-454","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pairing-Based Functional Commitments for\u00a0Circuits with\u00a0Shorter Parameters"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4864-1125","authenticated-orcid":false,"given":"David","family":"Balb\u00e1s","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7274-6600","authenticated-orcid":false,"given":"Dario","family":"Fiore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9126-1887","authenticated-orcid":false,"given":"Russell W. F.","family":"Lai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,23]]},"reference":[{"key":"14_CR1","doi-asserted-by":"publisher","unstructured":"Albrecht, M.R., Cini, V., Lai, R.W.F., Malavolta, G., Thyagarajan, S.A.K.: Lattice-based SNARKs: publicly verifiable, preprocessing, and recursively composable - (extended abstract). In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO\u00a02022, Part\u00a0II. LNCS, vol. 13508, pp. 102\u2013132. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-15979-4_4","DOI":"10.1007\/978-3-031-15979-4_4"},{"key":"14_CR2","doi-asserted-by":"publisher","unstructured":"Anthoine, G., Balb\u00e1s, D., Fiore, D.: Fully-succinct multi-key homomorphic signatures from standard assumptions. In: Reyzin, L., Stebila, D. (eds.) CRYPTO\u00a02024, Part\u00a0III. LNCS, vol. 14922, pp. 317\u2013351. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-68382-4_10","DOI":"10.1007\/978-3-031-68382-4_10"},{"key":"14_CR3","doi-asserted-by":"publisher","unstructured":"Balb\u00e1s, D., Catalano, D., Fiore, D., Lai, R.W.F.: Chainable functional commitments for unbounded-depth circuits. In: Rothblum, G.N., Wee, H. (eds.) TCC\u00a02023, Part\u00a0III. LNCS, vol. 14371, pp. 363\u2013393. Springer, Cham (2023).https:\/\/doi.org\/10.1007\/978-3-031-48621-0_13","DOI":"10.1007\/978-3-031-48621-0_13"},{"key":"14_CR4","unstructured":"Balb\u00e1s, D., Fiore, D., Lai, R.W.F.: Circuit-succinct algebraic batch arguments from projective functional commitments. Cryptology ePrint Archive, Report 2025\/1943 (2025). https:\/\/eprint.iacr.org\/2025\/1943"},{"key":"14_CR5","doi-asserted-by":"publisher","unstructured":"Boyen, X.: The uber-assumption family (invited talk). In: Galbraith, S.D., Paterson, K.G. (eds.) PAIRING 2008. LNCS, vol.\u00a05209, pp. 39\u201356. Springer, Berlin, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-85538-5_3","DOI":"10.1007\/978-3-540-85538-5_3"},{"key":"14_CR6","doi-asserted-by":"publisher","unstructured":"de\u00a0Castro, L., Peikert, C.: Functional commitments for all functions, with transparent setup and from SIS. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0III. LNCS, vol. 14006, pp. 287\u2013320. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30620-4_10","DOI":"10.1007\/978-3-031-30620-4_10"},{"key":"14_CR7","doi-asserted-by":"publisher","unstructured":"Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC\u00a02013. LNCS, vol.\u00a07778, pp. 55\u201372. Springer, Berlin, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-36362-7_5","DOI":"10.1007\/978-3-642-36362-7_5"},{"key":"14_CR8","doi-asserted-by":"publisher","unstructured":"Catalano, D., Fiore, D., Messina, M.: Zero-knowledge sets with short proofs. In: Smart, N.P. (ed.) EUROCRYPT\u00a02008. LNCS, vol.\u00a04965, pp. 433\u2013450. Springer, Berlin, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78967-3_25","DOI":"10.1007\/978-3-540-78967-3_25"},{"key":"14_CR9","doi-asserted-by":"publisher","unstructured":"Catalano, D., Fiore, D., Tucker, I.: Additive-homomorphic functional commitments and applications to homomorphic signatures. In: Agrawal, S., Lin, D. (eds.) ASIACRYPT\u00a02022, Part\u00a0IV. LNCS, vol. 13794, pp. 159\u2013188. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-22972-5_6","DOI":"10.1007\/978-3-031-22972-5_6"},{"key":"14_CR10","unstructured":"Chiesa, A., Guan, Z., Knabenhans, C., Yu, Z.: On the Fiat-Shamir security of succinct arguments from functional commitments. Cryptology ePrint Archive, Report 2025\/902 (2025). https:\/\/eprint.iacr.org\/2025\/902"},{"key":"14_CR11","doi-asserted-by":"publisher","unstructured":"Choudhuri, A.R., Jain, A., Jin, Z.: Non-interactive batch arguments for NP from standard assumptions. In: Malkin, T., Peikert, C. (eds.) CRYPTO\u00a02021, Part\u00a0IV. LNCS, vol. 12828, pp. 394\u2013423. Springer, Cham, Virtual Event (2021). https:\/\/doi.org\/10.1007\/978-3-030-84259-8_14","DOI":"10.1007\/978-3-030-84259-8_14"},{"key":"14_CR12","doi-asserted-by":"publisher","unstructured":"Choudhuri, A.R., Jain, A., Jin, Z.: SNARGs for $$\\cal{P}$$ from LWE. In: 62nd FOCS, pp. 68\u201379. IEEE Computer Society Press (2022). https:\/\/doi.org\/10.1109\/FOCS52979.2021.00016","DOI":"10.1109\/FOCS52979.2021.00016"},{"key":"14_CR13","doi-asserted-by":"publisher","unstructured":"Escala, A., Herold, G., Kiltz, E., R\u00e0fols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO\u00a02013, Part\u00a0II. LNCS, vol.\u00a08043, pp. 129\u2013147. Springer, Berlin, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40084-1_8","DOI":"10.1007\/978-3-642-40084-1_8"},{"key":"14_CR14","doi-asserted-by":"publisher","unstructured":"Garg, R., Lu, G., Waters, B., Wu, D.J.: Reducing the CRS size in registered ABE systems. In: Reyzin, L., Stebila, D. (eds.) CRYPTO\u00a02024, Part\u00a0III. LNCS, vol. 14922, pp. 143\u2013177. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-68382-4_5","DOI":"10.1007\/978-3-031-68382-4_5"},{"key":"14_CR15","doi-asserted-by":"publisher","unstructured":"Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 99\u2013108. ACM Press (2011). https:\/\/doi.org\/10.1145\/1993636.1993651","DOI":"10.1145\/1993636.1993651"},{"key":"14_CR16","doi-asserted-by":"publisher","unstructured":"Gonz\u00e1lez, A., Zacharakis, A.: Fully-succinct publicly verifiable delegation from constant-size assumptions. In: Nissim, K., Waters, B. (eds.) TCC\u00a02021, Part\u00a0I. LNCS, vol. 13042, pp. 529\u2013557. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90459-3_18","DOI":"10.1007\/978-3-030-90459-3_18"},{"key":"14_CR17","doi-asserted-by":"publisher","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 469\u2013477. ACM Press (2015). https:\/\/doi.org\/10.1145\/2746539.2746576","DOI":"10.1145\/2746539.2746576"},{"key":"14_CR18","doi-asserted-by":"publisher","unstructured":"Jawale, R., Kalai, Y.T., Khurana, D., Zhang, R.Y.: SNARGs for bounded depth computations and PPAD hardness from sub-exponential LWE. In: Khuller, S., Williams, V.V. (eds.) 53rd ACM STOC, pp. 708\u2013721. ACM Press (2021). https:\/\/doi.org\/10.1145\/3406325.3451055","DOI":"10.1145\/3406325.3451055"},{"key":"14_CR19","doi-asserted-by":"publisher","unstructured":"Kalai, Y., Lombardi, A., Vaikuntanathan, V., Wichs, D.: Boosting batch arguments and RAM delegation. In: Saha, B., Servedio, R.A. (eds.) 55th ACM STOC, pp. 1545\u20131552. ACM Press (2023). https:\/\/doi.org\/10.1145\/3564246.3585200","DOI":"10.1145\/3564246.3585200"},{"key":"14_CR20","doi-asserted-by":"publisher","unstructured":"Kalai, Y.T., Paneth, O., Yang, L.: How to delegate computations publicly. In: Charikar, M., Cohen, E. (eds.) 51st ACM STOC, pp. 1115\u20131124. ACM Press (2019). https:\/\/doi.org\/10.1145\/3313276.3316411","DOI":"10.1145\/3313276.3316411"},{"key":"14_CR21","doi-asserted-by":"publisher","unstructured":"Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT\u00a02010. LNCS, vol.\u00a06477, pp. 177\u2013194. Springer, Berlin, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-17373-8_11","DOI":"10.1007\/978-3-642-17373-8_11"},{"key":"14_CR22","doi-asserted-by":"publisher","unstructured":"Khovratovich, D., Rothblum, R.D., Soukhanov, L.: How to prove false statements: Practical attacks on Fiat-Shamir. In: Kalai, Y.T., Kamara, S.F. (eds.) CRYPTO\u00a02025, Part\u00a0VI. LNCS, vol. 16005, pp. 3\u201326. Springer, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-01887-8_1","DOI":"10.1007\/978-3-032-01887-8_1"},{"key":"14_CR23","doi-asserted-by":"publisher","unstructured":"Lai, R.W.F., Malavolta, G.: Subvector commitments with application to succinct arguments. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO\u00a02019, Part\u00a0I. LNCS, vol. 11692, pp. 530\u2013560. Springer, Cham (Aug 2019). https:\/\/doi.org\/10.1007\/978-3-030-26948-7_19","DOI":"10.1007\/978-3-030-26948-7_19"},{"key":"14_CR24","doi-asserted-by":"publisher","unstructured":"Libert, B., Ramanna, S.C., Yung, M.: Functional commitment schemes: from polynomial commitments to pairing-based accumulators from simple assumptions. In: Chatzigiannakis, I., Mitzenmacher, M., Rabani, Y., Sangiorgi, D. (eds.) ICALP 2016. LIPIcs, vol.\u00a055, pp. 30:1\u201330:14. Schloss Dagstuhl (2016). https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2016.30","DOI":"10.4230\/LIPIcs.ICALP.2016.30"},{"key":"14_CR25","doi-asserted-by":"publisher","unstructured":"Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC\u00a02010. LNCS, vol.\u00a05978, pp. 499\u2013517. Springer, Berlin, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-11799-2_30","DOI":"10.1007\/978-3-642-11799-2_30"},{"key":"14_CR26","doi-asserted-by":"publisher","unstructured":"Lipmaa, H., Pavlyk, K.: Succinct functional commitment for a large class of arithmetic circuits. In: Moriai, S., Wang, H. (eds.) ASIACRYPT\u00a02020, Part\u00a0III. LNCS, vol. 12493, pp. 686\u2013716. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64840-4_23","DOI":"10.1007\/978-3-030-64840-4_23"},{"key":"14_CR27","doi-asserted-by":"publisher","unstructured":"Peikert, C., Pepin, Z., Sharp, C.: Vector and functional commitments from lattices. In: Nissim, K., Waters, B. (eds.) TCC\u00a02021, Part\u00a0III. LNCS, vol. 13044, pp. 480\u2013511. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90456-2_16","DOI":"10.1007\/978-3-030-90456-2_16"},{"key":"14_CR28","doi-asserted-by":"publisher","unstructured":"Wee, H.: Functional commitments and SNARGs for P\/poly from SIS. In: Kalai, Y.T., Kamara, S.F. (eds.) CRYPTO\u00a02025, Part\u00a0VI. LNCS, vol. 16005, pp. 617\u2013640. Springer, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-01887-8_20","DOI":"10.1007\/978-3-032-01887-8_20"},{"key":"14_CR29","doi-asserted-by":"publisher","unstructured":"Wee, H., Wu, D.J.: Lattice-based functional commitments: fast verification and cryptanalysis. In: Guo, J., Steinfeld, R. (eds.) ASIACRYPT\u00a02023, Part\u00a0V. LNCS, vol. 14442, pp. 201\u2013235. Springer, Singapore (2023). https:\/\/doi.org\/10.1007\/978-981-99-8733-7_7","DOI":"10.1007\/978-981-99-8733-7_7"},{"key":"14_CR30","doi-asserted-by":"publisher","unstructured":"Wee, H., Wu, D.J.: Succinct vector, polynomial, and functional commitments from lattices. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0III. LNCS, vol. 14006, pp. 385\u2013416. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30620-4_13","DOI":"10.1007\/978-3-031-30620-4_13"},{"key":"14_CR31","doi-asserted-by":"publisher","unstructured":"Wee, H., Wu, D.J.: Succinct functional commitments for circuits from k-Lin. In: Joye, M., Leander, G. (eds.) EUROCRYPT\u00a02024, Part\u00a0II. LNCS, vol. 14652, pp. 280\u2013310. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-58723-8_10","DOI":"10.1007\/978-3-031-58723-8_10"}],"container-title":["Lecture Notes in Computer Science","Public-Key Cryptography \u2013 PKC 2026"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-26734-4_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T16:24:41Z","timestamp":1779467081000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-26734-4_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032267337","9783032267344"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-26734-4_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"23 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PKC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"IACR International Conference on Public-Key Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"West Palm Beach, FL","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":"25 May 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 May 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pkc2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/pkc.iacr.org\/2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}