{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T01:12:57Z","timestamp":1779325977975,"version":"3.51.4"},"publisher-location":"Singapore","reference-count":25,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819987320","type":"print"},{"value":"9789819987337","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023]]},"DOI":"10.1007\/978-981-99-8733-7_2","type":"book-chapter","created":{"date-parts":[[2023,12,17]],"date-time":"2023-12-17T08:02:20Z","timestamp":1702800140000},"page":"33-65","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Verifiable Decentralized Multi-client Functional Encryption for\u00a0Inner Product"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7892-9146","authenticated-orcid":false,"given":"Dinh Duy","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1136-4064","authenticated-orcid":false,"given":"Duong Hieu","family":"Phan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6668-683X","authenticated-orcid":false,"given":"David","family":"Pointcheval","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,18]]},"reference":[{"key":"2_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1007\/978-3-030-34618-8_19","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2019","author":"M Abdalla","year":"2019","unstructured":"Abdalla, M., Benhamouda, F., Gay, R.: From single-input to multi-client inner-product functional encryption. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 552\u2013582. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34618-8_19"},{"key":"2_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1007\/978-3-030-17259-6_5","volume-title":"Public-Key Cryptography \u2013 PKC 2019","author":"M Abdalla","year":"2019","unstructured":"Abdalla, M., Benhamouda, F., Kohlweiss, M., Waldner, H.: Decentralizing inner-product functional encryption. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 128\u2013157. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17259-6_5"},{"key":"2_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/978-3-319-96878-0_22","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"S Agrawal","year":"2018","unstructured":"Agrawal, S., Ganesh, C., Mohassel, P.: Non-interactive zero-knowledge proofs for composite statements. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 643\u2013673. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_22"},{"key":"2_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-662-53015-3_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"S Agrawal","year":"2016","unstructured":"Agrawal, S., Libert, B., Stehl\u00e9, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 333\u2013362. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53015-3_12"},{"key":"2_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/978-3-662-53890-6_19","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016","author":"S Badrinarayanan","year":"2016","unstructured":"Badrinarayanan, S., Goyal, V., Jain, A., Sahai, A.: Verifiable functional encryption. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 557\u2013587. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53890-6_19"},{"key":"2_CR6","unstructured":"Bell, J., Gasc\u00f3n, A., Lepoint, T., Li, B., Meiklejohn, S., Raykova, M., Yun, C.: ACORN: input validation for secure aggregation. Cryptology ePrint Archive, Report 2022\/1461 (2022). https:\/\/eprint.iacr.org\/2022\/1461"},{"key":"2_CR7","doi-asserted-by":"publisher","unstructured":"Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: 20th ACM STOC, pp. 103\u2013112. ACM Press, May 1988. https:\/\/doi.org\/10.1145\/62212.62222","DOI":"10.1145\/62212.62222"},{"key":"2_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/978-3-642-19571-6_16","volume-title":"Theory of Cryptography","author":"D Boneh","year":"2011","unstructured":"Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253\u2013273. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-19571-6_16"},{"key":"2_CR9","doi-asserted-by":"publisher","unstructured":"B\u00fcnz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy, pp. 315\u2013334. IEEE Computer Society Press, May 2018. https:\/\/doi.org\/10.1109\/SP.2018.00020","DOI":"10.1109\/SP.2018.00020"},{"key":"2_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/978-3-030-26954-8_7","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"G Castagnos","year":"2019","unstructured":"Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Two-party ECDSA from hash proof systems and efficient instantiations. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 191\u2013221. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26954-8_7"},{"key":"2_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1007\/978-3-030-45388-6_10","volume-title":"Public-Key Cryptography \u2013 PKC 2020","author":"G Castagnos","year":"2020","unstructured":"Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Bandwidth-efficient threshold EC-DSA. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 266\u2013296. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45388-6_10"},{"key":"2_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/978-3-319-16715-2_26","volume-title":"Topics in Cryptology \u2014 CT-RSA 2015","author":"G Castagnos","year":"2015","unstructured":"Castagnos, G., Laguillaumie, F.: Linearly homomorphic encryption from $$\\sf DDH$$. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 487\u2013505. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-16715-2_26"},{"key":"2_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1007\/978-3-030-03329-3_25","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"G Castagnos","year":"2018","unstructured":"Castagnos, G., Laguillaumie, F., Tucker, I.: Practical fully secure unrestricted inner product functional encryption modulo p. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 733\u2013764. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03329-3_25"},{"key":"2_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/978-3-030-03329-3_24","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"J Chotard","year":"2018","unstructured":"Chotard, J., Dufour Sans, E., Gay, R., Phan, D.H., Pointcheval, D.: Decentralized multi-client functional encryption for inner product. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 703\u2013732. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03329-3_24"},{"key":"2_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1007\/978-3-030-56784-2_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2020","author":"J Chotard","year":"2020","unstructured":"Chotard, J., Dufour-Sans, E., Gay, R., Phan, D.H., Pointcheval, D.: Dynamic decentralized functional encryption. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12170, pp. 747\u2013775. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56784-2_25"},{"key":"2_CR16","doi-asserted-by":"publisher","unstructured":"Couteau, G., Goudarzi, D., Kloo\u00df, M., Reichle, M.: Sharp: Short relaxed range proofs. In: Yin, H., Stavrou, A., Cremers, C., Shi, E. (eds.) ACM CCS 2022, pp. 609\u2013622. ACM Press, November 2022. https:\/\/doi.org\/10.1145\/3548606.3560628","DOI":"10.1145\/3548606.3560628"},{"key":"2_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-030-77883-5_9","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"G Couteau","year":"2021","unstructured":"Couteau, G., Kloo\u00df, M., Lin, H., Reichle, M.: Efficient range proofs with transparent setup from bounded integer commitments. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 247\u2013277. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77883-5_9"},{"key":"2_CR18","doi-asserted-by":"publisher","unstructured":"Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: 31st FOCS. pp. 308\u2013317. IEEE Computer Society Press, October 1990. https:\/\/doi.org\/10.1109\/FSCS.1990.89549","DOI":"10.1109\/FSCS.1990.89549"},{"issue":"4","key":"2_CR19","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s00145-006-0224-0","volume":"19","author":"M Girault","year":"2006","unstructured":"Girault, M., Poupard, G., Stern, J.: On the fly authentication and signature schemes based on groups of unknown order. J. Cryptol. 19(4), 463\u2013487 (2006). https:\/\/doi.org\/10.1007\/s00145-006-0224-0","journal-title":"J. Cryptol."},{"key":"2_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1007\/978-3-642-55220-5_32","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"S Goldwasser","year":"2014","unstructured":"Goldwasser, S., Gordon, S.D., Goyal, V., Jain, A., Katz, J., Liu, F.-H., Sahai, A., Shi, E., Zhou, H.-S.: Multi-input functional encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578\u2013602. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-55220-5_32"},{"key":"2_CR21","unstructured":"Gordon, S.D., Katz, J., Liu, F.H., Shi, E., Zhou, H.S.: Multi-input functional encryption. Cryptology ePrint Archive, Report 2013\/774 (2013). https:\/\/eprint.iacr.org\/2013\/774"},{"key":"2_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1007\/978-3-030-34618-8_18","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2019","author":"B Libert","year":"2019","unstructured":"Libert, B., \u0162i\u0163iu, R.: Multi-client functional encryption for linear functions in the standard model from LWE. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 520\u2013551. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34618-8_18"},{"key":"2_CR23","unstructured":"Nguyen, D.D., Phan, D.H., Pointcheval, D.: Verifiable decentralized multi-client functional encryption for inner product. Cryptology ePrint Archive, Paper 2023\/268 (2023). https:\/\/eprint.iacr.org\/2023\/268, https:\/\/eprint.iacr.org\/2023\/268"},{"key":"2_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/3-540-68339-9_33","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201996","author":"D Pointcheval","year":"1996","unstructured":"Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387\u2013398. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/3-540-68339-9_33"},{"key":"2_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BFb0054113","volume-title":"Advances in Cryptology \u2014 EUROCRYPT\u201998","author":"V Shoup","year":"1998","unstructured":"Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 1\u201316. Springer, Heidelberg (1998). https:\/\/doi.org\/10.1007\/BFb0054113"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2023"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-99-8733-7_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T01:02:59Z","timestamp":1765933379000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-99-8733-7_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9789819987320","9789819987337"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-981-99-8733-7_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"18 December 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ASIACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on the Theory and Application of Cryptology and Information Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Guangzhou","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 December 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 December 2023","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":"asiacrypt2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2023\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"HotCRP","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"375","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"106","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"12","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}