{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T16:54:53Z","timestamp":1778345693289,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662479995","type":"print"},{"value":"9783662480007","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-662-48000-7_31","type":"book-chapter","created":{"date-parts":[[2015,7,30]],"date-time":"2015-07-30T22:27:46Z","timestamp":1438295266000},"page":"630-656","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":167,"title":["Multi-identity and Multi-key Leveled FHE from Learning with Errors"],"prefix":"10.1007","author":[{"given":"Michael","family":"Clear","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ciar\u00e1n","family":"McGoldrick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,8,1]]},"reference":[{"key":"31_CR1","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, p. 169 (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"31_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1007\/978-3-642-13013-7_25","volume-title":"Public Key Cryptography \u2013 PKC 2010","author":"NP Smart","year":"2010","unstructured":"Smart, N.P., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420\u2013443. Springer, Heidelberg (2010)"},{"key":"31_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/978-3-642-13190-5_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"M Dijk van","year":"2010","unstructured":"van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24\u201343. Springer, Heidelberg (2010)"},{"key":"31_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/978-3-642-22792-9_29","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"Z Brakerski","year":"2011","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-lwe and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505\u2013524. Springer, Heidelberg (2011)"},{"key":"31_CR5","first-page":"97","volume-title":"FOCS 2011","author":"Z Brakerski","year":"2011","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) FOCS 2011, pp. 97\u2013106. IEEE, Olympia (2011)"},{"key":"31_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/978-3-642-40041-4_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"C Gentry","year":"2013","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75\u201392. Springer, Heidelberg (2013)"},{"key":"31_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"D Boneh","year":"2001","unstructured":"Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213\u2013229. Springer, Heidelberg (2001)"},{"key":"31_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1007\/3-540-45325-3_32","volume-title":"Cryptography and Coding","author":"C Cocks","year":"2001","unstructured":"Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360\u2013363. Springer, Heidelberg (2001)"},{"key":"31_CR9","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM symposium on Theory of Computing, STOC 2005, pp. 84\u201393. ACM, New York, NY, USA (2005)","DOI":"10.1145\/1060590.1060603"},{"key":"31_CR10","unstructured":"Clear, M., McGoldrick, C.: Bootstrappable identity-based fully homomorphic encryption. Cryptology ePrint Archive, report 2014\/491 (2014). \n                      http:\/\/eprint.iacr.org\/"},{"key":"31_CR11","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40\u201349. IEEE Computer Society (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"31_CR12","series-title":"Lecture Notes in Computer Science","first-page":"1","volume-title":"Cryptology and Network Security","author":"M Clear","year":"2014","unstructured":"Clear, M., McGoldrick, C.: Bootstrappable identity-based fully homomorphic encryption. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds.) CANS 2014. LNCS, vol. 8813, pp. 1\u201319. Springer, Heidelberg (2014)"},{"key":"31_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-642-25385-0_2","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2011","author":"S Agrawal","year":"2011","unstructured":"Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21\u201340. Springer, Heidelberg (2011)"},{"key":"31_CR14","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the 44th Symposium on Theory of Computing, STOC 2012, pp. 1219\u20131234. ACM, New York, NY, USA (2012)","DOI":"10.1145\/2213977.2214086"},{"key":"31_CR15","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 197\u2013206. ACM, New York, (2008)"},{"key":"31_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/978-3-642-13190-5_28","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"S Agrawal","year":"2010","unstructured":"Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553\u2013572. Springer, Heidelberg (2010)"},{"key":"31_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/978-3-642-14623-7_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"S Agrawal","year":"2010","unstructured":"Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98\u2013115. Springer, Heidelberg (2010)"},{"key":"31_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/978-3-642-13190-5_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"D Cash","year":"2010","unstructured":"Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523\u2013552. Springer, Heidelberg (2010)"},{"key":"31_CR19","unstructured":"Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. IACR Cryptology ePrint Archive 2014, p. 798 (2014). \n                      http:\/\/eprint.iacr.org\/2014\/798"},{"key":"31_CR20","series-title":"Lecture Notes in Computer Science","volume-title":"Advances in Cryptology - EUROCRYPT 2010","year":"2010","unstructured":"Gilbert, H. (ed.): Advances in Cryptology - EUROCRYPT 2010. LNCS, vol. 6110. Springer, Heidelberg (2010)"},{"key":"31_CR21","series-title":"Lecture Notes in Computer Science","first-page":"1","volume-title":"Automata, Languages and Programming","author":"M Ajtai","year":"1999","unstructured":"Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1\u20139. Springer, Heidelberg (1999)"},{"key":"31_CR22","unstructured":"Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. Cryptology ePrint Archive, report 2008\/521 (2008). \n                      http:\/\/eprint.iacr.org\/2008\/521"},{"key":"31_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1007\/978-3-642-29011-4_41","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"D Micciancio","year":"2012","unstructured":"Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700\u2013718. Springer, Heidelberg (2012)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology -- CRYPTO 2015"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-48000-7_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T20:09:13Z","timestamp":1565381353000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-48000-7_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662479995","9783662480007"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-48000-7_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"1 August 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}