{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:41:39Z","timestamp":1774629699427,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662536438","type":"print"},{"value":"9783662536445","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","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":[[2016]]},"DOI":"10.1007\/978-3-662-53644-5_9","type":"book-chapter","created":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T03:24:08Z","timestamp":1476933848000},"page":"217-238","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":105,"title":["Multi-key FHE from LWE, Revisited"],"prefix":"10.1007","author":[{"given":"Chris","family":"Peikert","sequence":"first","affiliation":[]},{"given":"Sina","family":"Shiehian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,10,21]]},"reference":[{"key":"9_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-662-53018-4_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"M Albrecht","year":"2016","unstructured":"Albrecht, M., Bai, S., Ducas, L.: A subfield lattice attack on overstretched NTRU assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 153\u2013178. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53018-4_6"},{"key":"9_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/978-3-662-44371-2_17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"J Alperin-Sheriff","year":"2014","unstructured":"Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 297\u2013314. Springer, Heidelberg (2014). doi:\n                      10.1007\/978-3-662-44371-2_17"},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/978-3-642-03356-8_35","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"B Applebaum","year":"2009","unstructured":"Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595\u2013618. Springer, Heidelberg (2009). doi:\n                      10.1007\/978-3-642-03356-8_35"},{"key":"9_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-29011-4_29","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"G Asharov","year":"2012","unstructured":"Asharov, G., Jain, A., L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483\u2013501. Springer, Heidelberg (2012). doi:\n                      10.1007\/978-3-642-29011-4_29"},{"key":"9_CR5","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehl\u00e9, D.: Classical hardness of learning with errors. In: STOC, pp. 575\u2013584 (2013)","DOI":"10.1145\/2488608.2488680"},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/978-3-662-53018-4_8","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"Z Brakerski","year":"2016","unstructured":"Brakerski, Z., Perlman, R.: Lattice-based fully dynamic multi-key FHE with short ciphertexts. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 190\u2013213. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53018-4_8"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Lattice-based FHE as secure as PKE. In: ITCS, pp. 1\u201312 (2014)","DOI":"10.1145\/2554797.2554799"},{"key":"9_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-662-48000-7_31","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"M Clear","year":"2015","unstructured":"Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 630\u2013656. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-48000-7_31"},{"key":"9_CR9","unstructured":"Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009). \n                      http:\/\/crypto.stanford.edu\/craig"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/978-3-642-14623-7_9","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"C Gentry","year":"2010","unstructured":"Gentry, C., Halevi, S., Vaikuntanathan, V.: i-hop homomorphic encryption and rerandomizable Yao circuits. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 155\u2013172. Springer, Heidelberg (2010). doi:\n                      10.1007\/978-3-642-14623-7_9"},{"key":"9_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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. LNCS, vol. 8042, pp. 75\u201392. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-40041-4_5"},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: STOC, pp. 469\u2013477 (2015)","DOI":"10.1145\/2746539.2746576"},{"key":"9_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BFb0054868","volume-title":"Algorithmic Number Theory","author":"J Hoffstein","year":"1998","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267\u2013288. Springer, Heidelberg (1998). doi:\n                      10.1007\/BFb0054868"},{"key":"9_CR14","unstructured":"Kirchner, P., Fouque, P.-A.: Comparison between subfield and straightforward attacks on NTRU. Cryptology ePrint Archive, Report 2016\/717 (2016). \n                      http:\/\/eprint.iacr.org\/2016\/717"},{"key":"9_CR15","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: STOC, pp. 1219\u20131234 (2012)","DOI":"10.1145\/2213977.2214086"},{"issue":"6","key":"9_CR16","doi-asserted-by":"publisher","first-page":"43:1","DOI":"10.1145\/2535925","volume":"60","author":"V Lyubashevsky","year":"2013","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices, learning with errors over rings. J. ACM 60(6), 43:1\u201343:35 (2013). Preliminary version in Eurocrypt 2010","journal-title":"J. ACM"},{"key":"9_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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). doi:\n                      10.1007\/978-3-642-29011-4_41"},{"key":"9_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1007\/978-3-662-49896-5_26","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"P Mukherjee","year":"2016","unstructured":"Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 735\u2013763. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49896-5_26"},{"key":"9_CR19","doi-asserted-by":"crossref","unstructured":"Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: STOC, pp. 333\u2013342 (2009)","DOI":"10.1145\/1536414.1536461"},{"issue":"6","key":"9_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1568318.1568324","volume":"56","author":"O Regev","year":"2009","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 1\u201340 (2009). Preliminary version in STOC 2005","journal-title":"J. ACM"}],"container-title":["Lecture Notes in Computer Science","Theory of Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-53644-5_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T00:13:02Z","timestamp":1603411982000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-53644-5_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783662536438","9783662536445"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-53644-5_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"21 October 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TCC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Theory of Cryptography Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Beijing","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":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 November 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 November 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tcc2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}