{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T02:12:26Z","timestamp":1792462346791,"version":"4.5.0"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662543870","type":"print"},{"value":"9783662543887","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"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":[[2017]]},"DOI":"10.1007\/978-3-662-54388-7_10","type":"book-chapter","created":{"date-parts":[[2017,2,25]],"date-time":"2017-02-25T09:12:22Z","timestamp":1488013942000},"page":"271-301","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["FHE over the Integers: Decomposed and Batched in the Post-Quantum Regime"],"prefix":"10.1007","author":[{"given":"Daniel","family":"Benarroch","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zvika","family":"Brakerski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tancr\u00e8de","family":"Lepoint","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,2,26]]},"reference":[{"key":"10_CR1","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: 10.1007\/978-3-662-44371-2_17"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1007\/978-3-642-32009-5_50","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"Z Brakerski","year":"2012","unstructured":"Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868\u2013886. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-32009-5_50"},{"key":"10_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-36362-7_1","volume-title":"Public-Key Cryptography \u2013 PKC 2013","author":"Z Brakerski","year":"2013","unstructured":"Brakerski, Z., Gentry, C., Halevi, S.: Packed ciphertexts in LWE-based homomorphic encryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 1\u201313. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-36362-7_1"},{"key":"10_CR4","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309\u2013325. ACM (2012)","DOI":"10.1145\/2090236.2090262"},{"key":"10_CR5","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: FOCS, pp. 97\u2013106. IEEE Computer Society (2011). Full version in https:\/\/eprint.iacr.org\/2011\/344.pdf"},{"key":"10_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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). doi: 10.1007\/978-3-642-22792-9_29"},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Lattice-based FHE as secure as PKE. In: ITCS, pp. 1\u201312. ACM (2014)","DOI":"10.1145\/2554797.2554799"},{"key":"10_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1007\/978-3-642-29011-4_30","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"Y Chen","year":"2012","unstructured":"Chen, Y., Nguyen, P.Q.: Faster algorithms for approximate common divisors: breaking fully-homomorphic-encryption challenges over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 502\u2013519. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-29011-4_30"},{"key":"10_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/978-3-642-38348-9_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"JH Cheon","year":"2013","unstructured":"Cheon, J.H., Coron, J.-S., Kim, J., Lee, M.S., Lepoint, T., Tibouchi, M., Yun, A.: Batch fully homomorphic encryption over the integers. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 315\u2013335. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-38348-9_20"},{"key":"10_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/978-3-662-46800-5_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"JH Cheon","year":"2015","unstructured":"Cheon, J.H., Stehl\u00e9, D.: Fully homomophic encryption over the integers revisited. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 513\u2013536. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-46800-5_20"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-662-53887-6_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016","author":"I Chillotti","year":"2016","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: Faster fully homomorphic encryption: bootstrapping in less than 0.1 seconds. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 3\u201333. Springer, Heidelberg (2016). doi: 10.1007\/978-3-662-53887-6_1"},{"key":"10_CR12","doi-asserted-by":"crossref","unstructured":"Cohn, H., Heninger, N.: Approximate Common Divisors via Lattices. The Open Book Series, vol. 1, no. 1, pp. 271\u2013293 (2013)","DOI":"10.2140\/obs.2013.1.271"},{"key":"10_CR13","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Batch fully homomorphic encryption over the integers. IACR Cryptology ePrint Archive, 2013:36 (2013)"},{"key":"10_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-642-54631-0_18","volume-title":"Public-Key Cryptography \u2013 PKC 2014","author":"J-S Coron","year":"2014","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Scale-invariant fully homomorphic encryption over the integers. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 311\u2013328. Springer, Heidelberg (2014). doi: 10.1007\/978-3-642-54631-0_18"},{"key":"10_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/978-3-642-22792-9_28","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"J-S Coron","year":"2011","unstructured":"Coron, J.-S., Mandal, A., Naccache, D., Tibouchi, M.: Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487\u2013504. Springer, Heidelberg (2011). doi: 10.1007\/978-3-642-22792-9_28"},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-642-29011-4_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"J-S Coron","year":"2012","unstructured":"Coron, J.-S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 446\u2013464. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-29011-4_27"},{"key":"10_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/978-3-662-46800-5_24","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"L Ducas","year":"2015","unstructured":"Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 617\u2013640. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-46800-5_24"},{"key":"10_CR18","doi-asserted-by":"crossref","unstructured":"Galbraith, S.D., Gebregiyorgis, S.W., Murphy, S.: Algorithms for the approximate common divisor problem. IACR Cryptology ePrint Archive, 2016:215 (2016)","DOI":"10.1112\/S1461157016000218"},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169\u2013178. ACM (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"10_CR20","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: 10.1007\/978-3-642-40041-4_5"},{"issue":"4","key":"10_CR21","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1137\/S0097539793244708","volume":"28","author":"J H\u00e5stad","year":"1999","unstructured":"H\u00e5stad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364\u20131396 (1999)","journal-title":"SIAM J. Comput."},{"key":"10_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/3-540-44670-2_6","volume-title":"Cryptography and Lattices","author":"N Howgrave-Graham","year":"2001","unstructured":"Howgrave-Graham, N.: Approximate integer common divisors. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 51\u201366. Springer, Heidelberg (2001). doi: 10.1007\/3-540-44670-2_6"},{"issue":"9","key":"10_CR23","doi-asserted-by":"publisher","first-page":"2848","DOI":"10.1109\/TC.2015.2500576","volume":"65","author":"P Alhassan Khedr","year":"2016","unstructured":"Alhassan Khedr, P., Gulak, G., Vaikuntanathan, V.: SHIELD: scalable homomorphic implementation of encrypted data-classifiers. IEEE Trans. Comput. 65(9), 2848\u20132858 (2016)","journal-title":"IEEE Trans. Comput."},{"key":"10_CR24","unstructured":"Kim, J., Lee, M.S., Yun, A., Cheon, J.H.: CRT-based fully homomorphic encryption over the integers. IACR Cryptology ePrint Archive, 2013:57 (2013)"},{"issue":"1","key":"10_CR25","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1137\/0214016","volume":"14","author":"JC Lagarias","year":"1985","unstructured":"Lagarias, J.C.: The computational complexity of simultaneous diophantine approximation problems. SIAM J. Comput. 14(1), 196\u2013209 (1985)","journal-title":"SIAM J. Comput."},{"key":"10_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/3-540-44670-2_12","volume-title":"Cryptography and Lattices","author":"PQ Nguyen","year":"2001","unstructured":"Nguyen, P.Q., Stern, J.: The two faces of lattices in cryptology. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 146\u2013180. Springer, Heidelberg (2001). doi: 10.1007\/3-540-44670-2_12"},{"key":"10_CR27","unstructured":"Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169\u2013177. Academic Press (1978)"},{"key":"10_CR28","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: FOCS, pp. 124\u2013134. IEEE Computer Society (1994)","DOI":"10.1109\/SFCS.1994.365700"},{"issue":"1","key":"10_CR29","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10623-012-9720-4","volume":"71","author":"NP Smart","year":"2014","unstructured":"Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Cryptogr. 71(1), 57\u201381 (2014)","journal-title":"Des. Codes Cryptogr."},{"key":"10_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-642-13190-5_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"M Dijk","year":"2010","unstructured":"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). doi: 10.1007\/978-3-642-13190-5_2"}],"container-title":["Lecture Notes in Computer Science","Public-Key Cryptography \u2013 PKC 2017"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-54388-7_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,15]],"date-time":"2025-06-15T18:59:25Z","timestamp":1750013965000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-54388-7_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783662543870","9783662543887"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-54388-7_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"26 February 2017","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 Workshop on Public Key Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Amsterdam","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 March 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 March 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pkc2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iacr.org\/workshops\/pkc2017\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}