{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:29:46Z","timestamp":1774448986435,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642290107","type":"print"},{"value":"9783642290114","type":"electronic"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-29011-4_27","type":"book-chapter","created":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T07:05:53Z","timestamp":1333609553000},"page":"446-464","source":"Crossref","is-referenced-by-count":152,"title":["Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers"],"prefix":"10.1007","author":[{"given":"Jean-S\u00e9bastien","family":"Coron","sequence":"first","affiliation":[]},{"given":"David","family":"Naccache","sequence":"additional","affiliation":[]},{"given":"Mehdi","family":"Tibouchi","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"27_CR1","unstructured":"Bernstein, D.J.: How to Find Smooth Parts of Integers (2004), \n                    \n                      http:\/\/cr.yp.to\/papers.html#smoothparts"},{"key":"27_CR2","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient Fully Homomorphic Encryption from (Standard) LWE. In: Proceedings of FOCS 2011 (2011); Full version available at IACR eprint","DOI":"10.1109\/FOCS.2011.12"},{"key":"27_CR3","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.\u00a06841, pp. 505\u2013524. Springer, Heidelberg (2011)"},{"key":"27_CR4","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully Homomorphic Encryption without Bootstrapping. Cryptology ePrint Archive, Report 2011\/277","DOI":"10.1145\/2090236.2090262"},{"key":"27_CR5","doi-asserted-by":"crossref","unstructured":"Chen, Y., Nguyen, P.Q.: Faster Algorithms for Approximate Common Divisors: Breaking Fully-Homomorphic-Encryption Challenges over the Integers. Cryptology ePrint Archive, Report 2011\/436","DOI":"10.1007\/978-3-642-29011-4_30"},{"key":"27_CR6","doi-asserted-by":"crossref","unstructured":"Coron, J.S., Naccache, D., Tibouchi, M.: Public-key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers. Full version of this paper. Cryptology ePrint Archive, Report 2011\/440","DOI":"10.1007\/978-3-642-29011-4_27"},{"key":"27_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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.\u00a06841, pp. 487\u2013504. Springer, Heidelberg (2011); Full version available at IACR eprint"},{"key":"27_CR8","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 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.\u00a06110, pp. 24\u201343. Springer, Heidelberg (2010)"},{"key":"27_CR9","doi-asserted-by":"crossref","unstructured":"Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009), \n                    \n                      http:\/\/crypto.stanford.edu\/craig","DOI":"10.1145\/1536414.1536440"},{"key":"27_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/978-3-642-20465-4_9","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"C. Gentry","year":"2011","unstructured":"Gentry, C., Halevi, S.: Implementing Gentry\u2019s Fully-Homomorphic Encryption Scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol.\u00a06632, pp. 129\u2013148. Springer, Heidelberg (2011)"},{"key":"27_CR11","doi-asserted-by":"crossref","unstructured":"Lauter, K., Naehrig, M., Vaikuntanathan, V.: Can Homomorphic Encryption be Practical? Cryptology ePrint Archive, Report 2011\/405","DOI":"10.1145\/2046660.2046682"},{"key":"27_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-49649-1_1","volume-title":"Advances in Cryptology - ASIACRYPT\u201998","author":"A.K. Lenstra","year":"1998","unstructured":"Lenstra, A.K.: Generating RSA Moduli with a Predetermined Portion. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 1\u201310. Springer, Heidelberg (1998)"},{"issue":"3","key":"27_CR13","doi-asserted-by":"publisher","first-page":"649","DOI":"10.2307\/1971363","volume":"126","author":"H.W. Lenstra","year":"1987","unstructured":"Lenstra, H.W.: Factoring integers with elliptic curves. Annals of Mathematics\u00a0126(3), 649\u2013673 (1987)","journal-title":"Annals of Mathematics"},{"key":"27_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1007\/978-3-642-13013-7_25","volume-title":"Public Key Cryptography \u2013 PKC 2010","author":"N.P. 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.\u00a06056, pp. 420\u2013443. Springer, Heidelberg (2010)"},{"key":"27_CR15","unstructured":"Stein, W.A., et al.: Sage Mathematics Software (Version 4.7.2), The Sage Development Team (2011), \n                    \n                      http:\/\/www.sagemath.org"},{"key":"27_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/978-3-642-17373-8_22","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"D. Stehl\u00e9","year":"2010","unstructured":"Stehl\u00e9, D., Steinfeld, R.: Faster Fully Homomorphic Encryption. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol.\u00a06477, pp. 377\u2013394. Springer, Heidelberg (2010)"},{"key":"27_CR17","unstructured":"https:\/\/github.com\/coron\/fhe"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2012"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-29011-4_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T00:54:01Z","timestamp":1558313641000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-29011-4_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642290107","9783642290114"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-29011-4_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}