{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,13]],"date-time":"2026-11-13T03:06:07Z","timestamp":1794539167394,"version":"4.9.1"},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662543641","type":"print"},{"value":"9783662543658","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\/978-3-662-54365-8_1","type":"book-chapter","created":{"date-parts":[[2017,2,25]],"date-time":"2017-02-25T04:12:23Z","timestamp":1487995943000},"page":"3-15","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["LP Solutions of Vectorial Integer Subset Sums \u2013 Cryptanalysis of Galbraith\u2019s Binary Matrix LWE"],"prefix":"10.1007","author":[{"given":"Gottfried","family":"Herold","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"May","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,2,26]]},"reference":[{"key":"1_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1007\/978-3-642-40041-4_23","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"D Boneh","year":"2013","unstructured":"Boneh, D., Lewi, K., Montgomery, H., Raghunathan, A.: Key homomorphic PRFs and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 410\u2013428. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-40041-4_23"},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehl\u00e9, D.: Classical hardness of learning with errors. In: Boneh, D., Roughgarden, T., Feigenbaum, J., (eds.), 45th ACM STOC, Palo Alto, CA, USA, 1\u20134 June, pp. 575\u2013584. ACM Press (2013)","DOI":"10.1145\/2488608.2488680"},{"key":"1_CR3","doi-asserted-by":"crossref","unstructured":"Buchmann, J.A., G\u00f6pfert, F., Player, R., Wunderer, T.: On the hardness of LWE with binary error: revisiting the hybrid lattice-reduction and meet-in-the-middle attack. IACR Cryptology ePrint Archive, p. 89 (2016)","DOI":"10.1007\/978-3-319-31517-1_2"},{"key":"1_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-662-49890-3_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"W Castryck","year":"2016","unstructured":"Castryck, W., Iliashenko, I., Vercauteren, F.: Provably weak instances of ring-LWE revisited. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 147\u2013167. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49890-3_6"},{"key":"1_CR5","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:\n                      10.1007\/978-3-642-29011-4_27"},{"key":"1_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/978-3-662-47989-6_4","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"Y Elias","year":"2015","unstructured":"Elias, Y., Lauter, K.E., Ozman, E., Stange, K.E.: Provably weak instances of ring-LWE. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 63\u201392. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-47989-6_4"},{"key":"1_CR7","unstructured":"Farkas, J.: Theorie der einfachen Ungleichungen. J. f\u00fcr die reine und angewandte Mathematik (Crelle\u2019s Journal) 124, 1\u201327 (1902). \n                      http:\/\/resolver.sub.uni-goettingen.de\/purl?GDZPPN002165023"},{"key":"1_CR8","unstructured":"Galbraith, S.D.: Space-efficient variants of cryptosystems based on learning with errors (2013). \n                      https:\/\/www.math.auckland.ac.nz\/sgal018\/pubs.html"},{"key":"1_CR9","series-title":"Algorithms and Combinatorics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78240-4","volume-title":"Geometric Algorithms and Combinatorial Optimization","author":"M Gr\u00f6tschel","year":"2012","unstructured":"Gr\u00f6tschel, M., Lov\u00e1sz, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics. Springer, Heidelberg (2012). doi:\n                      10.1007\/978-3-642-78240-4\n                      \n                    . ISBN 978-3-642-78240-4"},{"key":"1_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1007\/978-3-642-33027-8_31","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2012","author":"T G\u00fcneysu","year":"2012","unstructured":"G\u00fcneysu, T., Lyubashevsky, V., P\u00f6ppelmann, T.: Practical lattice-based cryptography: a signature scheme for embedded systems. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 530\u2013547. Springer, Heidelberg (2012). doi:\n                      10.1007\/978-3-642-33027-8_31"},{"key":"1_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-662-47989-6_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"P Kirchner","year":"2015","unstructured":"Kirchner, P., Fouque, P.-A.: An improved BKW algorithm for LWE with applications to cryptography and lattices. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 43\u201362. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-47989-6_3"},{"key":"1_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/978-3-642-19074-2_21","volume-title":"Topics in Cryptology \u2013 CT-RSA 2011","author":"R Lindner","year":"2011","unstructured":"Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319\u2013339. Springer, Heidelberg (2011). doi:\n                      10.1007\/978-3-642-19074-2_21"},{"key":"1_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-13190-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"V Lyubashevsky","year":"2010","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1\u201323. Springer, Heidelberg (2010). doi:\n                      10.1007\/978-3-642-13190-5_1"},{"key":"1_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-3-642-38348-9_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"V Lyubashevsky","year":"2013","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: A toolkit for ring-LWE cryptography. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 35\u201354. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-38348-9_3"},{"key":"1_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-3-642-40041-4_2","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"D Micciancio","year":"2013","unstructured":"Micciancio, D., Peikert, C.: Hardness of SIS and LWE with small parameters. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 21\u201339. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-40041-4_2"},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84\u201393. ACM (2005)","DOI":"10.1145\/1060590.1060603"}],"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\/978-3-662-54365-8_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,23]],"date-time":"2020-02-23T20:09:33Z","timestamp":1582488573000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-54365-8_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783662543641","9783662543658"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-54365-8_1","relation":{"is-part-of":[{"id-type":"doi","id":"https:\/\/doi.org\/10.1007\/978-3-662-54365-8","asserted-by":"object"}]},"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"}}]}}