{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T11:59:35Z","timestamp":1793102375002,"version":"4.5.0"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030172589","type":"print"},{"value":"9783030172596","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"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":[[2019]]},"DOI":"10.1007\/978-3-030-17259-6_17","type":"book-chapter","created":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T23:02:48Z","timestamp":1554678168000},"page":"504-533","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["More Efficient Algorithms for the NTRU Key Generation Using the Field Norm"],"prefix":"10.1007","author":[{"given":"Thomas","family":"Pornin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Prest","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,4,6]]},"reference":[{"key":"17_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":"MR Albrecht","year":"2016","unstructured":"Albrecht, M.R., Bai, S., Ducas, L.: A subfield lattice attack on overstretched NTRU assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part I. LNCS, vol. 9814, pp. 153\u2013178. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53018-4_6"},{"key":"17_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/BFb0023990","volume-title":"STACS 85","author":"L Babai","year":"1985","unstructured":"Babai, L.: On Lov\u00e1sz\u2019 lattice reduction and the nearest lattice point problem. In: Mehlhorn, K. (ed.) STACS 1985. LNCS, vol. 182, pp. 13\u201320. Springer, Heidelberg (1985). https:\/\/doi.org\/10.1007\/BFb0023990. http:\/\/dl.acm.org\/citation.cfm?id=18858.18860"},{"key":"17_CR3","unstructured":"Bernstein, D.J., Chuengsatiansup, C., Lange, T., van Vredendaal, C.: NTRU prime. Technical report, National Institute of Standards and Technology (2017). https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/round-1-submissions"},{"key":"17_CR4","unstructured":"Campbell, P., Groves, M.: Practical post-quantum hierarchical identity-based encryption. In: 16th IMA International Conference on Cryptography and Coding (2017). http:\/\/www.qub.ac.uk\/sites\/CSIT\/FileStore\/Filetoupload,785752, en.pdf"},{"key":"17_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_27"},{"key":"17_CR6","unstructured":"Cheon, J.H., Jeong, J., Lee, C.: An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low level encoding of zero. Cryptology ePrint Archive, Report 2016\/139 (2016). http:\/\/eprint.iacr.org\/2016\/139"},{"issue":"90","key":"17_CR7","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","volume":"19","author":"JW Cooley","year":"1965","unstructured":"Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19(90), 297\u2013301 (1965)","journal-title":"Math. Comput."},{"key":"17_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1007\/978-3-662-45608-8_2","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2014","author":"L Ducas","year":"2014","unstructured":"Ducas, L., Lyubashevsky, V., Prest, T.: Efficient identity-based encryption over NTRU lattices. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 22\u201341. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-45608-8_2"},{"key":"17_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139856065","volume-title":"Modern Computer Algebra","author":"J von zur Gathen","year":"2013","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 3rd edn. Cambridge University Press, Cambridge (2013)","edition":"3"},{"key":"17_CR10","doi-asserted-by":"crossref","unstructured":"Gentleman, W.M., Sande, G.: Fast Fourier transforms: for fun and profit. In: Proceedings of the 7\u201310 November 1966, Fall Joint Computer Conference, pp. 563\u2013578. ACM (1966)","DOI":"10.1145\/1464291.1464352"},{"key":"17_CR11","doi-asserted-by":"publisher","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 197\u2013206. ACM Press, May 2008. https:\/\/doi.org\/10.1145\/1374376.1374407","DOI":"10.1145\/1374376.1374407"},{"key":"17_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/3-540-36563-X_9","volume-title":"Topics in Cryptology \u2014 CT-RSA 2003","author":"J Hoffstein","year":"2003","unstructured":"Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: digital signatures using the NTRU lattice. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 122\u2013140. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/3-540-36563-X_9"},{"key":"17_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). https:\/\/doi.org\/10.1007\/BFb0054868"},{"key":"17_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-56620-7_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","author":"P Kirchner","year":"2017","unstructured":"Kirchner, P., Fouque, P.-A.: Revisiting lattice attacks on overstretched NTRU parameters. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part I. LNCS, vol. 10210, pp. 3\u201326. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56620-7_1"},{"key":"17_CR15","doi-asserted-by":"publisher","unstructured":"Micciancio, D., Warinschi, B.: A linear space algorithm for computing the herite normal form. In: Kaltofen, E., Villard, G. (eds.) Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, ISSAC 2001, ORCCA & University of Western Ontario, London, Ontario, Canada, 22\u201325 July 2001, pp. 231\u2013236. ACM (2001). https:\/\/doi.org\/10.1145\/384101.384133","DOI":"10.1145\/384101.384133"},{"key":"17_CR16","unstructured":"NIST: Security requirements for cryptographic modules (2001). https:\/\/nvlpubs.nist.gov\/nistpubs\/FIPS\/NIST.FIPS.140-2.pdf"},{"key":"17_CR17","unstructured":"NIST: Submission requirements and evaluation criteria for the post-quantum cryptography standardization process (2016). https:\/\/csrc.nist.gov\/Projects\/Post-Quantum-Cryptography"},{"key":"17_CR18","unstructured":"Prest, T., et al.: Falcon. Technical report, National Institute of Standards and Technology (2017). https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/round-1-submissions"},{"issue":"3\u20134","key":"17_CR19","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/BF02242355","volume":"7","author":"A Sch\u00f6nhage","year":"1971","unstructured":"Sch\u00f6nhage, A., Strassen, V.: Schnelle multiplikation gro\u00dfer zahlen. Computing 7(3\u20134), 281\u2013292 (1971). https:\/\/doi.org\/10.1007\/BF02242355","journal-title":"Computing"},{"key":"17_CR20","unstructured":"Smart, N.P., et al.: LIMA. Technical report, National Institute of Standards and Technology (2017). https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/round-1-submissions"},{"key":"17_CR21","unstructured":"Stehl\u00e9, D., Steinfeld, R.: Making NTRUEncrypt and NTRUSign as secure as standard worst-case problems over ideal lattices. Cryptology ePrint Archive, Report 2013\/004 (2013). http:\/\/eprint.iacr.org\/2013\/004"}],"container-title":["Lecture Notes in Computer Science","Public-Key Cryptography \u2013 PKC 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-17259-6_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T12:39:39Z","timestamp":1709815179000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-17259-6_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030172589","9783030172596"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-17259-6_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"6 April 2019","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":"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":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 April 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 April 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pkc2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/pkc.iacr.org\/2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}