{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T16:52:49Z","timestamp":1770742369425,"version":"3.49.0"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031229114","type":"print"},{"value":"9783031229121","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-22912-1_4","type":"book-chapter","created":{"date-parts":[[2022,12,31]],"date-time":"2022-12-31T15:38:49Z","timestamp":1672501129000},"page":"78-99","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Entropic Hardness of\u00a0Module-LWE from\u00a0Module-NTRU"],"prefix":"10.1007","author":[{"given":"Katharina","family":"Boudgoust","sequence":"first","affiliation":[]},{"given":"Corentin","family":"Jeudy","sequence":"additional","affiliation":[]},{"given":"Adeline","family":"Roux-Langlois","sequence":"additional","affiliation":[]},{"given":"Weiqiang","family":"Wen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,1,1]]},"reference":[{"issue":"3","key":"4_CR1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.46586\/tches.v2018.i3.173-213","volume":"2018","author":"MR Albrecht","year":"2018","unstructured":"Albrecht, M.R., Deo, A., Paterson, K.G.: Cold boot attacks on ring and module LWE keys under the NTT. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2018(3), 173\u2013213 (2018)","journal-title":"IACR Trans. Cryptogr. Hardw. Embed. Syst."},{"key":"4_CR2","unstructured":"Bernstein, D. J., et al.: NTRU prime round-3 candidate to the NIST post-quantum cryptography standardisation project (2020)"},{"key":"4_CR3","doi-asserted-by":"crossref","unstructured":"Bos, J. W., et al.: CRYSTALS - kyber: a CCA-secure module-lattice-based KEM. In: Euro S and P, pp. 353\u2013367. IEEE (2018)","DOI":"10.1109\/EuroSP.2018.00032"},{"key":"4_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/978-3-030-64834-3_10","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"K Boudgoust","year":"2020","unstructured":"Boudgoust, K., Jeudy, C., Roux-Langlois, A., Wen, W.: Towards classical hardness of\u00a0module-LWE: the linear rank case. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 289\u2013317. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_10"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/978-3-030-75539-3_21","volume-title":"Topics in Cryptology \u2013 CT-RSA 2021","author":"K Boudgoust","year":"2021","unstructured":"Boudgoust, K., Jeudy, C., Roux-Langlois, A., Wen, W.: On the hardness of module-LWE with\u00a0binary secret. In: Paterson, K.G. (ed.) CT-RSA 2021. LNCS, vol. 12704, pp. 503\u2013526. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-75539-3_21"},{"key":"4_CR6","doi-asserted-by":"crossref","unstructured":"Boudgoust, K., Jeudy, C., Roux-Langlois, A., Wen, W.: Entropic hardness of module-LWE from module-NTRU. IACR Cryptol. ePrint Arch, p. 245 (2022)","DOI":"10.1007\/978-3-031-22912-1_4"},{"key":"4_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1007\/978-3-030-45724-2_19","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"Z Brakerski","year":"2020","unstructured":"Brakerski, Z., D\u00f6ttling, N.: Hardness of LWE on general entropic distributions. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 551\u2013575. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45724-2_19"},{"key":"4_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-030-64375-1_1","volume-title":"Theory of Cryptography","author":"Z Brakerski","year":"2020","unstructured":"Brakerski, Z., D\u00f6ttling, N.: Lossiness and entropic hardness for\u00a0ring-LWE. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12550, pp. 1\u201327. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64375-1_1"},{"key":"4_CR9","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":"4_CR10","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. ACM (2013)","DOI":"10.1145\/2488608.2488680"},{"key":"4_CR11","unstructured":"Chen, C., et al.: NTRU round-3 candidate to the NIST post-quantum cryptography standardisation project (2020)"},{"key":"4_CR12","doi-asserted-by":"crossref","unstructured":"Chuengsatiansup, C., Prest, T., Stehl\u00e9, D., Wallet, A., Xagawa, K.: Modfalcon: compact signatures based on module-NTRU lattices. In: AsiaCCS, pp. 853\u2013866. ACM (2020)","DOI":"10.1145\/3320269.3384758"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Ducas, L., et al.: Crystals-dilithium: a lattice-based digital signature scheme. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2018(1), 238\u2013268 (2018)","DOI":"10.46586\/tches.v2018.i1.238-268"},{"key":"4_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/978-3-662-44371-2_19","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"L Ducas","year":"2014","unstructured":"Ducas, L., Micciancio, D.: Improved short lattice signatures in the standard model. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 335\u2013352. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44371-2_19"},{"key":"4_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-92068-5_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2021","author":"L Ducas","year":"2021","unstructured":"Ducas, L., van Woerden, W.: NTRU fatigue: how stretched is overstretched? In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13093, pp. 3\u201332. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-92068-5_1"},{"key":"4_CR16","unstructured":"Goldwasser, S., Tauman Kalai, Y., Peikert, C., Vaikuntanathan, V.: Robustness of the learning with errors assumption. In: ICS, pp. 230\u2013240. Tsinghua University Press (2010)"},{"key":"4_CR17","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"},{"issue":"3","key":"4_CR18","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/s10623-014-9938-4","volume":"75","author":"A Langlois","year":"2015","unstructured":"Langlois, A., Stehl\u00e9, D.: Worst-case to average-case reductions for module lattices. Des. Codes Cryptogr. 75(3), 565\u2013599 (2015)","journal-title":"Des. Codes Cryptogr."},{"key":"4_CR19","unstructured":"Lin, H., Wang, Y., Wang, M.: Hardness of module-LWE and ring-LWE on general entropic distributions. IACR Cryptol. ePrint Arch, p. 1238 (2020)"},{"key":"4_CR20","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). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1"},{"issue":"1","key":"4_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4086\/toc.2018.v014a013","volume":"14","author":"D Micciancio","year":"2018","unstructured":"Micciancio, D.: On the hardness of learning with errors with binary secrets. Theory Comput. 14(1), 1\u201317 (2018)","journal-title":"Theory Comput."},{"key":"4_CR22","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). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_41"},{"issue":"1","key":"4_CR23","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1137\/S0097539705447360","volume":"37","author":"D Micciancio","year":"2007","unstructured":"Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM J. Comput. 37(1), 267\u2013302 (2007)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"4_CR24","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/s00037-008-0251-3","volume":"17","author":"C Peikert","year":"2008","unstructured":"Peikert, C.: Limits on the hardness of lattice problems in phl$${}_{\\text{ php }}$$ norms. Comput. Complex. 17(2), 300\u2013351 (2008)","journal-title":"Comput. Complex."},{"issue":"4","key":"4_CR25","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1561\/0400000074","volume":"10","author":"C Peikert","year":"2016","unstructured":"Peikert, C.: A decade of lattice cryptography. Found. Trends Theor. Comput. Sci. 10(4), 283\u2013424 (2016)","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"4_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-92062-3_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2021","author":"A Pellet-Mary","year":"2021","unstructured":"Pellet-Mary, A., Stehl\u00e9, D.: On the hardness of the NTRU problem. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13090, pp. 3\u201335. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-92062-3_1"},{"key":"4_CR27","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"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1016\/j.aim.2008.01.010","volume":"218","author":"M Rudelson","year":"2008","unstructured":"Rudelson, M., Vershynin, R.: The littlewood-offord problem and invertibility of random matrices. Adv. Math. 218, 600\u2013633 (2008)","journal-title":"Adv. Math."},{"key":"4_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/978-3-642-10366-7_36","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2009","author":"D Stehl\u00e9","year":"2009","unstructured":"Stehl\u00e9, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 617\u2013635. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-10366-7_36"},{"key":"4_CR30","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1090\/S0002-9904-1947-08909-6","volume":"53","author":"J von Neumann","year":"1947","unstructured":"von Neumann, J., Goldstine, H.H.: Numerical inverting of matrices of high order. Bull. Amer. Math. Soc. 53, 1021\u20131099 (1947)","journal-title":"Bull. Amer. Math. Soc."}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 INDOCRYPT 2022"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-22912-1_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,19]],"date-time":"2023-03-19T14:41:59Z","timestamp":1679236919000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-22912-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031229114","9783031229121"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-22912-1_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"1 January 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"INDOCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptology in India","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kolkata","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 December 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 December 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"indocrypt2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.tcgcrest.org\/indocrypt-2022\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"74","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"42% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.22","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4.59","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}