{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T04:14:52Z","timestamp":1742876092645,"version":"3.40.2"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031866012","type":"print"},{"value":"9783031866029","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[[2025]]},"DOI":"10.1007\/978-3-031-86602-9_3","type":"book-chapter","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T23:57:01Z","timestamp":1742860621000},"page":"63-88","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Discrete Gaussian Sampling for BKZ-Reduced Basis"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2549-951X","authenticated-orcid":false,"given":"Amaury","family":"Pouly","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8657-9337","authenticated-orcid":false,"given":"Yixin","family":"Shen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,15]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Albrecht, M., Ducas, L.: Lattice attacks on NTRU and LWE: a history of refinements, pp. 15\u201340. London Mathematical Society Lecture Note Series, Cambridge University Press (2021)","DOI":"10.1017\/9781108854207.004"},{"key":"3_CR2","doi-asserted-by":"publisher","unstructured":"Aggarwal, D., Chen, Y., Kumar, R., Shen, Y.: Improved (provable) algorithms for the shortest vector problem via bounded distance decoding. In: Bl\u00e4ser, M., Monmege, B. (eds.) 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021, March 16-19, 2021, Saarbr\u00fccken, Germany (Virtual Conference). LIPIcs, vol. 187, pp. 4:1\u20134:20. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2021). https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2021.4","DOI":"10.4230\/LIPIcs.STACS.2021.4"},{"key":"3_CR3","doi-asserted-by":"publisher","unstructured":"Aggarwal, D., Dadush, D., Regev, O., Stephens-Davidowitz, N.: Solving the shortest vector problem in $$2^{{\\rm n}}$$ time using discrete gaussian sampling: extended abstract. In: Servedio, R.A., Rubinfeld, R. (eds.) Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015, pp. 733\u2013742. ACM (2015). https:\/\/doi.org\/10.1145\/2746539.2746606","DOI":"10.1145\/2746539.2746606"},{"key":"3_CR4","doi-asserted-by":"publisher","unstructured":"Ajtai, M.: The shortest vector problem in l2 is np-hard for randomized reductions (extended abstract). In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 10\u201319. STOC \u201998, Association for Computing Machinery, New York, NY, USA (1998). https:\/\/doi.org\/10.1145\/276698.276705","DOI":"10.1145\/276698.276705"},{"key":"3_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/978-3-030-17656-3_25","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"MR Albrecht","year":"2019","unstructured":"Albrecht, M.R., Ducas, L., Herold, G., Kirshanova, E., Postlethwaite, E.W., Stevens, M.: The general sieve kernel and new records in lattice reduction. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 717\u2013746. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17656-3_25"},{"key":"3_CR6","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehl\u00e9, D.: Classical hardness of learning with errors. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 575\u2013584. STOC \u201913, Association for Computing Machinery, New York, NY, USA (2013). https:\/\/doi.org\/10.1145\/2488608.2488680","DOI":"10.1145\/2488608.2488680"},{"key":"3_CR7","unstructured":"Chen, Y.: R\u00e9duction de r\u00e9seau et s\u00e9curit\u00e9 concr\u00e8te du chiffrement compl\u00e8tement homomorphe, Ph.D. thesis, th\u00e8se de doctorat dirig\u00e9e par Nguyen, Phong Q. Informatique Paris 7 (2013). http:\/\/www.theses.fr\/2013PA077242"},{"key":"3_CR8","doi-asserted-by":"publisher","unstructured":"Chuengsatiansup, C., Prest, T., Stehl\u00e9, D., Wallet, A., Xagawa, K.: ModFalcon: compact signatures based on module-NTRU lattices. In: Proceedings of the 15th ACM Asia Conference on Computer and Communications Security, pp. 853\u2013866. ASIA CCS \u201920, Association for Computing Machinery, New York, NY, USA (2020). https:\/\/doi.org\/10.1145\/3320269.3384758","DOI":"10.1145\/3320269.3384758"},{"key":"3_CR9","doi-asserted-by":"publisher","unstructured":"Chung, K.M., Dadush, D., Liu, F.H., Peikert, C.: On the lattice smoothing parameter problem. In: 2013 IEEE Conference on Computational Complexity, pp. 230\u2013241 (2013). https:\/\/doi.org\/10.1109\/CCC.2013.31","DOI":"10.1109\/CCC.2013.31"},{"key":"3_CR10","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/978-3-031-38548-3_6","volume-title":"Advances in Cryptology - CRYPTO 2023","author":"L Ducas","year":"2023","unstructured":"Ducas, L., Espitau, T., Postlethwaite, E.W.: Finding short integer solutions when the modulus is small. In: Handschuh, H., Lysyanskaya, A. (eds.) CRYPTO 2023, pp. 150\u2013176. Springer, Cham (2023)"},{"issue":"10","key":"3_CR11","doi-asserted-by":"publisher","first-page":"3401","DOI":"10.1109\/TIT.2005.855591","volume":"51","author":"U Erez","year":"2005","unstructured":"Erez, U., Litsyn, S., Zamir, R.: Lattices which are good for (almost) everything. IEEE Trans. Inf. Theory 51(10), 3401\u20133416 (2005). https:\/\/doi.org\/10.1109\/TIT.2005.855591","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1007\/978-3-030-65277-7_20","volume-title":"Progress in Cryptology \u2013 INDOCRYPT 2020","author":"T Espitau","year":"2020","unstructured":"Espitau, T., Joux, A., Kharchenko, N.: On a Dual\/Hybrid approach to small secret LWE. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds.) INDOCRYPT 2020. LNCS, vol. 12578, pp. 440\u2013462. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-65277-7_20"},{"key":"3_CR13","unstructured":"Fouque, P.A., et al.: Falcon: fast-Fourier lattice-based compact signatures over NTRU (2019). https:\/\/api.semanticscholar.org\/CorpusID:231637439"},{"key":"3_CR14","doi-asserted-by":"publisher","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 197\u2013206. STOC \u201908, Association for Computing Machinery, New York, NY, USA (2008). https:\/\/doi.org\/10.1145\/1374376.1374407","DOI":"10.1145\/1374376.1374407"},{"key":"3_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/978-3-642-22792-9_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"G Hanrot","year":"2011","unstructured":"Hanrot, G., Pujol, X., Stehl\u00e9, D.: Analyzing Blockwise lattice algorithms using dynamical systems. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 447\u2013464. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22792-9_25"},{"issue":"5","key":"3_CR16","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1007\/S10623-020-00719-W","volume":"88","author":"E Kirshanova","year":"2020","unstructured":"Kirshanova, E., Nguyen, H., Stehl\u00e9, D., Wallet, A.: On the smoothing parameter and last minimum of random orthogonal lattices. Des. Codes Cryptogr. 88(5), 931\u2013950 (2020). https:\/\/doi.org\/10.1007\/S10623-020-00719-W","journal-title":"Des. Codes Cryptogr."},{"key":"3_CR17","unstructured":"Klein, P.: Finding the closest lattice vector when it\u2019s unusually close. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 937-941. SODA \u201900, Society for Industrial and Applied Mathematics, USA (2000)"},{"key":"3_CR18","unstructured":"Li, J., Nguyen, P.Q.: A complete analysis of the BKZ lattice reduction algorithm. In: IACR Cryptology ePrint Archive, p. 1237 (2020). https:\/\/eprint.iacr.org\/2020\/1237"},{"key":"3_CR19","doi-asserted-by":"publisher","unstructured":"Li, J., Nguyen, P.Q.: A complete analysis of the BKZ lattice reduction algorithm. J. Cryptol. 38(1) (2024). https:\/\/doi.org\/10.1007\/s00145-024-09527-0","DOI":"10.1007\/s00145-024-09527-0"},{"issue":"10","key":"3_CR20","doi-asserted-by":"publisher","first-page":"6399","DOI":"10.1109\/TIT.2014.2343226","volume":"60","author":"C Ling","year":"2014","unstructured":"Ling, C., Luzzi, L., Belfiore, J.C., Stehl\u00e9, D.: Semantically secure lattice codes for the Gaussian wiretap channel. IEEE Trans. Inf. Theory 60(10), 6399\u20136416 (2014). https:\/\/doi.org\/10.1109\/TIT.2014.2343226","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR21","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). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_3"},{"key":"3_CR22","doi-asserted-by":"publisher","unstructured":"Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. In: 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 372\u2013381 (2004). https:\/\/doi.org\/10.1109\/FOCS.2004.72","DOI":"10.1109\/FOCS.2004.72"},{"key":"3_CR23","doi-asserted-by":"publisher","unstructured":"Micciancio, D., Regev, O.: Lattice-based Cryptography. In: Post-quantum Cryptography, pp. 147\u2013191. Springer, Berlin, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-540-88702-7_5","DOI":"10.1007\/978-3-540-88702-7_5"},{"key":"3_CR24","doi-asserted-by":"publisher","unstructured":"Pouly, A., Shen, Y.: Provable dual attacks on learning with errors. In: Advances in Cryptology \u2013 EUROCRYPT 2024: 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zurich, Switzerland, May 26\u201330, 2024, Proceedings, Part VII, pp. 256\u2013285. Springer, Berlin, Heidelberg (2024). https:\/\/doi.org\/10.1007\/978-3-031-58754-2_10","DOI":"10.1007\/978-3-031-58754-2_10"},{"key":"3_CR25","doi-asserted-by":"publisher","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6) (2009). https:\/\/doi.org\/10.1145\/1568318.1568324","DOI":"10.1145\/1568318.1568324"},{"key":"3_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/3-540-36494-3_14","volume-title":"STACS 2003","author":"CP Schnorr","year":"2003","unstructured":"Schnorr, C.P.: Lattice reduction by random sampling and birthday methods. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 145\u2013156. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/3-540-36494-3_14"},{"issue":"2","key":"3_CR27","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0304-3975(87)90064-8","volume":"53","author":"C Schnorr","year":"1987","unstructured":"Schnorr, C.: A hierarchy of polynomial time lattice basis reduction algorithms. Theor. Comput. Sci. 53(2), 201\u2013224 (1987)","journal-title":"Theor. Comput. Sci."},{"key":"3_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/978-3-642-20465-4_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"D Stehl\u00e9","year":"2011","unstructured":"Stehl\u00e9, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 27\u201347. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-20465-4_4"},{"key":"3_CR29","unstructured":"Stephens-Davidowitz, N.: On the Gaussian measure over lattices, PhD thesis, New York University (2017)"},{"issue":"6","key":"3_CR30","doi-asserted-by":"publisher","first-page":"3630","DOI":"10.1109\/TIT.2019.2901497","volume":"65","author":"Z Wang","year":"2019","unstructured":"Wang, Z., Ling, C.: Lattice Gaussian sampling by Markov chain monte Carlo: bounded distance decoding and trapdoor sampling. IEEE Trans. Inf. Theory 65(6), 3630\u20133645 (2019). https:\/\/doi.org\/10.1109\/TIT.2019.2901497","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR31","doi-asserted-by":"publisher","unstructured":"Zamir, R., Nazer, B., Kochman, Y., Bistritz, I.: Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation and Multiuser Information Theory. Cambridge University Press (2014). https:\/\/doi.org\/10.1017\/CBO9781139045520","DOI":"10.1017\/CBO9781139045520"}],"container-title":["Lecture Notes in Computer Science","Post-Quantum Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-86602-9_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T23:57:07Z","timestamp":1742860627000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-86602-9_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031866012","9783031866029"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-86602-9_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"15 March 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PQCrypto","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Post-Quantum Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Taipei","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Taiwan","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 April 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 April 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pqcrypto2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/pqcrypto2025.iis.sinica.edu.tw\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}