{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T10:56:46Z","timestamp":1778065006715,"version":"3.51.4"},"publisher-location":"Cham","reference-count":35,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031385537","type":"print"},{"value":"9783031385544","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023]]},"DOI":"10.1007\/978-3-031-38554-4_21","type":"book-chapter","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T19:03:06Z","timestamp":1691521386000},"page":"648-681","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Error Correction and\u00a0Ciphertext Quantization in\u00a0Lattice Cryptography"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3323-9985","authenticated-orcid":false,"given":"Daniele","family":"Micciancio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5761-9662","authenticated-orcid":false,"given":"Mark","family":"Schultz-Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,9]]},"reference":[{"key":"21_CR1","unstructured":"Albrecht, M., et al.: Homomorphic encryption security standard. HomomorphicEncryption.org, Toronto, Canada, Technical report (2018)"},{"key":"21_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/978-3-662-53887-6_7","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016","author":"M Albrecht","year":"2016","unstructured":"Albrecht, M., Grassi, L., Rechberger, C., Roy, A., Tiessen, T.: MiMC: efficient encryption and cryptographic hashing with minimal multiplicative complexity. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 191\u2013219. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53887-6_7"},{"key":"21_CR3","doi-asserted-by":"crossref","unstructured":"Ashur, T., Mahzoun, M., Toprakhisar, D.: Chaghri - a FHE-friendly block cipher. In: Yin, H., Stavrou, A., Cremers, C., Shi, E. (eds.) ACM CCS 2022: 29th Conference on Computer and Communications Security, Los Angeles, CA, USA, 7\u201311 November 2022, pp. 139\u2013150. ACM Press (2022)","DOI":"10.1145\/3548606.3559364"},{"issue":"1","key":"21_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02579403","volume":"6","author":"L Babai","year":"1986","unstructured":"Babai, L.: On lov\u00e1sz\u2019lattice reduction and the nearest lattice point problem. Combinatorica 6(1), 1\u201313 (1986)","journal-title":"Combinatorica"},{"key":"21_CR5","doi-asserted-by":"crossref","unstructured":"Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval and Johansson [30], pp. 719\u2013737 (2012)","DOI":"10.1007\/978-3-642-29011-4_42"},{"key":"21_CR6","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., D\u00f6ttling,N., Garg, S., Malavolta, G.: Leveraging linear decryption: rate-1 fully-homomorphic encryption and time-lock puzzles. In: Hofheinz and Rosen [21], pp. 407\u2013437 (2019)","DOI":"10.1007\/978-3-030-36033-7_16"},{"key":"21_CR7","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS 2012: 3rd Innovations in Theoretical Computer Science, Cambridge, MA, USA, 8\u201310 January 2012, pp. 309\u2013325. Association for Computing Machinery (2022)","DOI":"10.1145\/2090236.2090262"},{"key":"21_CR8","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) 52nd Annual Symposium on Foundations of Computer Science, Palm Springs, CA, USA, 22\u201325 October 2011, pp. 97\u2013106. IEEE Computer Society Press (2011)","DOI":"10.1109\/FOCS.2011.12"},{"issue":"4","key":"21_CR9","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1112\/plms\/s3-25.4.721","volume":"3","author":"G Butler","year":"1972","unstructured":"Butler, G.: Simultaneous packing and covering in euclidean space. Proc. Lond. Math. Soc. 3(4), 721\u2013735 (1972)","journal-title":"Proc. Lond. Math. Soc."},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"233","DOI":"10.4310\/MRL.2001.v8.n3.a1","volume":"8","author":"A Carbery","year":"2001","unstructured":"Carbery, A., Wright, J.: Distributional and l-q norm inequalities for polynomials over convex bodies in r-n. Math. Res. Lett. 8, 233\u2013248 (2001)","journal-title":"Math. Res. Lett."},{"key":"21_CR11","doi-asserted-by":"publisher","unstructured":"Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups, volume 290 of Grundlehren der mathematischen Wissenschaften. Springer, New York (1999). https:\/\/doi.org\/10.1007\/978-1-4757-6568-7","DOI":"10.1007\/978-1-4757-6568-7"},{"key":"21_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/978-3-319-89339-6_16","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2018","author":"J-P D\u2019Anvers","year":"2018","unstructured":"D\u2019Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2018. LNCS, vol. 10831, pp. 282\u2013305. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-89339-6_16"},{"issue":"1","key":"21_CR13","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/BF02843724","volume":"1","author":"H Davenport","year":"1952","unstructured":"Davenport, H.: The covering of space by spheres. Rendiconti del Circolo Matematico di Palermo 1(1), 92\u2013107 (1952)","journal-title":"Rendiconti del Circolo Matematico di Palermo"},{"key":"21_CR14","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). https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/839","DOI":"10.46586\/tches.v2018.i1.238-268"},{"key":"21_CR15","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10623-017-0332-x","volume":"86","author":"L Ducas","year":"2018","unstructured":"Ducas, L., van Woerden, W.P.: The closest vector problem in tensored root lattices of type a and in their duals. Des. Codes Cryptogr. 86, 137\u2013150 (2018)","journal-title":"Des. Codes Cryptogr."},{"key":"21_CR16","doi-asserted-by":"crossref","unstructured":"Gaunt, R.E.: The basic distributional theory for the product of zero mean correlated normal random variables. Statistica Neerlandica (2022)","DOI":"10.1111\/stan.12267"},{"key":"21_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/978-3-030-17656-3_23","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"N Genise","year":"2019","unstructured":"Genise, N., Micciancio, D., Polyakov, Y.: Building an efficient lattice gadget toolkit: subgaussian sampling and more. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 655\u2013684. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17656-3_23"},{"key":"21_CR18","doi-asserted-by":"crossref","unstructured":"Gentry, C., Halevi, S.: Compressible FHE with applications to PIR. In: Hofheinz and Rosen [21], pp. 438\u2013464 (2019)","DOI":"10.1007\/978-3-030-36033-7_17"},{"issue":"1","key":"21_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00145-021-09406-y","volume":"35","author":"S Guo","year":"2022","unstructured":"Guo, S., Kamath, P., Rosen, A., Sotiraki, K.: Limits on the efficiency of (ring) LWE-based non-interactive key exchange. J. Cryptol. 35(1), 1 (2022)","journal-title":"J. Cryptol."},{"key":"21_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/978-3-319-70500-2_12","volume-title":"Theory of Cryptography","author":"D Hofheinz","year":"2017","unstructured":"Hofheinz, D., H\u00f6velmanns, K., Kiltz, E.: A modular analysis of the fujisaki-okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341\u2013371. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70500-2_12"},{"key":"21_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-36030-6","volume-title":"Theory of Cryptography","year":"2019","unstructured":"Hofheinz, D., Rosen, A. (eds.): TCC 2019. LNCS, vol. 11891. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-36030-6"},{"key":"21_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-030-21568-2_15","volume-title":"Applied Cryptography and Network Security","author":"Z Jin","year":"2019","unstructured":"Jin, Z., Zhao, Y.: Generic and practical key establishment from lattice. In: Deng, R.H., Gauthier-Uma\u00f1a, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 302\u2013322. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-21568-2_15"},{"key":"21_CR23","unstructured":"Klartag, B.: Logarithmic bounds for isoperimetry and slices of convex sets (2023)"},{"issue":"1","key":"21_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4310\/CDM.2017.v2017.n1.a1","volume":"2017","author":"YT Lee","year":"2017","unstructured":"Lee, Y.T., Vempala, S.S.: The kannan-lov\u00e1sz-simonovits conjecture. Curr. Dev. Math. 2017(1), 1\u201336 (2017)","journal-title":"Curr. Dev. Math."},{"key":"21_CR25","doi-asserted-by":"publisher","unstructured":"Martinet, J.: Perfect Lattices in Euclidean Spaces, vol. 327 of Grundlehren der mathematischen Wissenschaften. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/978-3-662-05167-2","DOI":"10.1007\/978-3-662-05167-2"},{"issue":"3","key":"21_CR26","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1109\/TIT.2009.2039090","volume":"56","author":"RG McKilliam","year":"2010","unstructured":"McKilliam, R.G., Smith, W.D., Clarkson, I.V.L.: Linear-time nearest point algorithms for coxeter lattices. IEEE Trans. Inf. Theory 56(3), 1015\u20131022 (2010)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"21_CR27","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval and Johansson [30], pp. 700\u2013718 (2012)","DOI":"10.1007\/978-3-642-29011-4_41"},{"key":"21_CR28","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Polyakov, Y.: Bootstrapping in fhew-like cryptosystems. In: Proceedings of the 9th on Workshop on Encrypted Computing & Applied Homomorphic Cryptography, pp. 17\u201328 (2021)","DOI":"10.1145\/3474366.3486924"},{"key":"21_CR29","doi-asserted-by":"crossref","unstructured":"Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Mitzenmacher, M. (ed.) 41st Annual ACM Symposium on Theory of Computing, Bethesda, MD, USA, 31 May\u20132 June 2009, pp. 333\u2013342. ACM Press (2009)","DOI":"10.1145\/1536414.1536461"},{"key":"21_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-29011-4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","year":"2012","unstructured":"Pointcheval, D., Johansson, T. (eds.): EUROCRYPT 2012. LNCS, vol. 7237. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4"},{"key":"21_CR31","unstructured":"Poppelen, A.V.: Cryptographic Decoding of the Leech Lattice. Master\u2019s thesis, Utrecht University (2016). https:\/\/studenttheses.uu.nl\/handle\/20.500.12932\/24606"},{"key":"21_CR32","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th Annual ACM Symposium on Theory of Computing, pp. 84\u201393, Baltimore, MA, USA, 22\u201324 May 2005. ACM Press (2005)","DOI":"10.1145\/1060590.1060603"},{"key":"21_CR33","doi-asserted-by":"crossref","unstructured":"Saliba, C., Luzzi, L., Ling, C.: A reconciliation approach to key generation based on module-lwe. In: 2021 IEEE International Symposium on Information Theory (ISIT), pp. 1636\u20131641 (2021)","DOI":"10.1109\/ISIT45174.2021.9517882"},{"key":"21_CR34","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1214\/14-SS107","volume":"8","author":"A Saumard","year":"2014","unstructured":"Saumard, A., Wellner, J.A.: Log-concavity and strong log-concavity: a review. Stat. Surv. 8, 45 (2014)","journal-title":"Stat. Surv."},{"key":"21_CR35","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139045520","volume-title":"Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation and Multiuser Information Theory","author":"R Zamir","year":"2014","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, Cambridge (2014)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2023"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-38554-4_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T22:03:53Z","timestamp":1753567433000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-38554-4_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031385537","9783031385544"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-38554-4_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"9 August 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CRYPTO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Cryptology Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara, CA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 August 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 August 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"43","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2023\/","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":"HotCRP","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"479","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":"124","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":"26% - 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","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":"15","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)"}}]}}