{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:10:09Z","timestamp":1765357809555,"version":"3.40.2"},"publisher-location":"Cham","reference-count":44,"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_9","type":"book-chapter","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T23:50:33Z","timestamp":1742860233000},"page":"231-263","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reducing the\u00a0Number of\u00a0Qubits in\u00a0Solving LWE"],"prefix":"10.1007","author":[{"given":"Barbara Jiabao","family":"Benedikt","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,15]]},"reference":[{"key":"9_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2022.3174547","volume":"3","author":"S Aktar","year":"2022","unstructured":"Aktar, S., B\u00e4rtschi, A., Badawy, A., Eidenbenz, S.: A divide-and-conquer approach to Dicke state preparation. IEEE Trans. Quantum Eng. 3, 1\u201316 (2022)","journal-title":"IEEE Trans. Quantum Eng."},{"issue":"1","key":"9_CR2","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1137\/S0097539705447311","volume":"37","author":"A Ambainis","year":"2007","unstructured":"Ambainis, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210\u2013239 (2007)","journal-title":"SIAM J. Comput."},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-030-25027-0_9","volume-title":"Fundamentals of Computation Theory","author":"A B\u00e4rtschi","year":"2019","unstructured":"B\u00e4rtschi, A., Eidenbenz, S.: Deterministic preparation of Dicke states. In: G\u0105sieniec, L.A., Jansson, J., Levcopoulos, C. (eds.) FCT 2019. LNCS, vol. 11651, pp. 126\u2013139. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-25027-0_9"},{"key":"9_CR4","unstructured":"Bernstein, D.J., et al.: NTRU prime. Technical report, National Institute of Standards and Technology (2020). https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/post-quantum-cryptography-standardization\/round-3-submissions"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-319-72565-9_12","volume-title":"Selected Areas in Cryptography \u2013 SAC 2017","author":"DJ Bernstein","year":"2018","unstructured":"Bernstein, D.J., Chuengsatiansup, C., Lange, T., van Vredendaal, C.: NTRU prime: reducing attack surface at low cost. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 235\u2013260. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-72565-9_12"},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/978-3-030-64834-3_22","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"X Bonnetain","year":"2020","unstructured":"Bonnetain, X., Bricout, R., Schrottenloher, A., Shen, Y.: Improved classical and quantum algorithms for subset-sum. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 633\u2013666. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_22"},{"key":"9_CR7","doi-asserted-by":"crossref","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 (2013)","DOI":"10.1145\/2488608.2488680"},{"key":"9_CR8","doi-asserted-by":"crossref","unstructured":"Brassard, G., H\u00f8yer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation (2002)","DOI":"10.1090\/conm\/305\/05215"},{"key":"9_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BFb0054319","volume-title":"LATIN\u201998: Theoretical Informatics","author":"G Brassard","year":"1998","unstructured":"Brassard, G., H\u00d8yer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 163\u2013169. Springer, Heidelberg (1998). https:\/\/doi.org\/10.1007\/BFb0054319"},{"key":"9_CR10","doi-asserted-by":"crossref","unstructured":"B\u00e4rtschi, A., Eidenbenz, S.: Short-depth circuits for Dicke state preparation. In: 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 87\u201396 (2022)","DOI":"10.1109\/QCE53715.2022.00027"},{"key":"9_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/978-3-319-70697-9_8","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2017","author":"A Chailloux","year":"2017","unstructured":"Chailloux, A., Naya-Plasencia, M., Schrottenloher, A.: An efficient quantum collision search algorithm and implications on symmetric cryptography. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 211\u2013240. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70697-9_8"},{"key":"9_CR12","unstructured":"Chen, C., et al.: NTRU. Technical report, National Institute of Standards and Technology (2020). https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography\/post-quantum-cryptography-standardization\/round-3-submissions"},{"key":"9_CR13","doi-asserted-by":"crossref","first-page":"89497","DOI":"10.1109\/ACCESS.2019.2925425","volume":"7","author":"JH Cheon","year":"2019","unstructured":"Cheon, J.H., Hhan, M., Hong, S., Son, Y.: A hybrid of dual and meet-in-the-middle attack on sparse and ternary secret LWE. IEEE Access 7, 89497\u201389506 (2019)","journal-title":"IEEE Access"},{"key":"9_CR14","unstructured":"Chevignard, C., Fouque, P.A., Schrottenloher, A.: Reducing the number of qubits in quantum information set decoding. Cryptology ePrint Archive, Paper 2024\/907 (2024). https:\/\/eprint.iacr.org\/2024\/907"},{"issue":"3","key":"9_CR15","first-page":"181","volume":"2","author":"AM Childs","year":"2002","unstructured":"Childs, A.M., Farhi, E., Goldstone, J., Gutmann, S.: Finding cliques by quantum adiabatic evolution. Quantum Inf. Comput. 2(3), 181\u2013191 (2002)","journal-title":"Quantum Inf. Comput."},{"key":"9_CR16","unstructured":"Chopra, A.: GLYPH: a new instantiation of the GLP digital signature scheme. Cryptology ePrint Archive, Report 2017\/766 (2017). https:\/\/eprint.iacr.org\/2017\/766"},{"key":"9_CR17","doi-asserted-by":"crossref","unstructured":"Csisz\u00e1r, I., Shields, P.C., et\u00a0al.: Information theory and statistics: a tutorial. Found. Trends\u00ae Commun. Inf. Theory 1(4), 417\u2013528 (2004)","DOI":"10.1561\/0100000004"},{"issue":"1","key":"9_CR18","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1103\/PhysRev.93.99","volume":"93","author":"RH Dicke","year":"1954","unstructured":"Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99 (1954)","journal-title":"Phys. Rev."},{"key":"9_CR19","unstructured":"Ducas, L.: Accelerating Bliss: the geometry of ternary polynomials. Cryptology ePrint Archive, Report 2014\/874 (2014). https:\/\/eprint.iacr.org\/2014\/874"},{"key":"9_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1007\/978-3-642-40041-4_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"L Ducas","year":"2013","unstructured":"Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal Gaussians. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 40\u201356. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_3"},{"key":"9_CR21","doi-asserted-by":"crossref","unstructured":"Ducas, L., et al.: CRYSTALS-Dilithium: a lattice-based digital signature scheme. IACR TCHES 2018(1), 238\u2013268 (2018). https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/839","DOI":"10.46586\/tches.v2018.i1.238-268"},{"key":"9_CR22","unstructured":"Gidney, C.: Quirk: quantum circuit simulator. A drag-and-drop quantum circuit simulator. https:\/\/algassert.com\/quirk. Visited 08 Oct 2024"},{"key":"9_CR23","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"9_CR24","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). https:\/\/doi.org\/10.1007\/978-3-642-33027-8_31"},{"key":"9_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/978-3-030-44223-1_24","volume-title":"Post-Quantum Cryptography","author":"A Helm","year":"2020","unstructured":"Helm, A., May, A.: The power of few qubits and collisions \u2013 subset sum below Grover\u2019s bound. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 445\u2013460. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-44223-1_24"},{"key":"9_CR26","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":"9_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-642-13190-5_12","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"N Howgrave-Graham","year":"2010","unstructured":"Howgrave-Graham, N., Joux, A.: New generic algorithms for hard knapsacks. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 235\u2013256. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_12"},{"key":"9_CR28","unstructured":"IBM: The hardware and software for the era of quantum utility is here (2023). https:\/\/www.ibm.com\/quantum\/blog\/quantum-roadmap-2033. Visited 08 Oct 2024"},{"key":"9_CR29","doi-asserted-by":"crossref","unstructured":"Kaye, P., Mosca, M.: Quantum networks for generating arbitrary quantum states. In: Optical Fiber Communication Conference and International Conference on Quantum Information, p.\u00a0PB28. Optica Publishing Group (2001)","DOI":"10.1364\/ICQI.2001.PB28"},{"key":"9_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-030-92641-0_12","volume-title":"Cryptography and Coding","author":"E Kirshanova","year":"2021","unstructured":"Kirshanova, E., May, A.: How to\u00a0find ternary LWE keys using locality sensitive hashing. In: Paterson, M.B. (ed.) IMACC 2021. LNCS, vol. 13129, pp. 247\u2013264. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-92641-0_12"},{"issue":"7660","key":"9_CR31","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1038\/nature22986","volume":"546","author":"M Kues","year":"2017","unstructured":"Kues, M., et al.: On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546(7660), 622\u2013626 (2017)","journal-title":"Nature"},{"key":"9_CR32","unstructured":"Lyubashevsky, V., et al.: CRYSTALS-DILITHIUM. Technical report, National Institute of Standards and Technology (2022). https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"key":"9_CR33","doi-asserted-by":"crossref","unstructured":"Mahmudlu, H., et al.: Fully on-chip photonic turnkey quantum source for entangled qubit\/qudit state generation. Nat. Photonics, 1\u20137 (2023)","DOI":"10.21203\/rs.3.rs-1762235\/v1"},{"key":"9_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/978-3-030-84245-1_24","volume-title":"Advances in Cryptology \u2013 CRYPTO 2021","author":"A May","year":"2021","unstructured":"May, A.: How to meet ternary LWE keys. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 701\u2013731. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-84245-1_24"},{"key":"9_CR35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2020.3041479","volume":"1","author":"CS Mukherjee","year":"2020","unstructured":"Mukherjee, C.S., Maitra, S., Gaurav, V., Roy, D.: Preparing Dicke states on a quantum computer. IEEE Trans. Quantum Eng. 1, 1\u201317 (2020)","journal-title":"IEEE Trans. Quantum Eng."},{"key":"9_CR36","unstructured":"OpenSSH: Openssh release notes 9.0 (2022). https:\/\/www.openssh.com\/txt\/release-9.0. Visited 08 Oct 2024"},{"issue":"2","key":"9_CR37","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1088\/1367-2630\/9\/2\/043","volume":"9","author":"SK \u00d6zdemir","year":"2007","unstructured":"\u00d6zdemir, S.K., Shimamura, J., Imoto, N.: A necessary and sufficient condition to play games in quantum mechanical settings. New J. Phys. 9(2), 43 (2007)","journal-title":"New J. Phys."},{"key":"9_CR38","doi-asserted-by":"crossref","unstructured":"Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 333\u2013342 (2009)","DOI":"10.1145\/1536414.1536461"},{"key":"9_CR39","doi-asserted-by":"crossref","unstructured":"Perriello, S., Barenghi, A., Pelosi, G.: A complete quantum circuit to solve the information set decoding problem. In: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 366\u2013377 (2021)","DOI":"10.1109\/QCE52317.2021.00056"},{"key":"9_CR40","doi-asserted-by":"crossref","unstructured":"Raveh, D., Nepomechie, R.I.: q-analog qudit Dicke states. J. Phys. A Math. Theor. (2024)","DOI":"10.1088\/1751-8121\/ad1ea4"},{"issue":"6","key":"9_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1568318.1568324","volume":"56","author":"O Regev","year":"2009","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 1\u201340 (2009)","journal-title":"J. ACM (JACM)"},{"issue":"9","key":"9_CR42","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1038\/s41567-022-01658-0","volume":"18","author":"M Ringbauer","year":"2022","unstructured":"Ringbauer, M., et al.: A universal qudit quantum processor with trapped ions. Nat. Phys. 18(9), 1053\u20131057 (2022)","journal-title":"Nat. Phys."},{"issue":"3","key":"9_CR43","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379\u2013423 (1948)","journal-title":"Bell Syst. Tech. J."},{"key":"9_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/978-3-030-81293-5_7","volume-title":"Post-Quantum Cryptography","author":"I van Hoof","year":"2021","unstructured":"van Hoof, I., Kirshanova, E., May, A.: Quantum key search for ternary LWE. In: Cheon, J.H., Tillich, J.-P. (eds.) PQCrypto 2021 2021. LNCS, vol. 12841, pp. 117\u2013132. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-81293-5_7"}],"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_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T23:51:14Z","timestamp":1742860274000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-86602-9_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031866012","9783031866029"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-86602-9_9","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"}}]}}