{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:43:38Z","timestamp":1742913818743,"version":"3.40.3"},"publisher-location":"Cham","reference-count":33,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030457235"},{"type":"electronic","value":"9783030457242"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"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":[[2020]]},"DOI":"10.1007\/978-3-030-45724-2_11","type":"book-chapter","created":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T04:17:18Z","timestamp":1588306638000},"page":"311-340","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Optimal Merging in Quantum $$k$$-xor and k-sum Algorithms"],"prefix":"10.1007","author":[{"given":"Mar\u00eda","family":"Naya-Plasencia","sequence":"first","affiliation":[]},{"given":"Andr\u00e9","family":"Schrottenloher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,1]]},"reference":[{"issue":"4","key":"11_CR1","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1145\/1008731.1008735","volume":"51","author":"S Aaronson","year":"2004","unstructured":"Aaronson, S., Shi, Y.: Quantum lower bounds for the collision and the element distinctness problems. J. ACM 51(4), 595\u2013605 (2004)","journal-title":"J. ACM"},{"issue":"1","key":"11_CR2","doi-asserted-by":"publisher","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."},{"issue":"1","key":"11_CR3","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s00145-018-9304-1","volume":"32","author":"S Bai","year":"2019","unstructured":"Bai, S., Galbraith, S.D., Li, L., Sheffield, D.: Improved combinatorial algorithms for the inhomogeneous short integer solution problem. J. Cryptol. 32(1), 35\u201383 (2019). https:\/\/doi.org\/10.1007\/s00145-018-9304-1","journal-title":"J. Cryptol."},{"key":"11_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1007\/978-3-642-20465-4_21","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"A Becker","year":"2011","unstructured":"Becker, A., Coron, J., Joux, A.: Improved generic algorithms for hard knapsacks. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 364\u2013385. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-20465-4_21"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Belovs, A., Spalek, R.: Adversary lower bound for the $$k$$-sum problem. In: Innovations in Theoretical Computer Science, ITCS 2013, pp. 323\u2013328. ACM (2013)","DOI":"10.1145\/2422436.2422474"},{"issue":"5","key":"11_CR6","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1137\/S0097539796300933","volume":"26","author":"CH Bennett","year":"1997","unstructured":"Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.V.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510\u20131523 (1997). https:\/\/doi.org\/10.1137\/S0097539796300933","journal-title":"SIAM J. Comput."},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/978-3-642-38616-9_2","volume-title":"Post-Quantum Cryptography","author":"DJ Bernstein","year":"2013","unstructured":"Bernstein, D.J., Jeffery, S., Lange, T., Meurer, A.: Quantum algorithms for the subset-sum problem. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 16\u201333. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38616-9_2"},{"key":"11_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/978-3-642-10628-6_2","volume-title":"Progress in Cryptology - INDOCRYPT 2009","author":"DJ Bernstein","year":"2009","unstructured":"Bernstein, D.J., Lange, T., Niederhagen, R., Peters, C., Schwabe, P.: FSBday. In: Roy, B., Sendrier, N. (eds.) INDOCRYPT 2009. LNCS, vol. 5922, pp. 18\u201338. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-10628-6_2"},{"issue":"4","key":"11_CR9","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1145\/792538.792543","volume":"50","author":"A Blum","year":"2003","unstructured":"Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506\u2013519 (2003)","journal-title":"J. ACM"},{"issue":"1","key":"11_CR10","doi-asserted-by":"publisher","first-page":"380","DOI":"10.13154\/tosc.v2017.i1.380-397","volume":"2017","author":"L Both","year":"2017","unstructured":"Both, L., May, A.: The approximate k-list problem. IACR Trans. Symmetric Cryptol. 2017(1), 380\u2013397 (2017). https:\/\/doi.org\/10.13154\/tosc.v2017.i1.380-397","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"11_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/978-3-319-79063-3_2","volume-title":"Post-Quantum Cryptography","author":"L Both","year":"2018","unstructured":"Both, L., May, A.: Decoding linear codes with high error rate and its impact for LPN security. In: Lange, T., Steinwandt, R. (eds.) PQCrypto 2018. LNCS, vol. 10786, pp. 25\u201346. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-79063-3_2"},{"key":"11_CR12","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1090\/conm\/305\/05215","volume":"305","author":"G Brassard","year":"2002","unstructured":"Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Contemp. Math. 305, 53\u201374 (2002)","journal-title":"Contemp. Math."},{"key":"11_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BFb0054319","volume-title":"LATIN 1998: Theoretical Informatics","author":"G Brassard","year":"1998","unstructured":"Brassard, G., H\u00f8yer, 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":"11_CR14","doi-asserted-by":"crossref","unstructured":"Brassard, G., H\u00f8yer, P., Tapp, A.: Quantum algorithm for the collision problem. In: Encyclopedia of Algorithms, pp. 1662\u20131664 (2016)","DOI":"10.1007\/978-1-4939-2864-4_304"},{"key":"11_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/3-540-46416-6_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 1991","author":"P Camion","year":"1991","unstructured":"Camion, P., Patarin, J.: The knapsack hash function proposed at Crypto\u201989 can be broken. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 39\u201353. Springer, Heidelberg (1991). https:\/\/doi.org\/10.1007\/3-540-46416-6_3"},{"key":"11_CR16","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":"11_CR17","unstructured":"Dinur, I.: An algorithmic framework for the generalized birthday problem. Cryptology ePrint Archive, Report 2018\/575 (2018). https:\/\/eprint.iacr.org\/2018\/575"},{"key":"11_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1007\/978-3-642-32009-5_42","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"I Dinur","year":"2012","unstructured":"Dinur, I., Dunkelman, O., Keller, N., Shamir, A.: Efficient dissection of composite problems, with applications to cryptanalysis, knapsacks, and combinatorial search problems. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 719\u2013740. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_42"},{"key":"11_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1007\/978-3-319-96881-0_22","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"A Esser","year":"2018","unstructured":"Esser, A., Heuer, F., K\u00fcbler, R., May, A., Sohler, C.: Dissection-BKW. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 638\u2013666. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_22"},{"key":"11_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/978-3-030-03326-2_18","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"L Grassi","year":"2018","unstructured":"Grassi, L., Naya-Plasencia, M., Schrottenloher, A.: Quantum algorithms for the $$k$$-xor problem. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11272, pp. 527\u2013559. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03326-2_18"},{"key":"11_CR21","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 the Theory of Computing 1996, pp. 212\u2013219. ACM (1996). http:\/\/doi.acm.org\/10.1145\/237814.237866","DOI":"10.1145\/237814.237866"},{"key":"11_CR22","unstructured":"Helm, A., May, A.: Subset sum quantumly in 1.17$${}^{\\text{n}}$$. In: TQC. LIPIcs, vol. 111, pp. 5:1\u20135:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018)"},{"key":"11_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/978-3-319-70697-9_7","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2017","author":"A Hosoyamada","year":"2017","unstructured":"Hosoyamada, A., Sasaki, Y., Xagawa, K.: Quantum multicollision-finding algorithm. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 179\u2013210. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70697-9_7"},{"key":"11_CR24","unstructured":"Kaplan, M.: Quantum attacks against iterated block ciphers. CoRR abs\/1410.1434 (2014). http:\/\/arxiv.org\/abs\/1410.1434"},{"key":"11_CR25","unstructured":"Kuperberg, G.: Another subexponential-time quantum algorithm for the dihedral hidden subgroup problem. In: TQC. LIPIcs, vol. 22, pp. 20\u201334. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)"},{"issue":"1","key":"11_CR26","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1137\/090745854","volume":"40","author":"F Magniez","year":"2011","unstructured":"Magniez, F., Nayak, A., Roland, J., Santha, M.: Search via quantum walk. SIAM J. Comput. 40(1), 142\u2013164 (2011)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"11_CR27","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s00145-011-9097-y","volume":"25","author":"L Minder","year":"2012","unstructured":"Minder, L., Sinclair, A.: The extended $$k$$-tree algorithm. J. Cryptol. 25(2), 349\u2013382 (2012)","journal-title":"J. Cryptol."},{"key":"11_CR28","unstructured":"Naya-Plasencia, M., Schrottenloher, A.: Optimal merging in quantum k-xor and k-sum algorithms. IACR Cryptology ePrint Archive 2019, 501 (2019)"},{"key":"11_CR29","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)","DOI":"10.1119\/1.1463744"},{"key":"11_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1007\/978-3-662-48800-3_28","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2015","author":"I Nikoli\u0107","year":"2015","unstructured":"Nikoli\u0107, I., Sasaki, Y.: Refinements of the k-tree algorithm for the generalized birthday problem. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 683\u2013703. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-48800-3_28"},{"issue":"3","key":"11_CR31","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1137\/0210033","volume":"10","author":"R Schroeppel","year":"1981","unstructured":"Schroeppel, R., Shamir, A.: A $$\\text{ T }=O(2^{n\/2})$$, $$\\text{ S }={O} (2^{n\/4})$$ algorithm for certain NP-complete problems. SIAM J. Comput. 10(3), 456\u2013464 (1981)","journal-title":"SIAM J. Comput."},{"key":"11_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1007\/3-540-45708-9_19","volume-title":"Advances in Cryptology \u2014 CRYPTO 2002","author":"D Wagner","year":"2002","unstructured":"Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288\u2013304. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-45708-9_19"},{"key":"11_CR33","doi-asserted-by":"crossref","unstructured":"Zhandry, M.: A note on the quantum collision and set equality problems. Quantum Inf. Comput. 15(7\u20138), 557\u2013567 (2015). http:\/\/dl.acm.org\/citation.cfm?id=2871411.2871413","DOI":"10.26421\/QIC15.7-8-2"}],"updated-by":[{"updated":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"DOI":"10.1007\/978-3-030-45724-2_29","type":"correction","source":"publisher","label":"Correction"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-45724-2_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:10:27Z","timestamp":1682899827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-45724-2_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030457235","9783030457242"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-45724-2_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"1 May 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"1 May 2020","order":2,"name":"change_date","label":"Change Date","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"Correction","order":3,"name":"change_type","label":"Change Type","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"In the originally published version of the chapter 11, the title of the paper was incorrect. The title has been corrected as \u201cOptimal Merging in Quantum k<\/i>-xor and k<\/i>-sum Algorithms\u201d.","order":4,"name":"change_details","label":"Change Details","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Zagreb","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Croatia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 May 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 May 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2020\/","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":"IACR websubrev","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"375","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":"81","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":"22% - 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":"20","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)"}},{"value":"The conference was held virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}