{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T21:13:24Z","timestamp":1773177204510,"version":"3.50.1"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031147876","type":"print"},{"value":"9783031147883","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.springer.com\/tdm"},{"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.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-14788-3_18","type":"book-chapter","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T14:24:42Z","timestamp":1660141482000},"page":"318-332","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Implementation of\u00a0Parallel Number-Theoretic Transform Using Intel AVX-512 Instructions"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1357-5770","authenticated-orcid":false,"given":"Daisuke","family":"Takahashi","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,11]]},"reference":[{"key":"18_CR1","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF00162341","volume":"4","author":"DH Bailey","year":"1990","unstructured":"Bailey, D.H.: FFTs in external or hierarchical memory. J. Supercomput. 4, 23\u201335 (1990)","journal-title":"J. Supercomput."},{"key":"18_CR2","doi-asserted-by":"crossref","unstructured":"Boemer, F., Kim, S., Seifu, G., de Souza, F.D.M., Gopal, V.: Intel HEXL: accelerating homomorphic encryption with Intel AVX512-IFMA52. In: Proceedings of 9th Workshop on Encrypted Computing & Applied Homomorphic Cryptography (WAHC 2021), pp. 57\u201362 (2021)","DOI":"10.1145\/3474366.3486926"},{"key":"18_CR3","unstructured":"Boemer, F., et al.: Intel HEXL. https:\/\/github.com\/intel\/hexl"},{"key":"18_CR4","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1109\/TAU.1967.1161899","volume":"15","author":"WT Cochran","year":"1967","unstructured":"Cochran, W.T., et al.: What is the fast Fourier transform? IEEE Trans. Audio Electroacoust. 15, 45\u201355 (1967)","journal-title":"IEEE Trans. Audio Electroacoust."},{"key":"18_CR5","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","volume":"19","author":"JW Cooley","year":"1965","unstructured":"Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297\u2013301 (1965)","journal-title":"Math. Comput."},{"key":"18_CR6","unstructured":"Free Software Foundation Inc: GCC, the GNU Compiler Collection. https:\/\/gcc.gnu.org\/"},{"key":"18_CR7","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.jsc.2013.09.002","volume":"60","author":"D Harvey","year":"2014","unstructured":"Harvey, D.: Faster arithmetic for number-theoretic transforms. J. Symb. Comput. 60, 113\u2013119 (2014)","journal-title":"J. Symb. Comput."},{"key":"18_CR8","unstructured":"Intel Corporation: Intel 64 and IA-32 architectures software developer\u2019s manual, volume 1: Basic architecture. https:\/\/software.intel.com\/content\/dam\/develop\/public\/us\/en\/documents\/253665-sdm-vol-1.pdf (2020)"},{"key":"18_CR9","unstructured":"Intel Corporation: Intel C++ compiler 19.1 developer guide and reference (2020). https:\/\/software.intel.com\/content\/dam\/develop\/external\/us\/en\/documents\/19-1-cpp-compiler-devguide.pdf"},{"key":"18_CR10","first-page":"1","volume":"6","author":"DT Marr","year":"2002","unstructured":"Marr, D.T., et al.: Hyper-threading technology architecture and microarchitecture. Intel. Technol. J. 6, 1\u201311 (2002)","journal-title":"Intel. Technol. J."},{"key":"18_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/978-3-319-02297-0_21","volume-title":"Computer Algebra in Scientific Computing","author":"L Meng","year":"2013","unstructured":"Meng, L., Johnson, J.: Automatic parallel library generation for general-size modular FFT algorithms. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 243\u2013256. Springer, Cham (2013). https:\/\/doi.org\/10.1007\/978-3-319-02297-0_21"},{"key":"18_CR12","doi-asserted-by":"crossref","unstructured":"Meng, L., Johnson, J.R., Franchetti, F., Voronenko, Y., Maza, M.M., Xie, Y.: Spiral-generated modular FFT algorithms. In: Proceedings of 4th International Workshop on Parallel and Symbolic Computation (PASCO 2010), pp. 169\u2013170 (2010)","DOI":"10.1145\/1837210.1837235"},{"key":"18_CR13","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1090\/S0025-5718-1985-0777282-X","volume":"44","author":"PL Montgomery","year":"1985","unstructured":"Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44, 519\u2013521 (1985)","journal-title":"Math. Comput."},{"key":"18_CR14","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1090\/S0025-5718-1971-0301966-0","volume":"25","author":"JM Pollard","year":"1971","unstructured":"Pollard, J.M.: The fast Fourier transform in a finite field. Math. Comput. 25, 365\u2013374 (1971)","journal-title":"Math. Comput."},{"key":"18_CR15","unstructured":"Shoup, V.: NTL: a library for doing number theory. https:\/\/libntl.org"},{"key":"18_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/S0167-8191(84)90413-7","volume":"1","author":"PN Swarztrauber","year":"1984","unstructured":"Swarztrauber, P.N.: FFT algorithms for vector computers. Parallel Comput. 1, 45\u201363 (1984)","journal-title":"Parallel Comput."},{"key":"18_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/978-3-319-62392-4_29","volume-title":"Computational Science and Its Applications \u2013 ICCSA 2017","author":"D Takahashi","year":"2017","unstructured":"Takahashi, D.: An implementation of parallel 1-D real FFT on Intel Xeon phi processors. In: Gervasi, O., et al. (eds.) ICCSA 2017. LNCS, vol. 10404, pp. 401\u2013410. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-62392-4_29"},{"key":"18_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.parco.2018.02.002","volume":"75","author":"D Takahashi","year":"2018","unstructured":"Takahashi, D.: Computation of the 100 quadrillionth hexadecimal digit of $$\\pi $$ on a cluster of Intel Xeon phi processors. Parallel Comput. 75, 1\u201310 (2018)","journal-title":"Parallel Comput."},{"key":"18_CR19","unstructured":"The Clang Team: clang: a C language family frontend for LLVM. https:\/\/clang.llvm.org\/"},{"key":"18_CR20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970999","volume-title":"Computational Frameworks for the Fast Fourier Transform","author":"C Van Loan","year":"1992","unstructured":"Van Loan, C.: Computational Frameworks for the Fast Fourier Transform. SIAM Press, Philadelphia, PA (1992)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-14788-3_18","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T23:17:33Z","timestamp":1660259853000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-14788-3_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031147876","9783031147883"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-14788-3_18","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":"11 August 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Gebze","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Turkey","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":"22 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-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":"32","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":"20","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":"63% - 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":"3.25","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":"5.1","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)"}}]}}