{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T18:49:25Z","timestamp":1743101365652,"version":"3.40.3"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031229435"},{"type":"electronic","value":"9783031229442"}],"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\/978-3-031-22944-2_4","type":"book-chapter","created":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T18:03:58Z","timestamp":1673373838000},"page":"53-78","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reduction-Free Multiplication for\u00a0Finite Fields and\u00a0Polynomial Rings"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3654-2536","authenticated-orcid":false,"given":"Samira Carolina","family":"Oliva Madrigal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9354-3228","authenticated-orcid":false,"given":"G\u00f6kay","family":"Saldaml\u0131","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7958-7275","authenticated-orcid":false,"given":"Chen","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7638-9820","authenticated-orcid":false,"given":"Yue","family":"Geng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2402-523X","authenticated-orcid":false,"given":"Jing","family":"Tian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7227-4786","authenticated-orcid":false,"given":"Zhongfeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2572-9565","authenticated-orcid":false,"given":"\u00c7etin Kaya","family":"Ko\u00e7","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,11]]},"reference":[{"key":"4_CR1","volume-title":"Passages from the Life of a Philosopher","author":"C Babbage","year":"1864","unstructured":"Babbage, C.: Passages from the Life of a Philosopher. Longman, London (1864)"},{"key":"4_CR2","unstructured":"Bajard, J.C.: Useful Arithmetic for Cryptography, July 2013"},{"issue":"5","key":"4_CR3","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1109\/TC.1983.1676262","volume":"32","author":"GR Blakley","year":"1983","unstructured":"Blakley, G.R.: A computer algorithm for the product AB modulo M. IEEE Trans. Comput. 32(5), 497\u2013500 (1983)","journal-title":"IEEE Trans. Comput."},{"key":"4_CR4","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Garg, S., Tsabary, R.: FHE-based bootstrapping of designated-prover NIZK. IACR ePrint Archive, Paper 2020\/1168 (2020)","DOI":"10.1007\/978-3-030-64375-1_23"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/978-3-642-22792-9_29","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"Z Brakerski","year":"2011","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505\u2013524. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22792-9_29"},{"issue":"2","key":"4_CR6","first-page":"233","volume":"58","author":"RP Brent","year":"2011","unstructured":"Brent, R.P., Zimmermann, P.: The great trinomial hunt. Not. Am. Math. Soc. 58(2), 233\u2013239 (2011)","journal-title":"Not. Am. Math. Soc."},{"key":"4_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-319-70694-8_15","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2017","author":"JH Cheon","year":"2017","unstructured":"Cheon, J.H., Kim, A., Kim, M., Song, Y.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 409\u2013437. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_15"},{"key":"4_CR8","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1049\/el:19990407","volume":"35","author":"M Elia","year":"1999","unstructured":"Elia, M., Leone, M., Visentin, C.: Low complexity bit-parallel multipliers for $$GF(2^{m})$$ with generator polynomial $$x^{m} + x^{k} + 1$$. Electron. Lett. 35, 551\u2013552 (1999)","journal-title":"Electron. Lett."},{"issue":"4","key":"4_CR9","first-page":"485","volume":"54","author":"H Fan","year":"2005","unstructured":"Fan, H., Dai, Y.: Fast bit-parallel $$GF(2^n)$$ multiplier for all trinomials. IEEE Trans. Circuits Syst. I Regul. Pap. 54(4), 485\u2013490 (2005)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"12","key":"4_CR10","doi-asserted-by":"publisher","first-page":"2606","DOI":"10.1109\/TCSI.2006.883855","volume":"53","author":"H Fan","year":"2006","unstructured":"Fan, H., Hasan, M.A.: Fast bit parallel-shifted polynomial basis multipliers in $$GF(2^{n})$$. IEEE Trans. Circuits Syst. I Regul. Pap. 53(12), 2606\u20132615 (2006)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"4_CR11","unstructured":"Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. IACR ePrint Archive (2012)"},{"key":"4_CR12","doi-asserted-by":"crossref","unstructured":"F\u00fcrer, M.: Faster Integer Multiplication, April 2007","DOI":"10.1145\/1250790.1250800"},{"key":"4_CR13","unstructured":"Gallardo, L.H., Rahavandrainy, O.: On (unitary) perfect polynomials over $$\\mathbb{F} _2$$ with only Mersenne primes as odd divisors (2019)"},{"issue":"5","key":"4_CR14","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1109\/12.859542","volume":"49","author":"A Halbuto\u01e7ullar\u0131","year":"2000","unstructured":"Halbuto\u01e7ullar\u0131, A., Ko\u00e7, \u00c7.K.: Mastrovito multiplier for general irreducible polynomials. IEEE Trans. Comput. 49(5), 503\u2013518 (2000)","journal-title":"IEEE Trans. Comput."},{"issue":"10","key":"4_CR15","doi-asserted-by":"publisher","first-page":"1332","DOI":"10.1109\/TC.2009.70","volume":"58","author":"A Hariri","year":"2009","unstructured":"Hariri, A., Reyhani-Masoleh, A.: Bit-serial and bit-parallel montgomery multiplication and squaring over $$GF(2^{m})$$. IEEE Trans. Comput. 58(10), 1332\u20131345 (2009)","journal-title":"IEEE Trans. Comput."},{"key":"4_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/11545262_15","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2005","author":"ME Kaihara","year":"2005","unstructured":"Kaihara, M.E., Takagi, N.: Bipartite modular multiplication. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 201\u2013210. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11545262_15"},{"issue":"2","key":"4_CR17","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1109\/TC.2007.70793","volume":"57","author":"ME Kaihara","year":"2008","unstructured":"Kaihara, M.E., Takagi, N.: Bipartite modular multiplication method. IEEE Trans. Comput. 57(2), 157\u2013164 (2008)","journal-title":"IEEE Trans. Comput."},{"key":"4_CR18","unstructured":"Kannwischer, M.J.: Polynomial multiplication for post-quantum cryptography. Ph.D. thesis, Radboud Universiteit Nijmegen (2022)"},{"key":"4_CR19","first-page":"595","volume":"7","author":"A Karatsuba","year":"1963","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of multidigit numbers by automata. Soviet Physics-Doklady 7, 595\u2013596 (1963)","journal-title":"Soviet Physics-Doklady"},{"key":"4_CR20","unstructured":"Ko\u00e7, \u00c7.K.: High-speed RSA implementation. Technical report. TR 201, RSA Laboratories, 73 pages, November 1994"},{"key":"4_CR21","unstructured":"Li, Y., Chen, Y.: New bit-parallel Montgomery multiplier for trinomials using squaring operation. IACR ePrint Archive, Paper 2014\/268 (2014)"},{"issue":"9","key":"4_CR22","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1109\/TC.2017.2677913","volume":"66","author":"Y Li","year":"2017","unstructured":"Li, Y., Ma, X., Zhang, Y., Qi, C.: Mastrovito form of non-recursive Karatsuba multiplier for all trinomials. IEEE Trans. Comput. 66(9), 1573\u20131584 (2017)","journal-title":"IEEE Trans. Comput."},{"key":"4_CR23","unstructured":"Li, Y., Zhang, Y.: An Efficient CRT-based Bit-parallel Multiplier for Special Pentanomials. IACR ePrint Archive (2020)"},{"key":"4_CR24","unstructured":"Mastrovito, E.: VLSI architectures for computation in Galois fields, Ph.D. dissertation. Ph.D. thesis, Linkoping University (1991)"},{"issue":"170","key":"4_CR25","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(170), 519\u2013521 (1985)","journal-title":"Math. Comput."},{"key":"4_CR26","unstructured":"Moody, D.: The beginning of the end: the first NIST PQC standards. Technical report, NIST (2022)"},{"key":"4_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1007\/978-3-030-63618-0_9","volume-title":"Software Verification","author":"JA Navas","year":"2020","unstructured":"Navas, J.A., Dutertre, B., Mason, I.A.: Verification of an optimized NTT algorithm. In: Christakis, M., Polikarpova, N., Duggirala, P.S., Schrammel, P. (eds.) NSV\/VSTTE -2020. LNCS, vol. 12549, pp. 144\u2013160. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-63618-0_9"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.sysarc.2006.09.004","volume":"53","author":"C Negre","year":"2007","unstructured":"Negre, C.: Efficient parallel multiplier in shifted polynomial basis. J. Syst. Architect. 53, 109\u2013116 (2007)","journal-title":"J. Syst. Architect."},{"key":"4_CR29","unstructured":"NIST: Digital Signature Standard (DSS). Technical report. Federal Information Processing Standards Publications (FIPS PUBS) 186-4, U.S. Department of Commerce, July 2013"},{"key":"4_CR30","unstructured":"NIST: SHA-3 standard: permutation-based hash and extendable-output functions. Technical report. Federal Information Processing Standards Publications (FIPS PUBS) 202, U.S. Department of Commerce, August 2015"},{"key":"4_CR31","unstructured":"NIST: Post-Quantum Cryptography, Round 3 Submissions (2020)"},{"issue":"4","key":"4_CR32","first-page":"443","volume":"2020","author":"SS Roy","year":"2020","unstructured":"Roy, S.S., Basso, A.: High-speed instruction-set coprocessor for lattice-based key encapsulation mechanism: Saber in hardware. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2020(4), 443\u2013466 (2020)","journal-title":"IACR Trans. Cryptogr. Hardw. Embed. Syst."},{"key":"4_CR33","unstructured":"Saldamli, G., Baek, Y., Ertaul, L.: Partially interleaved modular Karatsuba-Ofman multiplication. IJCSNS 15(5), 503\u2013518 (2015)"},{"issue":"3","key":"4_CR34","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/BF02242355","volume":"7","author":"A Sch\u00f6nhage","year":"1971","unstructured":"Sch\u00f6nhage, A., Strassen, V.: Schnelle multiplikation gro\u00dfer zahlen. Computing 7(3), 281\u2013292 (1971)","journal-title":"Computing"},{"key":"4_CR35","doi-asserted-by":"crossref","unstructured":"Sun, J., Li, Y., Zhang, Y., Guo, X.: Efficient nonrecursive bit-parallel Karatsuba multiplier for a special class of trinomials. VLSI Des. (2018)","DOI":"10.1155\/2018\/9269157"},{"issue":"5","key":"4_CR36","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1109\/12.769434","volume":"48","author":"B Sunar","year":"1999","unstructured":"Sunar, B., Ko\u00e7, C.: Mastrovito multiplier for all trinomials. IEEE Trans. Comput. 48(5), 522\u2013527 (1999)","journal-title":"IEEE Trans. Comput."},{"issue":"7","key":"4_CR37","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1109\/TC.2002.1017695","volume":"51","author":"H Wu","year":"2002","unstructured":"Wu, H.: Bit-parallel finite field multiplier and squarer using polynomial basis. IEEE Trans. Comput. 51(7), 750\u2013758 (2002)","journal-title":"IEEE Trans. Comput."},{"issue":"1","key":"4_CR38","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0019-9958(69)90631-7","volume":"15","author":"N Zierler","year":"1969","unstructured":"Zierler, N.: Primitive trinomials whose degree is a Mersenne exponent. Inf. Control 15(1), 67\u201369 (1969)","journal-title":"Inf. Control"}],"container-title":["Lecture Notes in Computer Science","Arithmetic of Finite Fields"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-22944-2_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T10:14:02Z","timestamp":1673432042000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-22944-2_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031229435","9783031229442"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-22944-2_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"11 January 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WAIFI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on the Arithmetic of Finite Fields","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chengdu","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","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":"29 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 September 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"waifi2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/waifi.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":"25","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":"19","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":"76% - 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":"2","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":"3","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":"3 (invited papers from invited speakers)","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)"}}]}}