{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:44:09Z","timestamp":1740149049081,"version":"3.37.3"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T00:00:00Z","timestamp":1644796800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","award":["61702548","61902428"],"award-info":[{"award-number":["61702548","61902428"]}],"id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2022,2,14]]},"abstract":"<jats:p>Multiplication on polynomial rings has been widely used in public-key cryptographic schemes based on ideal lattices. It is an important module that significantly affects the efficiency of the schemes. Improved Preprocess-then-NTT (IPtNTT) is an algorithm which can fast realize multiplication on polynomial rings. Compared with the Number Theoretic Transform (NTT), the IPtNTT weakens the parameter restriction of lattice-based public-key cryptographic schemes. By optimizing the IPtNTT with the AVX2 instruction set, we reduce the clock cycles consumed by multiplication on polynomial rings to 15%\u201322%. According to the experimental results, we give specific suggestions on using AVX2 optimized IPtNTT to realize multiplication on polynomial rings with different parameters chosen in lattice-based public-key cryptosystems.<\/jats:p>","DOI":"10.1155\/2022\/4649158","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T01:07:26Z","timestamp":1644887246000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["Fast Implementation of Multiplication on Polynomial Rings"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3054-5143","authenticated-orcid":true,"given":"Boyu","family":"Wang","sequence":"first","affiliation":[{"name":"PLA SSF Information Engineering University, Zhengzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5882-3294","authenticated-orcid":true,"given":"Haiying","family":"Gao","sequence":"additional","affiliation":[{"name":"PLA SSF Information Engineering University, Zhengzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-1053","authenticated-orcid":true,"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"PLA SSF Information Engineering University, Zhengzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1145\/1568318.1568324"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13190-5_1"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-014-9938-4"},{"key":"4","first-page":"595","article-title":"Multiplication of multidigit numbers on automata","volume":"7","author":"A. Karatsuba","year":"1963","journal-title":"Soviet physics doklady"},{"issue":"2","key":"5","first-page":"293","article-title":"Multiplication of many-digital numbers by automatic computers","volume":"145","author":"A. A. Karatsuba","year":"1962","journal-title":"Russian Academy of Sciences"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-1965-0178586-1"},{"first-page":"117","article-title":"Preprocess-then-NTT technique and its applications to kyber and new hope","author":"S. Zhou","key":"7"},{"key":"8","article-title":"When NTT meets Karatsuba: preprocess-then-NTT technique revisited","volume":"2019","author":"Y. Zhu","year":"2019","journal-title":"IACR Cryptology ePrint Archieve"},{"volume-title":"Faster AVX2 Optimized NTT Multiplication for Ring-LWE Lattice cryptography","year":"2018","author":"G. Seiler","key":"9"},{"first-page":"54","article-title":"SWIFFT: a modest proposal for FFT hashing","author":"V. Lyubashevsky","key":"10"},{"volume-title":"Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform algorithms","year":"1999","author":"E. Chu","key":"11"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2022\/4649158.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2022\/4649158.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2022\/4649158.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T01:07:33Z","timestamp":1644887253000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2022\/4649158\/"}},"subtitle":[],"editor":[{"given":"Iqtadar","family":"Hussain","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,2,14]]},"references-count":11,"alternative-id":["4649158","4649158"],"URL":"https:\/\/doi.org\/10.1155\/2022\/4649158","relation":{},"ISSN":["1939-0122","1939-0114"],"issn-type":[{"type":"electronic","value":"1939-0122"},{"type":"print","value":"1939-0114"}],"subject":[],"published":{"date-parts":[[2022,2,14]]}}}