{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:11:22Z","timestamp":1750306282024,"version":"3.41.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2016,5,23]],"date-time":"2016-05-23T00:00:00Z","timestamp":1463961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100010418","name":"Institute for Information & communications Technology Promotion","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010418","id-type":"DOI","asserted-by":"crossref"}]},{"name":"MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC","award":["IITP-2016-H8501-16-1017"],"award-info":[{"award-number":["IITP-2016-H8501-16-1017"]}]},{"name":"Korea government"},{"name":"Development of high performance IoT device and Open Platform with Intelligent Software","award":["10043907"],"award-info":[{"award-number":["10043907"]}]},{"name":"IITP"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Embed. Comput. Syst."],"published-print":{"date-parts":[[2016,7,21]]},"abstract":"<jats:p>\n            In this article, we present a hybrid method to improve the performance of the Montgomery reduction by taking advantage of the Karatsuba technique. We divide the Montgomery reduction into two sub-parts, including one for the conventional Montgomery reduction and the other one for Karatsuba-aided multiplication. This approach reduces the multiplication complexity of\n            <jats:italic>n<\/jats:italic>\n            -limb Montgomery reduction from \u03b8(\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            +\n            <jats:italic>n<\/jats:italic>\n            ) to asymptotic complexity \u03b8 (7\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            \/8 +\n            <jats:italic>n<\/jats:italic>\n            ). Our practical implementation results over an 8-bit microcontroller also show performance enhancements by 11%.\n          <\/jats:p>","DOI":"10.1145\/2890502","type":"journal-article","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T21:47:58Z","timestamp":1464126478000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Hybrid Montgomery Reduction"],"prefix":"10.1145","volume":"15","author":[{"given":"Hwajeong","family":"Seo","sequence":"first","affiliation":[{"name":"Institute for Infocomm Research, Singapore"}]},{"given":"Zhe","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Waterloo, Canada"}]},{"given":"Yasuyuki","family":"Nogami","sequence":"additional","affiliation":[{"name":"Okayama University, Japan"}]},{"given":"Jongseok","family":"Choi","sequence":"additional","affiliation":[{"name":"Pusan National University, Republic of Korea"}]},{"given":"Howon","family":"Kim","sequence":"additional","affiliation":[{"name":"Pusan National University, Republic of Korea"}]}],"member":"320","published-online":{"date-parts":[[2016,5,23]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Atmel Corporation. 2008. 8-bit ARV\u00ae Microcontroller with 128K Bytes In-System Programmable Flash: ATmega128 ATmega128L. Datasheet available for download at http:\/\/www.atmel.com\/dyn\/resources\/prod_documents\/doc2467.pdf.  Atmel Corporation. 2008. 8-bit ARV \u00ae Microcontroller with 128K Bytes In-System Programmable Flash: ATmega128 ATmega128L. Datasheet available for download at http:\/\/www.atmel.com\/dyn\/resources\/prod_documents\/doc2467.pdf."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03356-8_19"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44709-3_18"},{"volume-title":"Zaverucha","year":"2014","author":"Bos Joppe W.","key":"e_1_2_1_4_1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1147\/sj.294.0526"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-015-0087-1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/11545262_6"},{"volume-title":"Cryptographic Hardware and Embedded Systems \u2014 CHES 2004 (Lecture Notes in Computer Science), Marc Joye and Jean-Jacques Quisquater (Eds.)","author":"Gura Nils","key":"e_1_2_1_8_1"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13389-015-0093-2"},{"volume-title":"Cryptographic Hardware and Embedded Systems--CHES","year":"2011","author":"Hutter Michael","key":"e_1_2_1_10_1"},{"key":"e_1_2_1_11_1","first-page":"595","article-title":"Multiplication of multidigit numbers on automata","volume":"7","author":"Karatsuba Anatolii","year":"1963","journal-title":"Soviet Physics Doklady"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/40.502403"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jss.2012.06.074"},{"volume-title":"Progress in Cryptology--AFRICACRYPT","year":"2014","author":"Liu Zhe","key":"e_1_2_1_14_1"},{"volume-title":"Proceedings of the Workshop on the Security of the Internet of Things (SOCIOT).","year":"2010","author":"Liu Zhe","key":"e_1_2_1_15_1"},{"volume-title":"Proceedings of the 16th International Conference on Information and Communications Security (ICICS\u201914)","year":"2014","author":"Liu Zhe","key":"e_1_2_1_16_1"},{"volume-title":"Power Analysis Attacks: Revealing the Secrets of Smart Cards","author":"Mangard Stefan","key":"e_1_2_1_17_1"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0777282-X"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2005.49"},{"volume-title":"Information Security Applications","author":"Seo Hwajeong","key":"e_1_2_1_20_1"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-03515-4_15"},{"key":"e_1_2_1_22_1","unstructured":"Hwajeong Seo Zhe Liu Johann Gro\u00dfsch\u00e4dl and Howon Kim. 2015. Efficient arithmetic on ARM-NEON and its application for high-speed RSA implementation. IACR Cryptology ePrint Archive 465.  Hwajeong Seo Zhe Liu Johann Gro\u00dfsch\u00e4dl and Howon Kim. 2015. Efficient arithmetic on ARM-NEON and its application for high-speed RSA implementation. IACR Cryptology ePrint Archive 465."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:20020235"}],"container-title":["ACM Transactions on Embedded Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2890502","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2890502","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:38:55Z","timestamp":1750221535000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2890502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,23]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,7,21]]}},"alternative-id":["10.1145\/2890502"],"URL":"https:\/\/doi.org\/10.1145\/2890502","relation":{},"ISSN":["1539-9087","1558-3465"],"issn-type":[{"type":"print","value":"1539-9087"},{"type":"electronic","value":"1558-3465"}],"subject":[],"published":{"date-parts":[[2016,5,23]]},"assertion":[{"value":"2015-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-05-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}