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Many approaches have been come up with to achieve this aim. An interesting perspective is that computers nowadays usually have multicore processors which could be used to do cryptographic computations in parallel style. Inspired by this idea, we present a new parallel and efficient algorithm to speed up scalar multiplication. First, we introduce a new regular halve-and-add method which is very efficient by utilizing <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>\u03bb<\/mml:mi><\/mml:math> projective coordinate. Then, we compare many different algorithms calculating double-and-add and halve-and-add. Finally, we combine the best double-and-add and halve-and-add methods to get a new faster parallel algorithm which costs around <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mn>12.0<\/mml:mn><mml:mo>%<\/mml:mo><\/mml:math> less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.<\/jats:p>","DOI":"10.1155\/2020\/4087873","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T23:31:09Z","timestamp":1593041469000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2057-8737","authenticated-orcid":true,"given":"Xingran","family":"Li","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9015-9351","authenticated-orcid":true,"given":"Wei","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"Data Assurances and Communications Security, Institute of Information Engineering, CAS, Beijing 100093, China"}]},{"given":"Bao","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-1987-0866109-5"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/12.869328"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-1987-0866113-7"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/bf01388526"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1995.1088"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/tc.2015.2389817"},{"year":"2006","key":"15"},{"volume-title":"A normal form for elliptic curves in characteristic 2","year":"2011","key":"21"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2010.12.001"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1109\/tc.2004.43"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s13389-011-0012-0"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/s13389-011-0017-8"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4087873.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4087873.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2020\/4087873.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T23:31:13Z","timestamp":1593041473000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2020\/4087873\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,24]]},"references-count":12,"alternative-id":["4087873","4087873"],"URL":"https:\/\/doi.org\/10.1155\/2020\/4087873","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"type":"print","value":"1939-0114"},{"type":"electronic","value":"1939-0122"}],"subject":[],"published":{"date-parts":[[2020,6,24]]}}}