{"id":"https://openalex.org/W1583217291","doi":"https://doi.org/10.1007/978-1-4419-5906-5_249","title":"Elliptic Curve Point Multiplication Using Halving","display_name":"Elliptic Curve Point Multiplication Using Halving","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1583217291","doi":"https://doi.org/10.1007/978-1-4419-5906-5_249","mag":"1583217291"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4419-5906-5_249","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4419-5906-5_249","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Cryptography and Security","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045103848","display_name":"Darrel Hankerson","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Darrel Hankerson","raw_affiliation_strings":["Department of Mathematics, Auburn University, Auburn, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Auburn University, Auburn, USA","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019674369","display_name":"Alfred Menezes","orcid":"https://orcid.org/0000-0003-3951-4298"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alfred Menezes","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045103848"],"corresponding_institution_ids":["https://openalex.org/I82497590"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16585662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"403","last_page":"406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9782999753952026,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9539999961853027,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5714176893234253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5653910636901855},{"id":"https://openalex.org/keywords/elliptic-curve-point-multiplication","display_name":"Elliptic curve point multiplication","score":0.5162558555603027},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4960575997829437},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.48673298954963684},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22870329022407532},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13669532537460327}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5714176893234253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5653910636901855},{"id":"https://openalex.org/C117121985","wikidata":"https://www.wikidata.org/wiki/Q78380999","display_name":"Elliptic curve point multiplication","level":3,"score":0.5162558555603027},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4960575997829437},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.48673298954963684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22870329022407532},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13669532537460327}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4419-5906-5_249","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4419-5906-5_249","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Cryptography and Security","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1487915764","https://openalex.org/W1808634574","https://openalex.org/W1950989567","https://openalex.org/W1981663184","https://openalex.org/W2115190247","https://openalex.org/W2121371977","https://openalex.org/W2165020108","https://openalex.org/W2561675875","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W2036954759","https://openalex.org/W2057797376","https://openalex.org/W2090319426","https://openalex.org/W2506252583","https://openalex.org/W2048249848","https://openalex.org/W2260716361","https://openalex.org/W1987422982","https://openalex.org/W1634503271","https://openalex.org/W2951901236","https://openalex.org/W2155244510"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}