{"id":"https://openalex.org/W1563238762","doi":"https://doi.org/10.1109/enc.2003.1232886","title":"Hardware implementation of the binary method for exponentiation in GF(2/sup m/)","display_name":"Hardware implementation of the binary method for exponentiation in GF(2/sup m/)","publication_year":2004,"publication_date":"2004-02-03","ids":{"openalex":"https://openalex.org/W1563238762","doi":"https://doi.org/10.1109/enc.2003.1232886","mag":"1563238762"},"language":"en","primary_location":{"id":"doi:10.1109/enc.2003.1232886","is_oa":false,"landing_page_url":"https://doi.org/10.1109/enc.2003.1232886","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Fourth Mexican International Conference on Computer Science, 2003. ENC 2003.","raw_type":"proceedings-article"},"type":"article","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/A5054800127","display_name":"Mario Alberto Garc\u00eda Mart\u00ednez","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165121","display_name":"Instituto Tecnologico de Orizaba","ror":"https://ror.org/05vpj2s72","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210165121"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"M.A. Garcia Martinez","raw_affiliation_strings":["Instituto Tecnologico de Orizaba, Veracruz, Mexico","Instituto Tecnologico de Orizaba, Mexico"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnologico de Orizaba, Veracruz, Mexico","institution_ids":["https://openalex.org/I4210165121"]},{"raw_affiliation_string":"Instituto Tecnologico de Orizaba, Mexico","institution_ids":["https://openalex.org/I4210165121"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109513044","display_name":"Gustavo Medell\u00edn Luna","orcid":"https://orcid.org/0009-0007-6463-436X"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"G. Morales Luna","raw_affiliation_strings":["Seccion de Computacion, CINVESTAV, Mexico","CINVESTAV\u2014IPN"],"affiliations":[{"raw_affiliation_string":"Seccion de Computacion, CINVESTAV, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"CINVESTAV\u2014IPN","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049574538","display_name":"Francisco Rodr\u00edguez Henr\u00edquez","orcid":null},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"F. Rodriguez Henriquez","raw_affiliation_strings":["Seccion de Computacion, CINVESTAV, Mexico","Ciencia de los ordenadores (SNI 2)"],"affiliations":[{"raw_affiliation_string":"Seccion de Computacion, CINVESTAV, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Ciencia de los ordenadores (SNI 2)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054800127"],"corresponding_institution_ids":["https://openalex.org/I4210165121"],"apc_list":null,"apc_paid":null,"fwci":1.5782,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8834536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"ii","issue":null,"first_page":"131","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/modular-exponentiation","display_name":"Modular exponentiation","score":0.8710945844650269},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7450072169303894},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6574761271476746},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.6552183628082275},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6266272068023682},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5951918363571167},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5479868650436401},{"id":"https://openalex.org/keywords/application-specific-integrated-circuit","display_name":"Application-specific integrated circuit","score":0.5054788589477539},{"id":"https://openalex.org/keywords/gf","display_name":"GF(2)","score":0.4897933006286621},{"id":"https://openalex.org/keywords/vhdl","display_name":"VHDL","score":0.4844391644001007},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.426244854927063},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.416579931974411},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.41069626808166504},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.33356979489326477},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.32390284538269043},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2850422263145447},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28017377853393555},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.27428188920021057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16335809230804443}],"concepts":[{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.8710945844650269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7450072169303894},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6574761271476746},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.6552183628082275},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6266272068023682},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5951918363571167},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5479868650436401},{"id":"https://openalex.org/C77390884","wikidata":"https://www.wikidata.org/wiki/Q217302","display_name":"Application-specific integrated circuit","level":2,"score":0.5054788589477539},{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.4897933006286621},{"id":"https://openalex.org/C36941000","wikidata":"https://www.wikidata.org/wiki/Q209455","display_name":"VHDL","level":3,"score":0.4844391644001007},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.426244854927063},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.416579931974411},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.41069626808166504},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.33356979489326477},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.32390284538269043},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2850422263145447},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28017377853393555},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.27428188920021057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16335809230804443},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/enc.2003.1232886","is_oa":false,"landing_page_url":"https://doi.org/10.1109/enc.2003.1232886","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Fourth Mexican International Conference on Computer Science, 2003. ENC 2003.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W977292009","https://openalex.org/W1569612250","https://openalex.org/W2032727957","https://openalex.org/W2097374372","https://openalex.org/W2125713877","https://openalex.org/W2130623996","https://openalex.org/W2156186849","https://openalex.org/W2156460937","https://openalex.org/W2158901426","https://openalex.org/W2318946948","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W3021014091","https://openalex.org/W6634295219","https://openalex.org/W6744529318"],"related_works":["https://openalex.org/W4235485585","https://openalex.org/W670148","https://openalex.org/W1507420113","https://openalex.org/W4242613270","https://openalex.org/W1517418331","https://openalex.org/W2014928558","https://openalex.org/W2508156398","https://openalex.org/W1587142857","https://openalex.org/W2100368733","https://openalex.org/W2039812289"],"abstract_inverted_index":{"Exponentiation":[0],"in":[1,15,112,116,126,144],"finite":[2],"or":[3,67],"Galois":[4],"fields,":[5],"GF(2/sup":[6,113],"m/),":[7],"is":[8,48],"a":[9],"basic":[10],"operation":[11],"for":[12,110],"several":[13],"algorithms":[14,55],"areas":[16],"such":[17],"as":[18],"cryptography,":[19],"error-correlation":[20],"codes":[21],"and":[22,44],"digital":[23],"signal":[24],"processing.":[25],"Nevertheless":[26],"the":[27,62,104,117],"involved":[28],"calculations":[29],"are":[30,37],"very":[31],"time":[32],"consuming,":[33],"especially":[34],"when":[35],"they":[36],"performed":[38],"by":[39,56,130],"software.":[40],"Due":[41],"to":[42,52,60,71],"performance":[43],"security":[45],"reasons,":[46],"it":[47],"often":[49],"more":[50],"convenient":[51],"implement":[53],"cryptographic":[54],"hardware.":[57],"In":[58],"order":[59],"overcome":[61],"well-known":[63],"drawback":[64],"of":[65,107],"little":[66],"inexistent":[68],"flexibility":[69],"associated":[70],"traditional":[72],"application":[73],"specific":[74],"integrated":[75],"circuits":[76],"(ASIC)":[77],"solutions,":[78],"we":[79],"propose":[80],"an":[81,108,141],"architecture":[82,109],"using":[83,99,123],"field":[84],"programmable":[85],"gate":[86],"arrays":[87],"(FPGA).":[88],"A":[89],"cheap":[90],"but":[91],"still":[92],"flexible":[93],"modular":[94],"exponentiation":[95,111],"can":[96],"be":[97],"implemented":[98],"these":[100],"devices.":[101],"We":[102],"provide":[103],"VHDL":[105],"description":[106],"m/)":[114],"based":[115],"square-and-multiply":[118],"method,":[119,122],"called":[120],"binary":[121],"two":[124],"multipliers":[125],"parallel":[127],"previously":[128],"developed":[129],"ourselves.":[131],"Our":[132],"structure,":[133],"compared":[134],"with":[135],"other":[136],"designs":[137],"reported":[138],"earlier,":[139],"introduces":[140],"important":[142],"saving":[143],"hardware":[145],"resources.":[146]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}