{"id":"https://openalex.org/W2325556986","doi":"https://doi.org/10.1109/tc.2016.2529625","title":"Binary-Ternary Plus-Minus Modular Inversion in RNS","display_name":"Binary-Ternary Plus-Minus Modular Inversion in RNS","publication_year":2016,"publication_date":"2016-02-25","ids":{"openalex":"https://openalex.org/W2325556986","doi":"https://doi.org/10.1109/tc.2016.2529625","mag":"2325556986"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2016.2529625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2016.2529625","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01314268","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066023491","display_name":"Karim Bigou","orcid":"https://orcid.org/0000-0001-9294-5594"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210133778","display_name":"Centre Inria de l'Universit\u00e9 de Rennes","ror":"https://ror.org/04040yw90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Karim Bigou","raw_affiliation_strings":["IRISA Laboratory, CNRS, INRIA Centre Rennes - Bretagne Atlantique, in Lannion 22300, France"],"affiliations":[{"raw_affiliation_string":"IRISA Laboratory, CNRS, INRIA Centre Rennes - Bretagne Atlantique, in Lannion 22300, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I4210133778","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042560711","display_name":"Arnaud Tisserand","orcid":"https://orcid.org/0000-0001-7042-3541"},"institutions":[{"id":"https://openalex.org/I4210133778","display_name":"Centre Inria de l'Universit\u00e9 de Rennes","ror":"https://ror.org/04040yw90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud Tisserand","raw_affiliation_strings":["IRISA Laboratory, CNRS, INRIA Centre Rennes - Bretagne Atlantique, in Lannion 22300, France"],"affiliations":[{"raw_affiliation_string":"IRISA Laboratory, CNRS, INRIA Centre Rennes - Bretagne Atlantique, in Lannion 22300, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I4210133778","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066023491"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2802519937","https://openalex.org/I4210133778"],"apc_list":null,"apc_paid":null,"fwci":1.327,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85249719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"65","issue":"11","first_page":"3495","last_page":"3501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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":0.9998000264167786,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.995199978351593,"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/T11130","display_name":"Coding theory and cryptography","score":0.9882000088691711,"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-arithmetic","display_name":"Modular arithmetic","score":0.7296236157417297},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6199045777320862},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5367421507835388},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.5299659371376038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5283917784690857},{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"Modular exponentiation","score":0.5279675722122192},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5173379778862},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.509914755821228},{"id":"https://openalex.org/keywords/elliptic-curve-cryptography","display_name":"Elliptic curve cryptography","score":0.5035633444786072},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.4623827338218689},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.45474502444267273},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45005014538764954},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.445640504360199},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.42005330324172974},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.41455695033073425},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37708157300949097},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2983003258705139},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.2163580358028412},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.16199618577957153},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.08229720592498779},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07317802309989929}],"concepts":[{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.7296236157417297},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6199045777320862},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5367421507835388},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.5299659371376038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5283917784690857},{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.5279675722122192},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5173379778862},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.509914755821228},{"id":"https://openalex.org/C167615521","wikidata":"https://www.wikidata.org/wiki/Q1048911","display_name":"Elliptic curve cryptography","level":4,"score":0.5035633444786072},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.4623827338218689},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.45474502444267273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45005014538764954},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.445640504360199},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.42005330324172974},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.41455695033073425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37708157300949097},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2983003258705139},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.2163580358028412},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.16199618577957153},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.08229720592498779},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07317802309989929},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tc.2016.2529625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2016.2529625","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01314268v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01314268","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers, 2016, 65 (11), pp.3495-3501. ⟨10.1109/TC.2016.2529625⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01314268v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01314268","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers, 2016, 65 (11), pp.3495-3501. ⟨10.1109/TC.2016.2529625⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337436","display_name":"Division of Grants and Agreements","ror":"https://ror.org/014eweh95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W109379091","https://openalex.org/W1489433220","https://openalex.org/W1491543582","https://openalex.org/W1493353711","https://openalex.org/W1504599740","https://openalex.org/W1517364441","https://openalex.org/W1559075275","https://openalex.org/W1562183207","https://openalex.org/W1565956254","https://openalex.org/W1572502182","https://openalex.org/W1581064268","https://openalex.org/W1592261758","https://openalex.org/W1879275280","https://openalex.org/W1923580562","https://openalex.org/W1988025868","https://openalex.org/W1989675557","https://openalex.org/W1992719330","https://openalex.org/W2026386874","https://openalex.org/W2044189196","https://openalex.org/W2063027372","https://openalex.org/W2093545730","https://openalex.org/W2097953324","https://openalex.org/W2109619217","https://openalex.org/W2113672208","https://openalex.org/W2132341963","https://openalex.org/W2149043711","https://openalex.org/W2155095649","https://openalex.org/W2157999631","https://openalex.org/W2172184773","https://openalex.org/W2176190288","https://openalex.org/W2264597891","https://openalex.org/W2407812901","https://openalex.org/W2543267652","https://openalex.org/W2563139900","https://openalex.org/W4233185505","https://openalex.org/W6673775960","https://openalex.org/W6713721715"],"related_works":["https://openalex.org/W3182915524","https://openalex.org/W2285294304","https://openalex.org/W1995898468","https://openalex.org/W2393695657","https://openalex.org/W32238348","https://openalex.org/W889033279","https://openalex.org/W2067075572","https://openalex.org/W2044536813","https://openalex.org/W2147776414","https://openalex.org/W2389867446"],"abstract_inverted_index":{"A":[0],"fast":[1],"RNS":[2],"modular":[3,43],"inversion":[4],"for":[5,69],"finite":[6,38],"fields":[7],"arithmetic":[8],"has":[9],"been":[10],"published":[11],"at":[12],"CHES":[13],"2013":[14],"conference.":[15],"It":[16],"is":[17],"based":[18,53],"on":[19,54,77],"the":[20,24,29],"binary":[21],"version":[22,52],"of":[23,31],"plus-minus":[25],"Euclidean":[26],"algorithm.":[27],"In":[28,45],"context":[30],"elliptic":[32],"curve":[33],"cryptography":[34],"(i.e.,":[35],"160-550":[36],"bits":[37],"fields),":[39],"it":[40],"significantly":[41],"speeds-up":[42],"inversions.":[44],"this":[46],"paper,":[47],"we":[48],"propose":[49],"an":[50],"improved":[51],"both":[55],"radix":[56,59],"2":[57],"and":[58],"3.":[60],"This":[61],"new":[62],"algorithm":[63],"leads":[64],"to":[65],"30":[66],"percent":[67,76],"speed-up":[68],"a":[70],"maximal":[71],"area":[72],"overhead":[73],"about":[74],"4":[75],"Virtex":[78],"5":[79],"FPGAs.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}