{"id":"https://openalex.org/W4414017165","doi":"https://doi.org/10.46586/tches.v2025.i4.588-620","title":"Generation of Fast Finite Field Arithmetic forCortex-M4 with ECDH and SQIsign Applications","display_name":"Generation of Fast Finite Field Arithmetic forCortex-M4 with ECDH and SQIsign Applications","publication_year":2025,"publication_date":"2025-09-05","ids":{"openalex":"https://openalex.org/W4414017165","doi":"https://doi.org/10.46586/tches.v2025.i4.588-620"},"language":"en","primary_location":{"id":"doi:10.46586/tches.v2025.i4.588-620","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.588-620","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12422/12150","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://tches.iacr.org/index.php/TCHES/article/download/12422/12150","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024814387","display_name":"F\u00e9lix Carvalho Rodrigues","orcid":"https://orcid.org/0000-0002-2776-5105"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Felix Carvalho Rodrigues","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003449263","display_name":"D\u00e9cio Luiz Gazzoni Filho","orcid":"https://orcid.org/0000-0002-6001-2172"},"institutions":[{"id":"https://openalex.org/I127110123","display_name":"Universidade Estadual de Londrina","ror":"https://ror.org/01585b035","country_code":"BR","type":"education","lineage":["https://openalex.org/I127110123"]},{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"D\u00e9cio Gazzoni Filho","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil; Department of Electrical Engineering, State University of Londrina, Londrina, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil; Department of Electrical Engineering, State University of Londrina, Londrina, Brazil","institution_ids":["https://openalex.org/I127110123","https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080410163","display_name":"Gora Adj","orcid":"https://orcid.org/0000-0002-9308-1510"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Gora Adj","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084691678","display_name":"Isaac A. Canales-Mart\u00ednez","orcid":"https://orcid.org/0000-0002-0776-5060"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Isaac A. Canales-Mart\u00ednez","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013733894","display_name":"Jorge Ch\u00e1vez-Saab","orcid":"https://orcid.org/0000-0002-7006-1779"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Jorge Ch\u00e1vez-Saab","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040849996","display_name":"Julio L\u00f3pez","orcid":"https://orcid.org/0000-0001-5139-0158"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Julio L\u00f3pez","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057429978","display_name":"Michael Scott","orcid":"https://orcid.org/0000-0002-1356-1224"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Michael Scott","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068036569","display_name":"Francisco Rodr\u00edguez\u2010Henr\u00edquez","orcid":"https://orcid.org/0000-0002-5916-6625"},"institutions":[{"id":"https://openalex.org/I4210087059","display_name":"Technology Innovation Institute","ror":"https://ror.org/001kv2y39","country_code":"AE","type":"facility","lineage":["https://openalex.org/I4210087059"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Francisco Rodr\u00edguez-Henr\u00edquez","raw_affiliation_strings":["Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE","institution_ids":["https://openalex.org/I4210087059"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0225,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86618057,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"2025","issue":"4","first_page":"588","last_page":"620"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.8928999900817871,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.8928999900817871,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.7807000279426575,"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"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.7574999928474426,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5778243541717529},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5693004131317139},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.48805534839630127},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3898216485977173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38279712200164795},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15926003456115723},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15288624167442322}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5778243541717529},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5693004131317139},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.48805534839630127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3898216485977173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38279712200164795},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15926003456115723},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15288624167442322}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tches.v2025.i4.588-620","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.588-620","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12422/12150","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e196e48cf69a408a960c9f344f256074","is_oa":true,"landing_page_url":"https://doaj.org/article/e196e48cf69a408a960c9f344f256074","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Transactions on Cryptographic Hardware and Embedded Systems, Vol 2025, Iss 4 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tches.v2025.i4.588-620","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tches.v2025.i4.588-620","pdf_url":"https://tches.iacr.org/index.php/TCHES/article/download/12422/12150","source":{"id":"https://openalex.org/S4210207404","display_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","issn_l":"2569-2925","issn":["2569-2925"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Cryptographic Hardware and Embedded Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414017165.pdf","grobid_xml":"https://content.openalex.org/works/W4414017165.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Finite":[0],"field":[1],"arithmetic":[2],"is":[3],"central":[4],"to":[5,96,120,168,184,195],"several":[6],"cryptographic":[7,147],"algorithms":[8],"on":[9],"embedded":[10],"devices":[11],"like":[12],"the":[13,56,83,108,113],"ARM":[14],"Cortex-M4,":[15],"particularly":[16],"for":[17,55,90,125,143],"elliptic":[18],"curve":[19],"and":[20,136,141],"isogenybased":[21],"cryptography.":[22],"However,":[23],"rapid":[24],"algorithm":[25],"evolution,":[26],"driven":[27],"by":[28,193],"initiatives":[29],"such":[30],"as":[31],"NIST\u2019s":[32],"post-quantum":[33],"standardization,":[34],"might":[35],"frequently":[36],"render":[37],"hand-optimized":[38,78],"implementations":[39,80,189],"obsolete.":[40],"We":[41],"address":[42],"this":[43,66,97],"challenge":[44],"with":[45,52,77],"m4-modarith,":[46],"a":[47,102,121,172],"library":[48],"generating":[49],"C":[50],"code":[51],"inline":[53],"assembly":[54,79],"Cortex-M4":[57,126],"that":[58,106],"rivals":[59],"custom-tuned":[60],"assembly,":[61],"enabling":[62],"agile":[63,152],"development":[64],"in":[65,82],"ever-changing":[67],"landscape.":[68],"Our":[69,149],"generated":[70],"modular":[71],"multiplications":[72],"obtains":[73],"fast":[74],"performances,":[75],"competitive":[76],"published":[81],"literature,":[84],"even":[85],"outperforming":[86],"some":[87],"of":[88,112,146,154,187,190],"them":[89],"Curve25519.":[91],"Two":[92],"contributions":[93],"are":[94],"pivotal":[95],"success.":[98],"First,":[99],"we":[100,129,180],"introduce":[101],"novel":[103],"multiplication":[104],"strategy":[105],"matches":[107],"memory":[109],"access":[110],"complexity":[111],"operand":[114],"caching":[115],"method":[116],"while":[117],"being":[118],"applicable":[119],"larger":[122],"cache":[123],"size":[124],"implementations.":[127],"Second,":[128],"generalize":[130],"an":[131,176],"efficient":[132],"pseudo-Mersenne":[133],"reduction":[134],"strategy,":[135],"formally":[137],"prove":[138],"its":[139],"correctness":[140],"applicability":[142],"most":[144],"primes":[145],"interest.":[148],"generator":[150,183],"allowed":[151],"optimization":[153],"SQIsign\u2019s":[155],"NIST":[156],"PQC":[157],"Round":[158],"2":[159],"submission,":[160],"improving":[161],"level":[162],"1":[163],"verification":[164],"from":[165],"123":[166],"Mcycles":[167],"only":[169],"54":[170],"Mcycles,":[171],"2.3x":[173],"speedup.":[174],"As":[175],"additional":[177],"case":[178],"study,":[179],"use":[181],"our":[182],"improve":[185],"performance":[186],"portable":[188],"RFC":[191],"7748":[192],"up":[194],"2.2x.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
