{"id":"https://openalex.org/W4280542304","doi":"https://doi.org/10.1007/s10623-022-01135-y","title":"A survey of elliptic curves for proof systems","display_name":"A survey of elliptic curves for proof systems","publication_year":2022,"publication_date":"2022-12-21","ids":{"openalex":"https://openalex.org/W4280542304","doi":"https://doi.org/10.1007/s10623-022-01135-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-022-01135-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01135-y","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://pure.au.dk/ws/files/421721754/A_survey_of_elliptic_curves_for_proof_systems.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020557476","display_name":"Diego F. Aranha","orcid":"https://orcid.org/0000-0002-2457-0783"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Diego F. Aranha","raw_affiliation_strings":["Aarhus University, Aarhus, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-2457-0783","affiliations":[{"raw_affiliation_string":"Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004547486","display_name":"Youssef El Housni","orcid":"https://orcid.org/0000-0003-2873-3479"},"institutions":[{"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/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Youssef El Housni","raw_affiliation_strings":["ConsenSys, gnark, Paris, France","Inria, Saclay, France","LIX, CNRS, \u00c9cole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France"],"raw_orcid":"https://orcid.org/0000-0003-2873-3479","affiliations":[{"raw_affiliation_string":"ConsenSys, gnark, Paris, France","institution_ids":[]},{"raw_affiliation_string":"Inria, Saclay, France","institution_ids":["https://openalex.org/I4210126360"]},{"raw_affiliation_string":"LIX, CNRS, \u00c9cole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039797547","display_name":"Aurore Guillevic","orcid":"https://orcid.org/0000-0002-0824-7273"},"institutions":[{"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/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["DK","FR"],"is_corresponding":false,"raw_author_name":"Aurore Guillevic","raw_affiliation_strings":["Aarhus University, Aarhus, Denmark","Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-0824-7273","affiliations":[{"raw_affiliation_string":"Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020557476"],"corresponding_institution_ids":["https://openalex.org/I204337017"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":4.0232,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.94413592,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"91","issue":"11","first_page":"3333","last_page":"3378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9972000122070312,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9850999712944031,"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/T11614","display_name":"Cloud Data Security Solutions","score":0.9534000158309937,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7011240720748901},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6670597791671753},{"id":"https://openalex.org/keywords/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.6625453233718872},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6213021874427795},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.5494737029075623},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.49108338356018066},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.4159421920776367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40517866611480713},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4050653576850891},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3653998374938965},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34666118025779724},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.17402145266532898}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7011240720748901},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6670597791671753},{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.6625453233718872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6213021874427795},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5494737029075623},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.49108338356018066},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.4159421920776367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40517866611480713},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4050653576850891},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3653998374938965},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34666118025779724},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17402145266532898},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10623-022-01135-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01135-y","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/0087bb4a-b2ea-4b83-abff-4840c32e5673","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/0087bb4a-b2ea-4b83-abff-4840c32e5673","pdf_url":"https://pure.au.dk/ws/files/421721754/A_survey_of_elliptic_curves_for_proof_systems.pdf","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aranha, D F, El Housni, Y & Guillevic, A 2023, 'A survey of elliptic curves for proof systems', Designs, Codes and Cryptography, vol. 91, no. 11, pp. 3333\u20133378. https://doi.org/10.1007/s10623-022-01135-y","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-03667798v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-03667798","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/hal-03667798","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-03667798v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03667798","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography, 2022, Special Issue: Mathematics of Zero-Knowledge, 91 (11), pp.3333-3378. &#x27E8;10.1007/s10623-022-01135-y&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/0087bb4a-b2ea-4b83-abff-4840c32e5673","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/0087bb4a-b2ea-4b83-abff-4840c32e5673","pdf_url":"https://pure.au.dk/ws/files/421721754/A_survey_of_elliptic_curves_for_proof_systems.pdf","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aranha, D F, El Housni, Y & Guillevic, A 2023, 'A survey of elliptic curves for proof systems', Designs, Codes and Cryptography, vol. 91, no. 11, pp. 3333\u20133378. https://doi.org/10.1007/s10623-022-01135-y","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4280542304.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1483726862","https://openalex.org/W1563556756","https://openalex.org/W1970606468","https://openalex.org/W1985592521","https://openalex.org/W2018746447","https://openalex.org/W2021553056","https://openalex.org/W2028982966","https://openalex.org/W2034710402","https://openalex.org/W2043007983","https://openalex.org/W2046569422","https://openalex.org/W2048054397","https://openalex.org/W2065422049","https://openalex.org/W2067047774","https://openalex.org/W2067596507","https://openalex.org/W2067700169","https://openalex.org/W2069448237","https://openalex.org/W2109806227","https://openalex.org/W2146689848","https://openalex.org/W2166670067","https://openalex.org/W2296489817","https://openalex.org/W2470176151","https://openalex.org/W2517744317","https://openalex.org/W2536137494","https://openalex.org/W2741945342","https://openalex.org/W2790485266","https://openalex.org/W2797042583","https://openalex.org/W2883585522","https://openalex.org/W2883748642","https://openalex.org/W2947480871","https://openalex.org/W2963284730","https://openalex.org/W2964305900","https://openalex.org/W2966295786","https://openalex.org/W2980673735","https://openalex.org/W2984674716","https://openalex.org/W3015292646","https://openalex.org/W3021066046","https://openalex.org/W3104760159","https://openalex.org/W3105190800","https://openalex.org/W3165713929","https://openalex.org/W3202783968","https://openalex.org/W3216932868","https://openalex.org/W4213010969","https://openalex.org/W4317928173","https://openalex.org/W6931496356","https://openalex.org/W6950025874"],"related_works":["https://openalex.org/W1870614684","https://openalex.org/W4394650907","https://openalex.org/W154364797","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1970588133","https://openalex.org/W2022025391","https://openalex.org/W2163538620"],"abstract_inverted_index":{"Elliptic":[0],"curves":[1,24,69,74,82,94],"have":[2,17],"become":[3],"key":[4],"ingredients":[5],"for":[6,95,102],"instantiating":[7],"zero-knowledge":[8],"proofs":[9],"and":[10,49,57,80,97,112],"more":[11],"generally":[12],"proof":[13,33],"systems.":[14,34],"Recently,":[15],"there":[16],"been":[18],"many":[19],"tailored":[20],"constructions":[21,92,101],"of":[22,32,55,66,93],"these":[23],"that":[25],"aim":[26],"at":[27,63],"efficiently":[28],"implementing":[29],"different":[30],"kinds":[31],"In":[35],"this":[36],"survey":[37],"we":[38],"provide":[39,90],"the":[40,51,67,99,109],"reader":[41],"with":[42],"a":[43,72,77],"comprehensive":[44],"overview":[45,62],"on":[46],"existing":[47,110],"work":[48,111],"revisit":[50],"contributions":[52],"in":[53],"terms":[54],"efficiency":[56],"security.":[58],"We":[59,89,105],"present":[60],"an":[61,85],"three":[64],"stages":[65],"process:":[68],"to":[70,75,83],"instantiate":[71,76],"SNARK,":[73,79],"recursive":[78,103],"also":[81,106],"express":[84],"elliptic-curve":[86],"related":[87],"statement.":[88],"new":[91],"SNARKs":[96],"generalize":[98],"state-of-the-art":[100],"SNARKs.":[104],"exhaustively":[107],"document":[108],"open-source":[113],"implementations.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
