{"id":"https://openalex.org/W7128522316","doi":"https://doi.org/10.1007/s00145-025-09567-0","title":"Study of Arithmetization Methods for STARKs","display_name":"Study of Arithmetization Methods for STARKs","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128522316","doi":"https://doi.org/10.1007/s00145-025-09567-0"},"language":"en","primary_location":{"id":"doi:10.1007/s00145-025-09567-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-025-09567-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-025-09567-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00145-025-09567-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125489324","display_name":"Tiago Martins","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tiago Martins","raw_affiliation_strings":["Chair of Applied Mechanics, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, D - 85748, Garching, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3200-2225","affiliations":[{"raw_affiliation_string":"Chair of Applied Mechanics, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, D - 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125549581","display_name":"Jo\u00e3o Farinha","orcid":null},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE","PT"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o Farinha","raw_affiliation_strings":["Chair of Applied Mechanics, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, D - 85748, Garching, Germany","Three Sigma, Lisbon, Portugal"],"raw_orcid":"https://orcid.org/0009-0008-1062-4569","affiliations":[{"raw_affiliation_string":"Chair of Applied Mechanics, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, D - 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Three Sigma, Lisbon, Portugal","institution_ids":["https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5125489324"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18658598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.6869999766349792,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.6869999766349792,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T11005","display_name":"Radiation Effects in Electronics","score":0.09610000252723694,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.06369999796152115,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/soundness","display_name":"Soundness","score":0.9484000205993652},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6798999905586243},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5705000162124634},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5533999800682068},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5347999930381775}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.9484000205993652},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6798999905586243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5939000248908997},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5705000162124634},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5533999800682068},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5347999930381775},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42100000381469727},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.365200012922287},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3391000032424927},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31299999356269836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30970001220703125},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.29019999504089355}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00145-025-09567-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-025-09567-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-025-09567-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00145-025-09567-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00145-025-09567-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00145-025-09567-0.pdf","source":{"id":"https://openalex.org/S190936789","display_name":"Journal of Cryptology","issn_l":"0933-2790","issn":["0933-2790","1432-1378"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128522316.pdf","grobid_xml":"https://content.openalex.org/works/W7128522316.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1589034595","https://openalex.org/W1964234068","https://openalex.org/W2082647621","https://openalex.org/W2087900794","https://openalex.org/W2536319456","https://openalex.org/W2613376966","https://openalex.org/W2885314357","https://openalex.org/W2968027060","https://openalex.org/W3126633261","https://openalex.org/W4298425892"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1,167],"technical":[2],"paper":[3,136],"explores":[4],"two":[5],"solutions":[6],"for":[7,34,57,71],"arithmetization":[8,126],"of":[9,45,84,105,121,124,164,177,187],"computational":[10,119],"integrity":[11],"statements":[12],"in":[13,184],"STARKs,":[14],"namely":[15,96],"the":[16,54,68,82,86,103,106,113,122,132,161,173,185],"algebraic":[17],"intermediate":[18],"representation,":[19],"AIR,":[20,151],"and":[21,52,79,152,175,182],"its":[22,77],"preprocessed":[23],"variant,":[24],"PAIR.":[25],"The":[26,61,135],"work":[27,114,168],"then":[28],"focuses":[29],"on":[30,102,110,131],"their":[31,49,129],"soundness":[32,78],"implications":[33],"Reed\u2013Solomon":[35,72],"proximity":[36,59,73],"testing.":[37,60],"It":[38],"proceeds":[39,115],"by":[40,97,116],"presenting":[41],"a":[42],"comparative":[43],"study":[44,62],"these":[46],"methods,":[47,127],"providing":[48],"theoretical":[50],"foundations":[51],"deriving":[53],"degree":[55,69,87],"bounds":[56],"low-degree":[58,133],"shows":[63],"that":[64],"using":[65],"PAIR":[66,140],"increases":[67],"bound":[70,88],"testing,":[74],"which":[75],"affects":[76],"complexity.":[80],"However,":[81],"possibility":[83],"reducing":[85],"with":[89,155],"multiple":[90],"selector":[91,107],"columns":[92],"is":[93,157],"also":[94],"explored,":[95],"following":[98],"an":[99],"approach":[100],"based":[101],"decomposition":[104],"values.":[108],"Focusing":[109],"performance":[111],"optimization,":[112],"qualitatively":[117],"comparing":[118],"demands":[120],"components":[123],"both":[125],"particularly":[128],"impact":[130],"extensions.":[134],"concludes":[137],"that,":[138],"while":[139],"might":[141],"simplify":[142],"constraint":[143],"enforcement,":[144],"it":[145],"can":[146],"be":[147],"easily":[148],"translated":[149],"to":[150,159],"system":[153],"testing":[154],"benchmarks":[156],"necessary":[158],"determine":[160],"application-specific":[162],"superiority":[163],"either":[165],"method.":[166],"should":[169],"provide":[170],"insight":[171],"into":[172],"strengths":[174],"limitations":[176],"each":[178],"method,":[179],"helping":[180],"researchers":[181],"practitioners":[183],"field":[186],"STARKs":[188],"make":[189],"informed":[190],"design":[191],"choices.":[192]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-02-11T00:00:00"}
