{"id":"https://openalex.org/W2048079788","doi":"https://doi.org/10.1137/070700371","title":"Sparse Algebraic Equations over Finite Fields","display_name":"Sparse Algebraic Equations over Finite Fields","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2048079788","doi":"https://doi.org/10.1137/070700371","mag":"2048079788"},"language":"en","primary_location":{"id":"doi:10.1137/070700371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700371","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-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/A5086199716","display_name":"Igor Semaev","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Igor Semaev","raw_affiliation_strings":["igor@ii.uib.no#TAB#"],"affiliations":[{"raw_affiliation_string":"igor@ii.uib.no#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086199716"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.33607811,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.96897495,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"2","first_page":"388","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9984999895095825,"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/mathematics","display_name":"Mathematics","score":0.6570993661880493},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6272834539413452},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5416285395622253},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5063666105270386},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4547835886478424},{"id":"https://openalex.org/keywords/cryptanalysis","display_name":"Cryptanalysis","score":0.42115098237991333},{"id":"https://openalex.org/keywords/system-of-polynomial-equations","display_name":"System of polynomial equations","score":0.4191305637359619},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38933679461479187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37246173620224},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3397238850593567},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25520169734954834},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.21278473734855652},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12935644388198853},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.09915918111801147},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09593772888183594},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07991945743560791}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6570993661880493},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6272834539413452},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5416285395622253},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5063666105270386},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4547835886478424},{"id":"https://openalex.org/C181149355","wikidata":"https://www.wikidata.org/wiki/Q897511","display_name":"Cryptanalysis","level":3,"score":0.42115098237991333},{"id":"https://openalex.org/C105335568","wikidata":"https://www.wikidata.org/wiki/Q7663735","display_name":"System of polynomial equations","level":3,"score":0.4191305637359619},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38933679461479187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37246173620224},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3397238850593567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25520169734954834},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.21278473734855652},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12935644388198853},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.09915918111801147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09593772888183594},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07991945743560791},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070700371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700371","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W173980447","https://openalex.org/W1583871653","https://openalex.org/W1965003774","https://openalex.org/W2029845343","https://openalex.org/W2043193943","https://openalex.org/W2057361103","https://openalex.org/W2062897452","https://openalex.org/W2100408583","https://openalex.org/W2400568052","https://openalex.org/W2591842745","https://openalex.org/W2950918963"],"related_works":["https://openalex.org/W2088138737","https://openalex.org/W2383813702","https://openalex.org/W2354152524","https://openalex.org/W2995990526","https://openalex.org/W2361864162","https://openalex.org/W2382456870","https://openalex.org/W1971748573","https://openalex.org/W2998978527","https://openalex.org/W2383125250","https://openalex.org/W288746350"],"abstract_inverted_index":{"A":[0],"system":[1,27],"of":[2,20,35,65,83,87],"algebraic":[3],"equations":[4,54,93],"over":[5],"a":[6,17],"finite":[7],"field":[8],"is":[9,28,55,68,73],"called":[10],"sparse":[11,91],"if":[12],"each":[13],"equation":[14],"depends":[15],"on":[16,61,80],"low":[18],"number":[19],"variables.":[21],"Efficiently":[22],"finding":[23],"solutions":[24],"to":[25],"the":[26,41,66,76,81,88,100],"an":[29,96],"underlying":[30],"hard":[31],"problem":[32,67],"in":[33],"cryptanalysis":[34],"modern":[36],"ciphers.":[37],"In":[38,90],"this":[39],"paper":[40],"deterministic":[42],"Agreeing-Gluing":[43],"algorithm":[44],"introduced":[45],"earlier":[46],"by":[47,104],"Raddum":[48],"and":[49],"Semaev":[50],"for":[51],"solving":[52,84,106],"such":[53],"studied.":[56],"Its":[57],"expected":[58],"running":[59],"time":[60],"uniformly":[62],"random":[63],"instances":[64,86],"rigorously":[69],"estimated.":[70],"The":[71],"estimate":[72],"at":[74],"present":[75],"best":[77],"theoretical":[78],"bound":[79],"complexity":[82,102],"average":[85],"problem.":[89],"Boolean":[92],"we":[94],"observe":[95],"exciting":[97],"difference":[98],"with":[99],"worst-case":[101],"provided":[103],"SAT":[105],"methods.":[107]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
