{"id":"https://openalex.org/W4321608667","doi":"https://doi.org/10.1109/tit.2023.3244631","title":"Constructing CM Fields for NFS to Accelerate DL Computation in Non-Prime Finite Fields","display_name":"Constructing CM Fields for NFS to Accelerate DL Computation in Non-Prime Finite Fields","publication_year":2023,"publication_date":"2023-02-23","ids":{"openalex":"https://openalex.org/W4321608667","doi":"https://doi.org/10.1109/tit.2023.3244631"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2023.3244631","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2023.3244631","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5103103191","display_name":"Yuqing Zhu","orcid":"https://orcid.org/0000-0002-9094-7569"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuqing Zhu","raw_affiliation_strings":["Beijing Key Laboratory of Security and Privacy in Intelligent Transportation and the School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-9094-7569","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Security and Privacy in Intelligent Transportation and the School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070828650","display_name":"Jiqiang Liu","orcid":"https://orcid.org/0000-0003-1147-4327"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiqiang Liu","raw_affiliation_strings":["Beijing Key Laboratory of Security and Privacy in Intelligent Transportation and the School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1147-4327","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Security and Privacy in Intelligent Transportation and the School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02079061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"69","issue":"6","first_page":"4045","last_page":"4055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994999766349792,"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":0.9994999766349792,"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/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"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/T10237","display_name":"Cryptography and Data Security","score":0.9987000226974487,"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/automorphism","display_name":"Automorphism","score":0.8778439164161682},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.8178914785385132},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6723741292953491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6403684020042419},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5085901021957397},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4928002655506134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4839080274105072},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4778853952884674},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.44862088561058044},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4377591907978058},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4219116270542145},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.41318532824516296},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3089689612388611},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3066827654838562},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28302818536758423},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24527844786643982},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.18270447850227356},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.11109504103660583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08421263098716736}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8778439164161682},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.8178914785385132},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6723741292953491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6403684020042419},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5085901021957397},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4928002655506134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4839080274105072},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4778853952884674},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.44862088561058044},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4377591907978058},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4219116270542145},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.41318532824516296},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3089689612388611},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3066827654838562},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28302818536758423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24527844786643982},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.18270447850227356},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.11109504103660583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08421263098716736},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2023.3244631","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2023.3244631","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1434595323","display_name":null,"funder_award_id":"62002015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2751604336","display_name":null,"funder_award_id":"2020YFB2103802","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3059132948","display_name":null,"funder_award_id":"2021RC259","funder_id":"https://openalex.org/F4320323066","funder_display_name":"Beijing Jiaotong University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323066","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W600997534","https://openalex.org/W1490637410","https://openalex.org/W1578625033","https://openalex.org/W1950331499","https://openalex.org/W1981455414","https://openalex.org/W2020929171","https://openalex.org/W2021384897","https://openalex.org/W2071483197","https://openalex.org/W2094556471","https://openalex.org/W2108834246","https://openalex.org/W2111310412","https://openalex.org/W2141506304","https://openalex.org/W2156186849","https://openalex.org/W2295494829","https://openalex.org/W2343001762","https://openalex.org/W2345633925","https://openalex.org/W2406585997","https://openalex.org/W2408939312","https://openalex.org/W2560395997","https://openalex.org/W2576352420","https://openalex.org/W2741945342","https://openalex.org/W2781216073","https://openalex.org/W2790485266","https://openalex.org/W2804627268","https://openalex.org/W2915040791","https://openalex.org/W2936696234","https://openalex.org/W2953438062","https://openalex.org/W2955323779","https://openalex.org/W2966648351","https://openalex.org/W2994293923","https://openalex.org/W3002042021","https://openalex.org/W3035895299","https://openalex.org/W3216932868","https://openalex.org/W4246140522","https://openalex.org/W4310346129","https://openalex.org/W6704723534","https://openalex.org/W6764948996","https://openalex.org/W6765021406","https://openalex.org/W6766664702"],"related_works":["https://openalex.org/W2893614166","https://openalex.org/W1597678101","https://openalex.org/W3203245720","https://openalex.org/W1490994218","https://openalex.org/W4229518224","https://openalex.org/W1992663735","https://openalex.org/W2117672015","https://openalex.org/W4243425381","https://openalex.org/W2514478013","https://openalex.org/W7780975"],"abstract_inverted_index":{"The":[0],"hardness":[1],"of":[2,14,53,116,125,128],"discrete":[3],"logarithm":[4],"problem":[5],"(DLP)":[6],"over":[7],"finite":[8],"fields":[9,100,106],"is":[10,21,84],"the":[11,19,24,31,40,46,59,64,76,81,96,105,114,137,164,182,188],"security":[12],"foundation":[13],"many":[15],"cryptographic":[16],"protocols.":[17],"When":[18],"characteristic":[20],"not":[22,85],"small,":[23],"state-of-the-art":[25],"algorithms":[26],"for":[27],"solving":[28],"DLP":[29],"are":[30],"number":[32,65,184,191],"field":[33,66,185,192],"sieve":[34,186],"(NFS)":[35],"and":[36,166,174,187],"its":[37],"variants.":[38],"In":[39],"relation":[41],"collection":[42],"step,":[43],"to":[44,51,57,74,98,136,159,181],"translate":[45],"relations":[47],"between":[48],"prime":[49],"ideals":[50],"those":[52],"elements":[54],"one":[55,70],"needs":[56],"use":[58,72],"Schirokauer":[60,82],"map.":[61],"Besides,":[62],"if":[63],"has":[67],"non-trivial":[68,111],"automorphisms,":[69],"can":[71],"them":[73],"accelerate":[75],"factor-base":[77],"logarithms":[78,115],"computation.":[79],"However,":[80],"map":[83],"compatible":[86],"with":[87,113,132,163],"automorphisms.":[88],"To":[89],"exploit":[90],"automorphism":[91],"efficiently,":[92],"we":[93,121,156,176],"focus":[94],"on":[95,107,171],"method":[97,180],"construct":[99,122],"in":[101],"NFS":[102],"such":[103],"that":[104],"both":[108,172],"sides":[109],"have":[110],"automorphisms":[112,138],"units":[117],"being":[118,139],"zero:":[119],"1)":[120],"two":[123],"families":[124],"CM":[126],"polynomials":[127,162],"arbitrary":[129],"even":[130],"degree":[131],"small":[133],"coefficients,":[134],"corresponding":[135],"<inline-formula":[140,148],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[141,149],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[142,150],"<tex-math":[143,151],"notation=\"LaTeX\">$x\\mapsto":[144,152],"-x$":[145],"</tex-math></inline-formula>":[146],"or":[147],"1/x$":[153],"</tex-math></inline-formula>;":[154],"2)":[155],"show":[157],"how":[158],"combine":[160],"these":[161],"JLSV1":[165],"Conjugation":[167],"polynomial":[168],"selection":[169],"methods":[170],"sides;":[173],"3)":[175],"also":[177],"generalize":[178],"our":[179],"multiple":[183],"extended":[189],"tower":[190],"sieve.":[193]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}