{"id":"https://openalex.org/W3013021797","doi":"https://doi.org/10.3934/amc.2020119","title":"New discrete logarithm computation for the medium prime case using the function field sieve","display_name":"New discrete logarithm computation for the medium prime case using the function field sieve","publication_year":2021,"publication_date":"2021-01-08","ids":{"openalex":"https://openalex.org/W3013021797","doi":"https://doi.org/10.3934/amc.2020119","mag":"3013021797"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2020119","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020119","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=d7f51db9-e046-4282-82a7-8c1217b53808","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/data/article/export-pdf?id=d7f51db9-e046-4282-82a7-8c1217b53808","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053441328","display_name":"Madhurima Mukhopadhyay","orcid":"https://orcid.org/0000-0001-6330-3293"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Madhurima Mukhopadhyay","raw_affiliation_strings":["Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, India 700108"],"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, India 700108","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036784831","display_name":"Palash Sarkar","orcid":"https://orcid.org/0000-0002-5346-2650"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Palash Sarkar","raw_affiliation_strings":["Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, India 700108"],"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, India 700108","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086053298","display_name":"Shashank Singh","orcid":"https://orcid.org/0000-0002-4374-3125"},"institutions":[{"id":"https://openalex.org/I288749910","display_name":"Indian Institute of Science Education and Research, Bhopal","ror":"https://ror.org/02rb21j89","country_code":"IN","type":"education","lineage":["https://openalex.org/I288749910"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shashank Singh","raw_affiliation_strings":["Electrical Engineering &amp; Computer Science, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, Madhya Pradesh, India"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering &amp; Computer Science, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, Madhya Pradesh, India","institution_ids":["https://openalex.org/I288749910"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058814816","display_name":"Emmanuel Thom\u00e9","orcid":"https://orcid.org/0000-0002-5669-2195"},"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"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":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Thom\u00e9","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, INRIA, Nancy, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, INRIA, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053441328"],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00379839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"3","first_page":"449","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9965000152587891,"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":0.9965000152587891,"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":0.9922000169754028,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/discrete-logarithm","display_name":"Discrete logarithm","score":0.9107058048248291},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7692786455154419},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7540088295936584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5469973683357239},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5179170966148376},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4972071945667267},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4421994090080261},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41353774070739746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36429864168167114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3347013592720032},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1495479941368103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1412486732006073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09199810028076172}],"concepts":[{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.9107058048248291},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7692786455154419},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7540088295936584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5469973683357239},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5179170966148376},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4972071945667267},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4421994090080261},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41353774070739746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36429864168167114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3347013592720032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1495479941368103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1412486732006073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09199810028076172},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3934/amc.2020119","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020119","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=d7f51db9-e046-4282-82a7-8c1217b53808","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02964002v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02964002","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":"Advances in Mathematics of Communications, 2022, 16 (3), pp.449-464. &#x27E8;10.3934/amc.2020119&#x27E9;","raw_type":"Journal articles"},{"id":"mag:3013021797","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/iacr/iacr2020.html#MukhopadhyaySST20","pdf_url":null,"source":{"id":"https://openalex.org/S2764847869","display_name":"IACR Cryptology ePrint Archive","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":["https://openalex.org/P4322614454"],"host_organization_lineage_names":["Cryptology ePrint Archive"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IACR Cryptology ePrint Archive","raw_type":null}],"best_oa_location":{"id":"doi:10.3934/amc.2020119","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020119","pdf_url":"https://www.aimsciences.org/data/article/export-pdf?id=d7f51db9-e046-4282-82a7-8c1217b53808","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3013021797.pdf","grobid_xml":"https://content.openalex.org/works/W3013021797.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W61549430","https://openalex.org/W311623651","https://openalex.org/W1482131745","https://openalex.org/W1518618574","https://openalex.org/W1535758889","https://openalex.org/W1565956864","https://openalex.org/W1758781646","https://openalex.org/W1969728959","https://openalex.org/W1993819992","https://openalex.org/W2056307179","https://openalex.org/W2065099844","https://openalex.org/W2091260227","https://openalex.org/W2156186849","https://openalex.org/W2213167237","https://openalex.org/W2312918952","https://openalex.org/W2476275171","https://openalex.org/W2905954184","https://openalex.org/W2913594971","https://openalex.org/W3034714558","https://openalex.org/W3035895299"],"related_works":["https://openalex.org/W3101100768","https://openalex.org/W3165713929","https://openalex.org/W3034714558","https://openalex.org/W2742341575","https://openalex.org/W1719113876","https://openalex.org/W3195774515","https://openalex.org/W3094101225","https://openalex.org/W2577487606","https://openalex.org/W2126923963","https://openalex.org/W3204461504","https://openalex.org/W2951802124","https://openalex.org/W3170337877","https://openalex.org/W2142778315","https://openalex.org/W2128141215","https://openalex.org/W1516480348","https://openalex.org/W2257714540","https://openalex.org/W3104998233","https://openalex.org/W3047247602","https://openalex.org/W1995540902","https://openalex.org/W2203317094"],"abstract_inverted_index":{"&lt;p":[0],"style='text-indent:20px;'&gt;The":[1],"present":[2],"work":[3],"reports":[4],"progress":[5],"in":[6],"discrete":[7,25,82],"logarithm":[8,26,83],"computation":[9,27,39,78,84],"for":[10,59,80],"the":[11,17,50,70,77],"general":[12],"medium":[13],"prime":[14],"case":[15],"using":[16],"function":[18],"field":[19,31],"sieve":[20],"algorithm.":[21],"A":[22],"new":[23],"record":[24],"over":[28,85],"a":[29,33],"1051-bit":[30],"having":[32],"22-bit":[34],"characteristic":[35,63],"was":[36],"performed.":[37],"This":[38],"builds":[40],"on":[41],"and":[42,53,64],"implements":[43],"previously":[44],"known":[45],"techniques.":[46],"Analysis":[47],"indicates":[48],"that":[49],"relation":[51],"collection":[52],"descent":[54],"steps":[55],"are":[56],"within":[57],"reach":[58],"fields":[60],"with":[61],"32-bit":[62],"moderate":[65],"extension":[66],"degrees.":[67],"It":[68],"is":[69],"linear":[71],"algebra":[72],"step":[73],"which":[74],"will":[75],"dominate":[76],"time":[79],"any":[81],"such":[86],"fields.&lt;/p&gt;":[87]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
