{"id":"https://openalex.org/W1981424768","doi":"https://doi.org/10.1145/2755996.2756643","title":"Implementation of the DKSS Algorithm for Multiplication of Large Numbers","display_name":"Implementation of the DKSS Algorithm for Multiplication of Large Numbers","publication_year":2015,"publication_date":"2015-06-24","ids":{"openalex":"https://openalex.org/W1981424768","doi":"https://doi.org/10.1145/2755996.2756643","mag":"1981424768"},"language":"en","primary_location":{"id":"doi:10.1145/2755996.2756643","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2755996.2756643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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/A5004097039","display_name":"Christoph L\u00fcders","orcid":"https://orcid.org/0000-0002-1458-4663"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christoph L\u00fcders","raw_affiliation_strings":["Universit\u00e4t Bonn, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004097039"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":1.5892,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8742096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"267","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9995999932289124,"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":0.9995999932289124,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991000294685364,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.8491947650909424},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7467979192733765},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6466073393821716},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6412957906723022},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.5916478633880615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.510052502155304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4626193344593048},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.42607763409614563},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42398571968078613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38955333828926086},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3255125880241394},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.28494465351104736},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.17000290751457214}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.8491947650909424},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7467979192733765},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6466073393821716},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6412957906723022},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.5916478633880615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.510052502155304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4626193344593048},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.42607763409614563},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42398571968078613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38955333828926086},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3255125880241394},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.28494465351104736},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.17000290751457214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2755996.2756643","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2755996.2756643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1562183207","https://openalex.org/W1649758727","https://openalex.org/W1709275931","https://openalex.org/W1754110195","https://openalex.org/W2001121794","https://openalex.org/W2004352620","https://openalex.org/W2005936791","https://openalex.org/W2018022095","https://openalex.org/W2045836768","https://openalex.org/W2061171222","https://openalex.org/W2083368929","https://openalex.org/W2106529515","https://openalex.org/W2122152100","https://openalex.org/W2123119012","https://openalex.org/W2131286165","https://openalex.org/W2163717605","https://openalex.org/W2170835539","https://openalex.org/W6651825174"],"related_works":["https://openalex.org/W2039853057","https://openalex.org/W1995312928","https://openalex.org/W2070298508","https://openalex.org/W2488627717","https://openalex.org/W3089760653","https://openalex.org/W4299282030","https://openalex.org/W2122152100","https://openalex.org/W4297799464","https://openalex.org/W2228278960","https://openalex.org/W3038599687"],"abstract_inverted_index":{"The":[0],"Sch\u00f6nhage-Strassen":[1],"algorithm":[2,38,79],"(SSA)":[3],"is":[4,88,109],"the":[5,65,78,120],"de-facto":[6],"standard":[7],"for":[8,123],"multiplication":[9,56],"of":[10,21,44,114],"large":[11],"integers.":[12],"For":[13,50],"N-bit":[14],"numbers":[15],"it":[16],"has":[17],"a":[18,40,53,60],"time":[19,42],"bound":[20,43],"O(N":[22],"log":[23,25,26,46],"N":[24],"N).":[27,49],"De,":[28],"Kurur,":[29],"Saha":[30],"and":[31,84],"Saptharishi":[32],"(DKSS)":[33],"presented":[34],"an":[35],"asymptotically":[36],"faster":[37],"with":[39],"better":[41],"N\u2022":[45,47],"2O(log*":[48],"this":[51],"paper,":[52],"simplified":[54],"DKSS":[55],"was":[57],"implemented.":[58],"Assuming":[59],"sensible":[61],"upper":[62],"limit":[63],"on":[64],"input":[66],"size,":[67],"some":[68,82],"required":[69],"constants":[70],"could":[71],"be":[72,112],"precomputed.":[73],"This":[74],"allowed":[75],"to":[76,80,111],"simplify":[77],"save":[81],"complexity":[83],"run-time.":[85],"Still,":[86],"run-time":[87],"about":[89,99],"30":[90],"times":[91,101],"larger":[92],"than":[93,103],"SSA,":[94],"while":[95],"memory":[96],"requirements":[97],"are":[98],"2.3":[100],"higher":[102],"SSA.":[104],"A":[105],"possible":[106],"crossover":[107],"point":[108],"estimated":[110],"out":[113],"reach":[115],"even":[116],"if":[117],"we":[118],"utilized":[119],"whole":[121],"universe":[122],"computer":[124],"memory.":[125]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
