{"id":"https://openalex.org/W2892262517","doi":"https://doi.org/10.1145/3243734.3243773","title":"Bandwidth-Hard Functions","display_name":"Bandwidth-Hard Functions","publication_year":2018,"publication_date":"2018-10-15","ids":{"openalex":"https://openalex.org/W2892262517","doi":"https://doi.org/10.1145/3243734.3243773","mag":"2892262517"},"language":"en","primary_location":{"id":"doi:10.1145/3243734.3243773","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3243734.3243773","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3243734.3243773","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3243734.3243773","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028278191","display_name":"Jeremiah Blocki","orcid":"https://orcid.org/0000-0002-5542-4674"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeremiah Blocki","raw_affiliation_strings":["Purdue University, West Lafayette, IN, USA"],"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002519367","display_name":"Ling Ren","orcid":"https://orcid.org/0000-0003-3437-7570"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ling Ren","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018283928","display_name":"Samson Zhou","orcid":"https://orcid.org/0000-0001-8288-5698"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samson Zhou","raw_affiliation_strings":["Purdue University, West Lafayette, IN, USA"],"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028278191"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.1847,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.84617152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1820","last_page":"1836"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9983999729156494,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9983999729156494,"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/T12326","display_name":"Network Packet Processing and Optimization","score":0.9790999889373779,"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"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9751999974250793,"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/computer-science","display_name":"Computer science","score":0.7337538003921509},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5642638206481934},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.5488163828849792},{"id":"https://openalex.org/keywords/memory-bandwidth","display_name":"Memory bandwidth","score":0.4776267409324646},{"id":"https://openalex.org/keywords/cache","display_name":"Cache","score":0.4345552623271942},{"id":"https://openalex.org/keywords/static-random-access-memory","display_name":"Static random-access memory","score":0.412563681602478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39508360624313354},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33346042037010193},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.1857704520225525}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7337538003921509},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5642638206481934},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.5488163828849792},{"id":"https://openalex.org/C188045654","wikidata":"https://www.wikidata.org/wiki/Q17148339","display_name":"Memory bandwidth","level":2,"score":0.4776267409324646},{"id":"https://openalex.org/C115537543","wikidata":"https://www.wikidata.org/wiki/Q165596","display_name":"Cache","level":2,"score":0.4345552623271942},{"id":"https://openalex.org/C68043766","wikidata":"https://www.wikidata.org/wiki/Q267416","display_name":"Static random-access memory","level":2,"score":0.412563681602478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39508360624313354},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33346042037010193},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.1857704520225525},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3243734.3243773","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3243734.3243773","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3243734.3243773","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3243734.3243773","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3243734.3243773","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3243734.3243773","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security","raw_type":"proceedings-article"},"sustainable_development_goals":[{"score":0.8600000143051147,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1962098393","display_name":null,"funder_award_id":"1649515 and 1704587","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4105555553","display_name":"SaTC: CORE: Improving Password Ecosystem: A Holistic Approach","funder_award_id":"1704587","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G697731757","display_name":"EAGER:   Complexity of Computation on Codes and Lattices","funder_award_id":"1649515","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2892262517.pdf","grobid_xml":"https://content.openalex.org/works/W2892262517.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1553435762","https://openalex.org/W1569144247","https://openalex.org/W1601379374","https://openalex.org/W1965460093","https://openalex.org/W1972501001","https://openalex.org/W1998350371","https://openalex.org/W2021496873","https://openalex.org/W2072573758","https://openalex.org/W2103149732","https://openalex.org/W2155690313","https://openalex.org/W2408009274","https://openalex.org/W2481891620","https://openalex.org/W2484106744","https://openalex.org/W2552182158","https://openalex.org/W2604788655","https://openalex.org/W2612601170","https://openalex.org/W2613194369","https://openalex.org/W2729715767","https://openalex.org/W2731103471","https://openalex.org/W2765893588","https://openalex.org/W2773116874","https://openalex.org/W2794597466","https://openalex.org/W2884834742","https://openalex.org/W4248175462"],"related_works":["https://openalex.org/W3151633427","https://openalex.org/W2212894501","https://openalex.org/W2793465010","https://openalex.org/W3024050170","https://openalex.org/W2039378765","https://openalex.org/W1982351223","https://openalex.org/W2097757554","https://openalex.org/W2887282140","https://openalex.org/W2149537422","https://openalex.org/W2984139344"],"abstract_inverted_index":{"Memory":[0,184],"Hard":[1,185],"Functions":[2],"(MHFs)":[3],"have":[4,29,44,130],"been":[5,45],"proposed":[6,46],"as":[7,162,271],"an":[8,213],"answer":[9],"to":[10,47,67,71,75,86,95,241],"the":[11,15,49,69,73,77,82,88,97,115,136,151,167,173,178,191,196,209,242,248,254,262,275,283,310],"growing":[12],"inequality":[13],"between":[14],"computational":[16],"speed":[17],"of":[18,40,52,101,117,140,154,181,195,211,251,265,274,312],"general":[19],"purpose":[20],"CPUs":[21],"and":[22,38,129,280,296],"Application":[23],"Specific":[24],"Integrated":[25],"Circuits":[26],"(ASICs).":[27],"MHFs":[28],"seen":[30],"widespread":[31],"applications":[32],"including":[33],"password":[34,276],"hashing,":[35],"key":[36],"stretching":[37],"proofs":[39],"work.":[41],"Several":[42],"metrics":[43],"quantify":[48,68,96],"\"memory":[50],"hardness\"":[51],"a":[53,121,182,314],"function.":[54,89],"Cumulative":[55],"memory":[56,133,138],"complexity":[57,64,139],"(CMC)":[58],"(or":[59],"amortized":[60,98],"Area":[61],"\u00d7":[62],"Time":[63],")":[65],"attempts":[66,94],"cost":[70,194,250,320],"acquire/build":[72],"hardware":[74,106],"evaluate":[76,87],"function":[78,104,228],"-":[79,107,282],"after":[80],"normalizing":[81],"time":[83],"it":[84],"takes":[85],"By":[90],"contrast,":[91],"bandwidth":[92,127,152,179,263,300],"hardness":[93,153,180,218,264],"energy":[99,236,249,319],"costs":[100],"evaluating":[102],"this":[103],"on":[105,247],"which":[108],"in":[109,172,253],"turn":[110],"is":[111,144,148,188,321],"largely":[112],"dominated":[113],"by":[114,190],"number":[116],"cache":[118,304],"misses.":[119],"Ideally,":[120],"good":[122],"MHF":[123,142,157,214],"would":[124],"be":[125],"both":[126],"hard":[128,301],"high":[131,216,230,235],"cumulative":[132,137],"complexity.":[134],"While":[135],"leading":[141],"candidates":[143,269],"well":[145,220],"understood,":[146],"little":[147],"known":[149],"about":[150],"many":[155],"prominent":[156,267],"candidates.":[158],"Our":[159],"contributions":[160],"are":[161,219,298],"follows:":[163],"First,":[164],"we":[165,206,224,260,307],"provide":[166],"first":[168,243,284],"reduction":[169],"proving":[170],"that,":[171],"parallel":[174,255],"random":[175,256],"oracle":[176,257],"model,":[177],"Data-Independent":[183],"Function":[186],"(iMHF)":[187],"described":[189],"red-blue":[192,315],"pebbling":[193,316],"directed":[197],"acyclic":[198],"graph":[199],"(DAG)":[200],"associated":[201],"with":[202,215,229,287,317],"that":[203,208,226,309],"iMHF.":[204],"Second,":[205],"show":[207,293,308],"goals":[210],"designing":[212],"CMC/bandwidth":[217],"aligned.":[221],"In":[222],"particular,":[223],"prove":[225],"any":[227],"CMC":[231],"also":[232],"has":[233],"relatively":[234],"costs.":[237],"This":[238],"result":[239],"leads":[240],"unconditional":[244],"lower":[245],"bound":[246],"scrypt":[252],"model.":[258],"Third,":[259],"analyze":[261],"several":[266],"iMHF":[268,286],"such":[270],"Argon2i,":[272,294],"winner":[273],"hashing":[277],"competition,":[278],"aATSample":[279,295],"DRSample":[281,297],"practical":[285],"essentially":[288],"asymptotically":[289],"optimal":[290],"CMC.":[291],"We":[292],"maximally":[299],"under":[302],"appropriate":[303],"size.":[305],"Finally,":[306],"problem":[311],"finding":[313],"minimum":[318],"NP-hard.":[322]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
