{"id":"https://openalex.org/W2131802958","doi":"https://doi.org/10.1109/tit.2011.2146570","title":"On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks","display_name":"On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks","publication_year":2011,"publication_date":"2011-06-21","ids":{"openalex":"https://openalex.org/W2131802958","doi":"https://doi.org/10.1109/tit.2011.2146570","mag":"2131802958"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2146570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2146570","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/A5044400426","display_name":"Somindu C. Ramanna","orcid":"https://orcid.org/0000-0002-0596-9553"},"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":"Somindu C. Ramanna","raw_affiliation_strings":["Applied Statistics Unit, Indian Statistical Institute, Kolkata, India","Appl. Stat. Unit, Indian Stat. Inst., Kolkata, India"],"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Appl. Stat. Unit, Indian Stat. Inst., Kolkata, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","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, Kolkata, India","Appl. Stat. Unit, Indian Stat. Inst., Kolkata, India"],"affiliations":[{"raw_affiliation_string":"Applied Statistics Unit, Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Appl. Stat. Unit, Indian Stat. Inst., Kolkata, India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044400426"],"corresponding_institution_ids":["https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":0.4276,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73611343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"57","issue":"7","first_page":"4798","last_page":"4816"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9972000122070312,"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":0.9972000122070312,"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/T11598","display_name":"Internet Traffic Analysis and Secure E-voting","score":0.9764999747276306,"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/T11241","display_name":"Advanced Malware Detection Techniques","score":0.9463000297546387,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/notation","display_name":"Notation","score":0.7265529632568359},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4510646164417267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39987802505493164},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3667988181114197},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3247494399547577},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13276264071464539}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7265529632568359},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4510646164417267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39987802505493164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3667988181114197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3247494399547577},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13276264071464539}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2011.2146570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2146570","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W81015123","https://openalex.org/W1483487117","https://openalex.org/W1590949317","https://openalex.org/W1639145229","https://openalex.org/W1639210492","https://openalex.org/W1879093391","https://openalex.org/W1975462169","https://openalex.org/W2047026958","https://openalex.org/W2095880256","https://openalex.org/W2108475361","https://openalex.org/W2132233293","https://openalex.org/W2327481811","https://openalex.org/W2751862591","https://openalex.org/W2752921537","https://openalex.org/W3159346169","https://openalex.org/W4231916799","https://openalex.org/W6660612422"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"Bellare":[0,190],"and":[1,77,163,183,191,244],"Kohno":[2,192],"(2004)":[3,193],"introduced":[4],"the":[5,11,33,37,55,81,120,164,185,229,239,248],"notion":[6,56],"of":[7,13,35,39,57,71,84,95,122,156,160,167,228,231,241],"balance":[8],"to":[9,22,45,144,169,213,217,262],"quantify":[10],"resistance":[12,38,216],"a":[14,23,46,108,153,209,224],"hash":[15,109],"function":[16,110],"<formula":[17,40,58,65,72,87,96,112,124,131,146,172,197,232,254],"formulatype=\"inline\"":[18,41,59,66,73,88,97,113,125,132,147,173,198,233,255],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,42,60,67,74,89,98,114,126,133,148,174,199,234,256],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[20,43,61,75,90,115,134,149,175,200,235,257],"Notation=\"TeX\">$h$</tex></formula>":[21,44,76],"generic":[24,47,218],"collision":[25],"attack.":[26,49],"Motivated":[27],"by":[28,189],"their":[29,205],"work,":[30,206],"we":[31,53,207,222],"consider":[32],"problem":[34],"quantifying":[36],"multicollision":[48,219],"To":[50],"this":[51],"end,":[52],"introduce":[54],"Notation=\"TeX\">$r$</tex>":[62,258],"</formula>":[63,138,259],"-balance":[64,237,260],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[68,99,127],"<tex":[69,100,128],"Notation=\"TeX\">$\\mu_{r}(h)$</tex></formula>":[70,101],"obtain":[78,170,245],"bounds":[79,104],"on":[80],"success":[82],"probability":[83,155],"finding":[85],"an":[86,171],"Notation=\"TeX\">$r$</tex></formula>":[91,150,176,236],"-collision":[92,177],"in":[93],"terms":[94],".":[102],"These":[103,180],"show":[105],"that":[106,250],"for":[107,194,247],"with":[111,152],"Notation=\"TeX\">$m$</tex></formula>":[116],"image":[117],"points,":[118],"if":[119],"number":[121,166],"trials":[123,168],"Notation=\"TeX\">$q$</tex></formula>":[129],"is":[130,142,178],"Notation=\"TeX\">$\\Theta\\left":[135],"(rm^{\\left":[136],"({{r-1}\\over{r}}\\right)\\mu_{r}(h)}\\right)$</tex>":[137],",":[139],"then":[140],"it":[141],"possible":[143],"find":[145],"-collisions":[151],"significant":[154],"success.":[157],"The":[158],"behavior":[159],"random":[161],"functions":[162,243,252],"expected":[165],"studied.":[179],"results":[181,187],"extend":[182],"complete":[184],"earlier":[186],"obtained":[188],"collisions":[195],"(i.e.,":[196],"Notation=\"TeX\">$r=2$</tex></formula>":[201],").":[202],"Going":[203],"beyond":[204],"provide":[208,214],"new":[210],"design":[211],"criteria":[212],"quantifiable":[215],"attacks.":[220],"Further,":[221],"make":[223],"detailed":[225],"probabilistic":[226],"investigation":[227],"variation":[230],"over":[238],"set":[240],"all":[242],"support":[246],"view":[249],"most":[251],"have":[253],"close":[261],"one.":[263]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
