{"id":"https://openalex.org/W65832523","doi":null,"title":"Analysis of affine equivalent boolean functions for cryptography","display_name":"Analysis of affine equivalent boolean functions for cryptography","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W65832523","mag":"65832523"},"language":"en","primary_location":{"id":"mag:65832523","doi":null,"is_oa":false,"landing_page_url":"https://eprints.qut.edu.au/15828/1/Joanne_Fuller_Thesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"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/A5050178354","display_name":"Joanne Fuller","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joanne Fuller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5050178354"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.006000000052154064,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-transformation","display_name":"affine transformation","score":0.7710000276565552},{"id":"https://openalex.org/keywords/bent-functions","display_name":"bent functions","score":0.6489999890327454},{"id":"https://openalex.org/keywords/algebraic-order","display_name":"algebraic order","score":0.5379999876022339},{"id":"https://openalex.org/keywords/balanced-boolean-functions","display_name":"balanced Boolean functions","score":0.7649999856948853},{"id":"https://openalex.org/keywords/nonlinearity","display_name":"nonlinearity","score":0.9419999718666077},{"id":"https://openalex.org/keywords/boolean-function-design","display_name":"Boolean function design","score":0.3779999911785126},{"id":"https://openalex.org/keywords/cryptographic-boolean-functions","display_name":"cryptographic Boolean functions","score":0.49000000953674316},{"id":"https://openalex.org/keywords/block-cipher","display_name":"block cipher","score":0.546999990940094},{"id":"https://openalex.org/keywords/stream-ciphers","display_name":"stream ciphers","score":0.9670000076293945},{"id":"https://openalex.org/keywords/hash-functions","display_name":"hash functions","score":0.9929999709129333},{"id":"https://openalex.org/keywords/algebraic-degree","display_name":"algebraic degree","score":0.3700000047683716},{"id":"https://openalex.org/keywords/algebraic-normal-form","display_name":"algebraic normal form","score":0.5619999766349792},{"id":"https://openalex.org/keywords/algebraic-immunity","display_name":"algebraic immunity","score":0.3190000057220459}],"concepts":[{"id":"https://openalex.org/C196836630","wikidata":"https://www.wikidata.org/wiki/Q4753279","display_name":"And-inverter graph","level":4,"score":0.7291370034217834},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7114986181259155},{"id":"https://openalex.org/C68481662","wikidata":"https://www.wikidata.org/wiki/Q176197","display_name":"Standard Boolean model","level":5,"score":0.6881693005561829},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.6547757387161255},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.568138062953949},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5666333436965942},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.5527358651161194},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4963400959968567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4920360743999481},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.489808052778244},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.4593390226364136},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4517847001552582},{"id":"https://openalex.org/C106544461","wikidata":"https://www.wikidata.org/wiki/Q543151","display_name":"Block cipher","level":3,"score":0.41912779211997986},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.4167085587978363},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3991541266441345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2929665446281433},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2613668143749237},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19114834070205688},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11087778210639954},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:65832523","doi":null,"is_oa":false,"landing_page_url":"https://eprints.qut.edu.au/15828/1/Joanne_Fuller_Thesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":79,"referenced_works":["https://openalex.org/W20271813","https://openalex.org/W103055543","https://openalex.org/W118952007","https://openalex.org/W127195055","https://openalex.org/W140633939","https://openalex.org/W158390298","https://openalex.org/W206720953","https://openalex.org/W836049037","https://openalex.org/W1488367145","https://openalex.org/W1490303615","https://openalex.org/W1491780949","https://openalex.org/W1495514252","https://openalex.org/W1497234828","https://openalex.org/W1512363553","https://openalex.org/W1516253199","https://openalex.org/W1528065150","https://openalex.org/W1531634792","https://openalex.org/W1534088294","https://openalex.org/W1536790875","https://openalex.org/W1557382432","https://openalex.org/W1565496777","https://openalex.org/W1571317543","https://openalex.org/W1575067221","https://openalex.org/W1575149347","https://openalex.org/W1579761987","https://openalex.org/W1582278613","https://openalex.org/W1583499453","https://openalex.org/W1587697857","https://openalex.org/W1589266564","https://openalex.org/W1591542597","https://openalex.org/W1606480398","https://openalex.org/W1629301835","https://openalex.org/W1639210492","https://openalex.org/W1654806544","https://openalex.org/W1670558497","https://openalex.org/W1781761117","https://openalex.org/W1838666760","https://openalex.org/W1839036866","https://openalex.org/W1906499095","https://openalex.org/W1964723977","https://openalex.org/W1975122896","https://openalex.org/W1980279697","https://openalex.org/W1983679212","https://openalex.org/W1983760747","https://openalex.org/W2000815164","https://openalex.org/W2004502213","https://openalex.org/W2011798878","https://openalex.org/W2014317997","https://openalex.org/W2035999274","https://openalex.org/W2036675812","https://openalex.org/W2038083595","https://openalex.org/W2039544376","https://openalex.org/W2041621301","https://openalex.org/W2050467723","https://openalex.org/W2062897622","https://openalex.org/W2069033591","https://openalex.org/W2090432705","https://openalex.org/W2091456407","https://openalex.org/W2104079506","https://openalex.org/W2109265351","https://openalex.org/W2109394932","https://openalex.org/W2113890807","https://openalex.org/W2120464016","https://openalex.org/W2121178597","https://openalex.org/W2121195548","https://openalex.org/W2124818982","https://openalex.org/W2127819467","https://openalex.org/W2129632939","https://openalex.org/W2131614218","https://openalex.org/W2133044087","https://openalex.org/W2142470358","https://openalex.org/W2148721664","https://openalex.org/W2154271831","https://openalex.org/W2166610027","https://openalex.org/W2231898687","https://openalex.org/W2309949946","https://openalex.org/W2501509697","https://openalex.org/W2613775171","https://openalex.org/W3140432360"],"related_works":["https://openalex.org/W1996798866","https://openalex.org/W2591007409","https://openalex.org/W1549834473","https://openalex.org/W3147183096","https://openalex.org/W7099498077","https://openalex.org/W2344561532","https://openalex.org/W4283766969","https://openalex.org/W2981485902","https://openalex.org/W2379033830","https://openalex.org/W2051491799"],"abstract_inverted_index":{"Boolean":[0,32,54,79,97,155,160,186,215,279,288,376,394,439],"functions":[1,33,55,80,98,161,280,406,453,464,485,518],"are":[2,18,162,446],"an":[3,73,129,219,582,607],"important":[4,130,443],"area":[5],"of":[6,14,21,39,53,64,78,85,96,114,153,214,225,239,254,263,272,278,287,295,304,317,348,361,381,392,404,414,465,474,486,489,522,530,547,575,591,605],"study":[7,52],"for":[8,56,99,141,260,275,321,373],"cryptography.":[9,100],"These":[10,366],"functions,":[11,377],"consisting":[12],"merely":[13],"one's":[15],"and":[16,25,47,81,94,136,200,297,315,364,396,429,454,492,540,558,581],"zero's,":[17],"the":[19,62,68,76,92,108,112,115,139,154,222,226,229,237,245,258,261,264,276,302,357,369,382,390,393,405,415,437,448,455,459,534,566,601],"heart":[20],"numerous":[22],"cryptographic":[23],"systems":[24],"their":[26,427],"ability":[27,286,515],"to":[28,61,90,127,221,291,329,335,343,353,387,450,457,470,513,516,536,585,600],"provide":[29,128],"secure":[30,65],"communication.":[31],"have":[34,330],"application":[35,95,438,529],"in":[36,67,82,121,157,185,267,356,389,407,436,526,550,559,598],"a":[37,142,150,182,211,240,324,331,339,378,397,487,520,527],"variety":[38,488,521],"such":[40,134,576,606],"systems,":[41],"including":[42,192,218],"block":[43],"ciphers,":[44],"stream":[45],"ciphers":[46],"hash":[48],"functions.":[49],"The":[50,118,146,206,252,285,313,346,472,480,495,545,573],"continued":[51,435],"cryptography":[57],"is":[58,181,299,420,433,477,508],"therefore":[59],"fundamental":[60,241,355],"provision":[63,358],"communication":[66],"future.":[69],"This":[70,179,232,431],"thesis":[71,123,207],"presents":[72],"investigation":[74],"into":[75,164,426],"analysis":[77,84,144,199,296,363,577],"particular,":[83],"affine":[86,230,531],"transformations":[87],"with":[88,189,210,417,468,511],"respect":[89,469,512],"both":[91,537],"design":[93,539,587],"Past":[101],"research":[102,119,188,265,290],"has":[103],"often":[104],"been":[105],"limited":[106],"by":[107,236],"difficulties":[109],"arising":[110],"from":[111,173,519],"magnitude":[113],"search":[116],"space.":[117],"presented":[120,266,597],"this":[122,268],"will":[124,208,233,256,281,326,350,542,555,562,578,595],"be":[125,177,234,283,327,351,354,543,556,563,579,596],"shown":[126,328,352,564],"step":[131],"towards":[132],"overcoming":[133],"restrictions":[135],"hence":[137],"forms":[138],"basis":[140],"new":[143,147,242,293,362,444],"methodology.":[145],"perspective":[148],"allows":[149],"reduced":[151],"view":[152],"space":[156,395],"which":[158],"all":[159,592],"grouped":[163],"connected":[165,383],"equivalence":[166,250,384,409,523,532],"classes":[167,416],"so":[168],"that":[169,247,308,401,565,588],"only":[170],"one":[171],"function":[172,187,216,289,440],"each":[174,408],"class":[175,193,195,385],"need":[176],"established.":[178],"approach":[180,342],"significant":[183],"development":[184,314],"many":[190,359],"applications,":[191],"distinguishing,":[194],"structures,":[196],"self":[197,398],"mapping":[198,399],"finite":[201,551],"field":[202,552],"based":[203,306,553],"s-box":[204,538,568,586],"analysis.":[205],"begin":[209],"brief":[212],"overview":[213],"theory;":[217],"introduction":[220],"main":[223],"theme":[224,432],"research,":[227],"namely":[228],"transformation.":[231],"followed":[235],"presentation":[238],"theorem":[243,253,347],"describing":[244],"connectivity":[246,255],"exists":[248],"between":[249],"classes.":[251,524],"form":[257],"foundation":[259],"remainder":[262],"thesis.":[269],"A":[270,411],"discussion":[271],"efficient":[273,318],"algorithms":[274,319],"manipulation":[277],"then":[282,434,509],"presented.":[284],"achieve":[292],"levels":[294],"understanding":[298,391],"centered":[300],"on":[301,323],"availability":[303],"computer":[305,325],"programs":[307],"can":[309],"perform":[310],"various":[311],"manipulations.":[312],"optimisation":[316],"specifically":[320],"execution":[322],"considerable":[332],"advantage":[333],"compared":[334],"those":[336],"constructed":[337],"using":[338],"more":[340],"traditional":[341],"algorithm":[344],"optimisation.":[345],"connectivety":[349],"avenues":[360],"application.":[365],"applications":[367],"include":[368],"first":[370,449,481],"non-exhaustive":[371],"test":[372],"determining":[374],"equivalent":[375],"visual":[379],"representation":[380],"structure":[386],"aid":[388],"constant":[400],"enables":[402],"enumeration":[403],"class.":[410],"detailed":[412],"survey":[413],"six":[418],"inputs":[419,467,493],"also":[421],"presented,":[422],"providing":[423],"valuable":[424],"insight":[425],"range":[428],"structure.":[430],"construction.":[441],"Two":[442],"methodologies":[445],"presented;":[447],"yield":[451,458],"bent":[452,484],"second":[456,496],"best":[460,602],"currently":[461],"known":[462,603],"balanced":[463],"eight":[466],"nonlinearity.":[471],"implementation":[473],"these":[475],"constructions":[476],"extremely":[478],"efficient.":[479],"construction":[482,497,507,541,584],"yields":[483],"algebraic":[490],"order":[491],"sizes.":[494],"provides":[498],"better":[499],"results":[500],"than":[501],"previously":[502],"proposed":[503],"heuristic":[504],"techniques.":[505],"Each":[506],"analysed":[510],"its":[514],"produce":[517],"Finally,":[525],"further":[528],"analysis,":[533],"impact":[535],"considered.":[544],"effect":[546,574],"linear":[548,571,593],"redundancy":[549,594],"s-boxes":[554],"examined":[557],"particular":[560],"it":[561],"AES":[567],"possesses":[569],"complete":[570],"redundancy.":[572],"discussed":[580],"alternative":[583],"ensures":[589],"removal":[590],"addition":[599],"example":[604],"s-box.":[608]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}