周期序列k-錯線性復雜度的期望與方差.pdf

1、南京航空航天大學碩士學位論文周期序列k錯線性復雜度的期望與方差姓名：吳成文申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：岳勤201012周期序列七一錯線性復雜度的期望與方差AbstractInstreamciphers，thelinearcomplexityofsequenceisusedtOiIlcasurlethesecurityofciphersAstrongsequenceshouldnotonlyhavealargelinearc

2、omplexitybutalsobecomeaslowdecreaseofthelinearcomplexityifafewbitsa∞changedThus，Ⅵ，eCallUSetheconceptofkerrorlinearcomplexitytoincasUl℃thestabilitysequenceInthispaperwemainlyinvestigatetheexpectedvalueandvarianceofthekerr

3、orlinearcomplexityofperiodicsequencesWewillmainlyUSenumbertheoryandfinitefieldtheoryinspecial，somemathameticsfactsofEulerfunctionandcyclotomiepolynomialandSOon，togivetheexpectedvalueandvarianceofthelinearcomplexityofperi

4、odicsequence，andtheboundaryoftheexpectedvalueofthelinearcomplexityofperiodicsequencesThemainresultsale弱follows：InChaptertwo，letSbeaperiodicN2P”sequenceoverafinitefield只，whereP，g躺distinctoddpliffle$andgisaprimitiverootmod

5、uloP2Usinganewmethod：iedecomposingthepolynomialoverafinitefield，、ⅣeshowanotherproofoftheexpectedvalueoflinearcomplexityE。oandthevarianceoflinearcomplexity圪，oMoreoverthebetterupperandlowerboundoftheexpectedvalueoflinearco

6、mplexityEoandthevarianceoflinearcomplexity圪。oalegivenhlChapterthree，letSbeaperiodicN2P”sequenceoverafinitefield‘，whereP，q玳distinctoddprimesandqisaprimitiverootmoduloP2，k_(p1)／2Wedefineanewhanmingweightxiaohangmingweight，

7、givetheexpectedvalueandvarianceofthekerrorlinearcomplexityofperiodicsequenceMoreoverweuseanothermethodtogivetheupperboundoftheexpectedvalueofthe1errorlinearcomplexityandtheupperandlowerboundoftheexpectedvalueofthekerrorl