▁ 7 6 8 ▁kil oby tes ▁of ▁the ▁generator ▁output ▁like ▁a ▁correctly ▁guess ed ▁key ▁would . ▁ ▁As ▁a ▁rule , ▁the ▁we aker ▁the ▁correlation ▁between ▁an ▁individual ▁register ▁and ▁the ▁generator ▁output , ▁the ▁more ▁known ▁plain text ▁is ▁required ▁to ▁find ▁that ▁register ' s ▁key ▁with ▁a ▁high ▁degree ▁of ▁confidence . ▁ ▁Read ers ▁with ▁a ▁background ▁in ▁probability ▁theory ▁should ▁be ▁able ▁to ▁see ▁easily ▁how ▁to ▁formal ise ▁this ▁argument ▁and ▁obtain ▁estimates ▁of ▁the ▁length ▁of ▁known ▁plain text ▁required ▁for ▁a ▁given ▁correlation ▁using ▁the ▁bin omial ▁distribution . ▁ ▁High er ▁order ▁correl ations ▁ ▁Definition ▁ ▁The ▁correl ations ▁which ▁were ▁explo ited ▁in ▁the ▁example ▁attack ▁on ▁the ▁Ge ffe ▁generator ▁are ▁examples ▁of ▁what ▁are ▁called ▁first ▁order ▁correl ations : ▁they ▁are ▁correl ations ▁between ▁the ▁value ▁of ▁the ▁generator ▁output ▁and ▁an ▁individual ▁L FS R . ▁ ▁It ▁is ▁possible ▁to ▁define ▁higher ▁order ▁correl ations ▁in ▁addition ▁to ▁these . ▁ ▁For ▁instance , ▁it ▁may ▁be ▁possible ▁that ▁while ▁a ▁given ▁Boolean ▁function ▁has ▁no ▁strong ▁correl ations ▁with ▁any ▁of ▁the ▁individual ▁registers ▁it ▁comb ines , ▁a ▁significant ▁correlation ▁may ▁exist ▁between ▁some ▁Boolean ▁function ▁of ▁two ▁of ▁the ▁registers , ▁e . g . ▁. ▁ ▁This ▁would ▁be ▁an ▁example ▁of ▁a ▁second ▁order ▁correlation . ▁ ▁We ▁can ▁define ▁third ▁order ▁correl ations ▁and ▁so ▁on ▁in ▁the ▁obvious ▁way . ▁ ▁High er ▁order ▁correlation ▁attacks