▁can ▁be ▁more ▁powerful ▁than ▁single ▁order ▁correlation ▁attacks , ▁however ▁this ▁effect ▁is ▁subject ▁to ▁a ▁" law ▁of ▁limit ing ▁returns ". ▁ ▁The ▁table ▁below ▁shows ▁a ▁measure ▁of ▁the ▁computational ▁cost ▁for ▁various ▁attacks ▁on ▁a ▁ke yst ream ▁generator ▁consisting ▁of ▁eight ▁ 8 - bit ▁L FS R s ▁combined ▁by ▁a ▁single ▁Boolean ▁function . ▁ ▁Under standing ▁the ▁calculation ▁of ▁cost ▁is ▁relatively ▁straightforward : ▁the ▁left most ▁term ▁of ▁the ▁sum ▁represents ▁the ▁size ▁of ▁the ▁keys pace ▁for ▁the ▁correl ated ▁gener ators , ▁and ▁the ▁right most ▁term ▁represents ▁the ▁size ▁of ▁the ▁keys pace ▁for ▁the ▁remaining ▁gener ators . ▁ ▁While ▁higher ▁order ▁correl ations ▁lead ▁to ▁more ▁powerful ▁attacks , ▁they ▁are ▁also ▁more ▁difficult ▁to ▁find , ▁as ▁the ▁space ▁of ▁available ▁Boolean ▁functions ▁to ▁correlate ▁against ▁the ▁generator ▁output ▁increases ▁as ▁the ▁number ▁of ▁arguments ▁to ▁the ▁function ▁does . ▁ ▁Term in ology ▁ ▁A ▁Boolean ▁function ▁ ▁of ▁n ▁variables ▁is ▁said ▁to ▁be ▁" m - th ▁order ▁correlation ▁imm une " ▁or ▁to ▁have ▁" m - th ▁order ▁correlation ▁imm unity " ▁for ▁some ▁integer ▁m ▁if ▁no ▁significant ▁correlation ▁exists ▁between ▁the ▁function ' s ▁output ▁and ▁any ▁Boolean ▁function ▁of ▁m ▁of ▁its ▁inputs . ▁ ▁For ▁example , ▁a ▁Boolean ▁function ▁which ▁has ▁no ▁first ▁order ▁or ▁second ▁order ▁correl ations ▁but ▁which ▁does ▁have ▁a ▁third ▁order ▁correlation ▁exhib its ▁ 2 nd ▁order ▁correlation ▁imm unity .