▁ ▁Obviously , ▁higher ▁correlation ▁imm unity ▁makes ▁a ▁function ▁more ▁suitable ▁for ▁use ▁in ▁a ▁ke yst ream ▁generator ▁( although ▁this ▁is ▁not ▁the ▁only ▁thing ▁which ▁needs ▁to ▁be ▁considered ). ▁ ▁Sie gent hal er ▁showed ▁that ▁the ▁correlation ▁imm unity ▁m ▁of ▁a ▁Boolean ▁function ▁of ▁algebraic ▁degree ▁d ▁of ▁n ▁variables ▁satisfies ▁m   +   d   ≤   n ; ▁for ▁a ▁given ▁set ▁of ▁input ▁variables , ▁this ▁means ▁that ▁a ▁high ▁algebraic ▁degree ▁will ▁restrict ▁the ▁maximum ▁possible ▁correlation ▁imm unity . ▁ ▁Furthermore , ▁if ▁the ▁function ▁is ▁bal anced ▁then ▁m   ≤   n   −   1 . ▁ ▁It ▁follows ▁that ▁it ▁is ▁impossible ▁for ▁a ▁function ▁of ▁n ▁variables ▁to ▁be ▁n - th ▁order ▁correlation ▁imm une . ▁ ▁This ▁also ▁follows ▁from ▁the ▁fact ▁that ▁any ▁such ▁function ▁can ▁be ▁written ▁using ▁a ▁Re ed - M ull er ▁basis ▁as ▁a ▁combination ▁of ▁X OR s ▁of ▁the ▁input ▁functions . ▁ ▁Ci pher ▁design ▁imp lications ▁ ▁Given ▁the ▁possibly ▁extreme ▁sever ity ▁of ▁a ▁correlation ▁attack ' s ▁impact ▁on ▁a ▁stream ▁ci pher ' s ▁security , ▁it ▁should ▁be ▁considered ▁essential ▁to ▁test ▁a ▁candidate ▁Boolean ▁combination ▁function ▁for ▁correlation ▁imm unity ▁before ▁dec iding ▁to ▁use ▁it ▁in ▁a ▁stream ▁ci pher . ▁ ▁However , ▁it ▁is ▁important ▁to ▁note ▁that ▁high ▁correlation ▁imm unity ▁is ▁a ▁necessary ▁but ▁not ▁sufficient ▁condition ▁for ▁a ▁Boolean ▁function ▁to ▁be