▁ ▁Comp ared ▁to ▁the ▁cost ▁of ▁launch ing ▁a ▁br ute ▁force ▁attack ▁on ▁the ▁entire ▁system , ▁with ▁complexity ▁ 2 3 2 , ▁this ▁represents ▁an ▁attack ▁effort ▁saving ▁factor ▁of ▁just ▁under ▁ 2 5 6 , ▁which ▁is ▁substantial . ▁ ▁If ▁a ▁second ▁register ▁is ▁correl ated ▁with ▁the ▁function , ▁we ▁may ▁repeat ▁this ▁process ▁and ▁drop ▁the ▁attack ▁complexity ▁to ▁ 2 8 ▁+ ▁ 2 8 ▁+ ▁ 2 1 6 ▁for ▁an ▁effort ▁saving ▁factor ▁of ▁just ▁under ▁ 6 5 0 2 8 . ▁ ▁In ▁this ▁sense , ▁correlation ▁attacks ▁can ▁be ▁considered ▁divide ▁and ▁conquer ▁algorithms . ▁ ▁Example ▁ ▁Bre aking ▁the ▁Ge ffe ▁generator ▁ ▁Cor relation ▁attacks ▁are ▁perhaps ▁best ▁explained ▁via ▁example . ▁ ▁We ▁will ▁consider ▁the ▁case ▁of ▁the ▁Ge ffe ▁ke yst ream ▁generator . ▁ ▁The ▁Ge ffe ▁generator ▁consists ▁of ▁three ▁L FS R s : ▁L FS R - 1 , ▁L FS R - 2 ▁and ▁L FS R - 3 . ▁ ▁If ▁we ▁denote ▁the ▁outputs ▁of ▁these ▁registers ▁by ▁, ▁ ▁and ▁, ▁respectively , ▁then ▁the ▁Boolean ▁function ▁that ▁comb ines ▁the ▁three ▁registers ▁to ▁provide ▁the ▁generator ▁output ▁is ▁given ▁by ▁ ▁( i . e . ▁( ▁AND ▁) ▁X OR ▁( NOT ▁ ▁AND ▁) ). ▁ ▁There ▁are ▁ 2 3 ▁= ▁ 8 ▁possible ▁values ▁for ▁the ▁outputs ▁of ▁the ▁three ▁registers , ▁and ▁the ▁value ▁of ▁this ▁combining ▁function