▁of ▁the ▁field . ▁ ▁Since ▁the ▁multip lic ative ▁group ▁of ▁a ▁finite ▁field ▁is ▁always ▁a ▁cy clic ▁group , ▁a ▁primitive ▁polynomial ▁f ▁is ▁a ▁polynomial ▁such ▁that ▁x ▁is ▁a ▁generator ▁of ▁the ▁multip lic ative ▁group ▁in ▁G F ( p )[ x ]/ f ( x ) ▁ ▁Pse udo - random ▁bit ▁generation ▁Prim itive ▁polynomials ▁over ▁G F ( 2 ), ▁the ▁field ▁with ▁two ▁elements , ▁can ▁be ▁used ▁for ▁pseud or andom ▁bit ▁generation . ▁In ▁fact , ▁every ▁linear ▁feedback ▁shift ▁register ▁with ▁maximum ▁cycle ▁length ▁( which ▁is ▁, ▁where ▁n ▁is ▁the ▁length ▁of ▁the ▁linear ▁feedback ▁shift ▁register ) ▁may ▁be ▁built ▁from ▁a ▁primitive ▁polynomial . ▁ ▁For ▁example , ▁given ▁the ▁primitive ▁polynomial ▁, ▁we ▁start ▁with ▁a ▁user - spec ified ▁non zero ▁ 1 0 - bit ▁seed ▁occup ying ▁bit ▁positions ▁ 1 ▁through ▁ 1 0 , ▁starting ▁from ▁the ▁least ▁significant ▁bit . ▁( The ▁seed ▁need ▁not ▁randomly ▁be ▁chosen , ▁but ▁it ▁can ▁be ). ▁ ▁We ▁then ▁take ▁the ▁ 1 0 th ▁and ▁ 3 rd ▁bits , ▁and ▁create ▁a ▁new ▁ 0 th ▁bit , ▁so ▁that ▁the ▁x or ▁of ▁the ▁three ▁bits ▁is ▁ 0 . ▁ ▁The ▁seed ▁is ▁then ▁shift ed ▁left ▁one ▁position ▁so ▁that ▁the ▁ 0 th ▁bit ▁moves ▁to ▁position ▁ 1 . ▁ ▁This ▁process ▁can ▁be ▁repeated ▁to ▁generate ▁ ▁pseudo - random ▁bits . ▁