Editing All one polynomial (section)

{{Short description|Polynomial in which all coefficients are one}}
In [[mathematics]], an '''all one polynomial''' (AOP) is a [[polynomial]] in which all [[coefficient]]s are one. Over the [[GF(2)|finite field of order two]], conditions for the AOP to be [[irreducible polynomial|irreducible]] are known, which allow this polynomial to be used to define efficient algorithms and circuits for [[multiplication]] in [[finite field]]s of [[characteristic (algebra)|characteristic]] two.<ref name="hehcc">{{citation
 | last1 = Cohen | first1 = Henri
 | last2 = Frey | first2 = Gerhard
 | last3 = Avanzi | first3 = Roberto
 | last4 = Doche | first4 = Christophe
 | last5 = Lange | first5 = Tanja | author5-link = Tanja Lange
 | last6 = Nguyen | first6 = Kim
 | last7 = Vercauteren | first7 = Frederik
 | isbn = 9781420034981
 | page = 215
 | publisher = CRC Press
 | series = Discrete Mathematics and Its Applications
 | title = Handbook of Elliptic and Hyperelliptic Curve Cryptography
 | url = https://books.google.com/books?id=w6b0yhURTkQC&pg=PA215
 | year = 2005}}.</ref> The AOP is a 1-[[equally spaced polynomial]].<ref>{{citation
 | last1 = Itoh | first1 = Toshiya
 | last2 = Tsujii | first2 = Shigeo
 | doi = 10.1016/0890-5401(89)90045-X
 | issue = 1
 | journal = Information and Computation
 | pages = 21–40
 | title = Structure of parallel multipliers for a class of fields GF(2<sup>''m''</sup>)
 | volume = 83
 | year = 1989| doi-access = free
 }}.</ref>