In mathematics, an all one polynomial (AOP) is a polynomial in which all coefficients are one. Over the finite field of order two, conditions for the AOP to be irreducible are known, which allow this polynomial to be used to define efficient algorithms and circuits for multiplication in finite fields of characteristic two.[1] The AOP is a 1-equally spaced polynomial.[2]
^Cohen, Henri; Frey, Gerhard; Avanzi, Roberto; Doche, Christophe; Lange, Tanja; Nguyen, Kim; Vercauteren, Frederik (2005), Handbook of Elliptic and Hyperelliptic Curve Cryptography, Discrete Mathematics and Its Applications, CRC Press, p. 215, ISBN 9781420034981.
^Itoh, Toshiya; Tsujii, Shigeo (1989), "Structure of parallel multipliers for a class of fields GF(2m)", Information and Computation, 83 (1): 21–40, doi:10.1016/0890-5401(89)90045-X.
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