F2X.<x> = GF(2)[]
aespoly = x^8 + x^4 + x^3 + x + 1
f256.<a> = GF(256, modulus=aespoly)
2*f256(1) # 0

(a+1)^255 # 1

(a+1)^(255/3) # a^7 + a^5 + a^4 + a^3 + a^2 + 1

a.minpoly()

a.minpoly().factor()

(x^64 + 1).factor()

(x^1000 + x^678 + x^2 + 1).factor()