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Re:Visualizing Galois Fields by cjg_ on Sunday May 20, 2012 @06:18AM (#3998429)
"The polynomial m(x ) (‘11B’) for the multiplication in GF(28) is the first one of the list of irreducible polynomials of degree 8, given in [LiNi86, p. 378]."

from the Rijndael submission to the AES competition, page 25 (http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended....)

LiNi86 refers to is R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, 1986.

So there is no apparent reason they choose this polynomial, i.e. other would also have worked.

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