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Cool article overall, especially since it was an actual CS related application of the abstract algebra class I took this semester. Also, is there any reason in
by hendzen 14y ago
Cool article overall, especially since it was an actual CS related application of the abstract algebra class I took this semester. Also, is there any reason in particular why that particular polynomial was chosen for AES?
- dlsym 14y agoI think it was chosen because the addition of two elements in GF(2^8) with their binary representation is a XOR. Which is a really efficient operation.
- hendzen 14y agoYes, but this is true regardless of the irreducible polynomial used to form the field. My question is why that specific polynomial was chosen; was it an arbitrary choice or was there some reason?
- tomerv 14y agoAs the article mentions: "That first one that worked (100011011) is the one used in AES" i.e., the polynomial that was chosen for AES (x^8 + x^4 + x^3 + x + 1) is the minimal irreducible polynomial of degree 8 (minimal in the sense of the natural ordering of polynomials). I guess that could be a good reason (but I'm not sure it's _the_ reason).
- deleted 14y ago[deleted]
- dlsym 14y agoI feel nerd sniped... http://xkcd.com/356/ http://xkcd.com/356/
- cjg_ 14y ago"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.pdf 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.