9
votes
0answers
94 views

Choice of multiplication polynomial in Rijndael s-box affine mapping

The Rijndael specification details the design choices for the s-box in section 7.2. They describe the choice of affine mapping as follows: We have chosen an affine mapping that has a very simple ...
1
vote
1answer
88 views

simple multiplication in GF(8)

I am trying to do multiplication in the GF($2^3$) defined by the irreducible minimum binary polynomial $X^3+X^2+1$. I want to multiply $A(x) * B(x)$ where $A(x) = x$ and $B(x) = x^2$. The ...
1
vote
2answers
715 views

Multiplicative inverse in $GF(2^8)$?

I know how to do multiplication over $GF(2^8)$. Logic is... ...
3
votes
1answer
369 views

AES mixcolumn stage

I'm studying AES, and am having problems with the "mixcolumn" stage. I read about finite fields, but I still don't know. How do I construct $GF(2^8)$? ...
-1
votes
2answers
265 views

Factoring a polynomial over a GF [closed]

I have the following question: What polynomial, when factored over the field $GF (2^8)$ based on the irreducible polynomial that is used in Rijndael, will factor into all the polynomials in the ...
4
votes
1answer
262 views

Best choice of finite field for AES on a 4-bit microcontroller?

As the finite field of $GF(2^8)$ are isomorphic to $GF((2^4)^2)$, $GF((2^2)^4)$ and $GF(((2^2)^2)^2)$, which of the fields is best suited and most efficient for 4-bit MCU and why? Would it be ...
12
votes
2answers
1k views

Design properties of the Rijndael finite field

So we've already had a question on replacing the Rijndael S-Box. My question is - can we use a different finite field other than the one given by $x^8 + x^4 + x^3 + x + 1$ in $GF(2^8)$. In other ...