All Questions
Tagged with matrix-multiplication aes
12 questions
2
votes
1
answer
259
views
How to check that an $km \times km$ block-binary matrix is an MDS matrix in $k$-bit words over $\operatorname{GF}(2)$
I have been reading about MDS matrices. It is defined as (paraphrased from Section 2.1)
An $n \times n$ matrix $M$ is MDS if and only if $bn(M) = n + 1$
where $bn$ (branch number) is defined as:
$bn(...
- 603
1
vote
1
answer
721
views
How do we reduce the multiplications in the AES mix column layer using $x^4 +1$
I recently learned AES uses $x^4 +1$ to reduce the multiplications in the MixCol layer. However, I used $p(x) = x^8 + x^4 + x^3 + x + 1$ not knowing it was the wrong polynomial and got the correct ...
- 1,025
1
vote
0
answers
492
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Expressing a given linear transformation in Galois Field GF(256) in terms of another linear transformation with a different reduction polynomial
Before giving a better and detailed description of what I ask, let me first tell why I need what I am looking for: Intel processors already provide instructions (AES-NI) for very efficient AES ...
- 11
2
votes
3
answers
977
views
How can I get the binary form of AES's MDS matrix in MixColumns tranformation?
I need to write a procedure for calculating the MixColumns's operation result in the following form:
$M*X^T,$
where $M$ is a 128x128 binary matrix, $X$ is a 128-bit vector (the state).
My question ...
- 81
0
votes
3
answers
562
views
Optimal MDS matrix - circulant or recursive?
One of the special matrix in $GF(2^q)$ is MDS matrix which can be used in the cryptography like mix column of AES. Two forms of MDS matrices are circulant and recursive.
Which form of MDS matrix (...
- 204
3
votes
1
answer
707
views
Prove the branch of number of Advanced Encryption Standard
In the Advanced Encryption Standard (AES) document: page 27 section 7.3.1, It defines branch number. It said
" Let F be a linear transformation acting on byte vectors and let the
byte weight ...
- 211
3
votes
1
answer
331
views
Why does AES use a Binary Field?
The key idea in AES is the use of matrix multiplication and the corresponding inverse (as opposed to Feistel). But the algorithm does that using a GF instead of simple modular arithmetic.
Is there ...
- 188
10
votes
1
answer
2k
views
How to calculate active s-boxes from branch number?
If MDS in AES has branch number 5 (so 5 active s-boxes in 2 rounds), wouldn't that mean 4 rounds of AES has $5*2=10$ active s-boxes?
AES paper says it has 25 ($5^2$?) active s-boxes in 4 rounds.
How ...
- 1,702
8
votes
2
answers
2k
views
How do Käsper and Schwabe's Bitsliced AES Mixcolumns work?
The only way I see it possible to do the matrix-multiplication in the MixColumns operation of AES is by shifting the bits in the multiplied number, and then reduce with the polynomial if needed.
...
- 367
2
votes
1
answer
1k
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How to perform AES MixColumns as matrix multiplication in GF(2) (boolean values)?
AES MixColumns is done by multiplying a $4 \times 4$ matrix and a column of the AES state (a vector). Addition and multiplication are done in $\operatorname{GF}(2^8)$.
In the paper White-box AES, the ...
- 233
1
vote
1
answer
5k
views
Affine transformation in AES: Matrix representation
I know that the affine transformation of the AES can be represented both as a polynomial evaluation over $\operatorname{GF}(2^8)$ and as a matrix-vector multiplication (see, e.g., p.212 C.4 of The ...
- 13
0
votes
1
answer
630
views
Direct sum of Binary numbers In Mixcolumns
I have just started learning cryptography and I am trying to make sense of the direct sum on some binary numbers.
I am trying to find a column of a state space after a Mixcolumns operation has been ...
- 121