# Questions tagged [mds]

An MDS matrix (Maximum Distance Separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography.

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### Sage code for finding generator matrix of MDS code

Let $L$ be an $[n,k]$ code. A $k\times n$ matrix $G$ whose rows form a basis for $L$ is called a generator matrix for $L$. A linear $[n,k,d]$ code with largest possible minimum distance is called ...
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### Changing Field of MDS Matrix Multiplication

Assume we have an $n \times n$ MDS matrix, whose entries are among $m \times m$ binary matrices. Can we see this matrix as a $n \times n$ matrix with entries from $GF(2^m)$? How can we replace this ...
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### AES MDS D-XOR and S-XOR count

I am trying to implement the D-XOR and S-XOR count in python but despite reading multiple articles on how to perform the calculation I have failed to understand the process used. I would appreciate it ...
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### MDS Matrix Elements

Can zero be one of the elements used in an MDS matrix (in the context of AES)? Based on what I have read all entries of an MDS Matrix need to be non-zero. Also, I would appreciate any help in ...
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### How to find the AES branch number?

By definition, branch number Definition: The branch number of a linear transformation $F$ is $$min_{a\neq0}(W(a) + W(F(a)))$$ Source here (7.3.1) For AES MixColumns $a \in GF(2^8)^4$ since ...
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### 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 ...
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### Rijndael S-boxes: Where do the $\mu$ and $\nu$ polynomial ring elements come from?

I've asked some other questions before about Rijndael's S-boxes, and step by step I'm coming to an understanding; but those steps often guide me to new questions. I did some lines of code to ...
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### Variants of AES? [closed]

Would variants of AES provide the same level of security as AES, say by just replacing the S-box with another one, MDS matrix of Mixcolumn, etc.?