Mixing
How do you calculate the branch number of a matrix?
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Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:
begin{pmatrix}
02 & 03 & 01 & 01 \
01 & 02 & 03 & 01 \
01 & 01 & 02 & 03 \
03 & 01 & 01 & 02
end{pmatrix}
These entries are hexadecimals (or bytes), e.g. in bits ${02}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).
I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.
I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.
A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.
linear-algebra matrices
asked Feb 16 at 13:00
Red Book 1
300314
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up vote
0
down vote
favorite
Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:
begin{pmatrix}
02 & 03 & 01 & 01 \
01 & 02 & 03 & 01 \
01 & 01 & 02 & 03 \
03 & 01 & 01 & 02
end{pmatrix}
These entries are hexadecimals (or bytes), e.g. in bits ${02}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).
I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.
I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.
A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.
linear-algebra matrices
asked Feb 16 at 13:00
Red Book 1
300314
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:
begin{pmatrix}
02 & 03 & 01 & 01 \
01 & 02 & 03 & 01 \
01 & 01 & 02 & 03 \
03 & 01 & 01 & 02
end{pmatrix}
These entries are hexadecimals (or bytes), e.g. in bits ${02}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).
I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.
I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.
A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.
linear-algebra matrices
asked Feb 16 at 13:00
Red Book 1
300314
Can anyone explain what a branch number is and how to calculate it? I have checked several books on matrices but it seems uncommon. In particular, the matrix:
begin{pmatrix}
02 & 03 & 01 & 01 \
01 & 02 & 03 & 01 \
01 & 01 & 02 & 03 \
03 & 01 & 01 & 02
end{pmatrix}
These entries are hexadecimals (or bytes), e.g. in bits ${02}$ is $00000010$, and comes from the Mix column layer in the $AES$ cipher (just in case that makes a difference).
I have read this matrix has the maximum branch number of $n+1 = 5$, but I do not understand where this came from or what it means.
I also read this is an $MDS$ matrix and I think branch numbers and $MDS$ matrices are linked somehow but, again, I don't know how. I have looked for video tutorials on $MDS$ matrices and branch numbers but there is nothing for beginners.
A couple of simple examples for branch numbers and/or $MDS$ matrices would be really helpful.
linear-algebra matrices
linear-algebra matrices
asked Feb 16 at 13:00
Red Book 1
300314
asked Feb 16 at 13:00
Red Book 1
300314
asked Feb 16 at 13:00
Red Book 1
300314
asked Feb 16 at 13:00
Red Book 1
300314
asked Feb 16 at 13:00
Red Book 1
300314
300314
add a comment |
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