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Is there a square matrix with applications in Cryptography such that the determinant of this matrix is 0 and all its sub minors are non-singular?

I am looking for a square matrix whose determinant is 0, however, all sub-minors of this matrix are non singular. This matrix needs to have applications in Cryptography. The matrix may be over any ...
Kurious Koder's user avatar
2 votes
1 answer
264 views

How to calculate the branch number of a linear mapping?

Is there an efficient algorithm which can be used to determine the branch number of any given linear mapping?
Monster's user avatar
  • 35
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 ...
Red Book 1's user avatar
  • 1,025
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 ...
JoaoAlby's user avatar
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 ...
Rikeijin's user avatar
  • 211