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Added Wed 13 Apr 2022 I have written a short note with experimental data, which shows not all pseudo keys are good keys. Public key cryptography based on non-invertible matrices We got public key ...

A Hadamard matrix is an $n\times n$-matrix $H$ where each entry in $H$ is $\pm 1$ and where $H/\sqrt{n}$ is orthogonal. It is well-known that if $H$ is an $n\times n$-Hadamard matrix, then $n<3$ or ...

Let $H=\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}.$ Let $A^{\otimes N}$ denote the tensor product of the matrix $A$ with itself taken $N$ times. We say that a vector $v$ of ...

Thinking about Diffe-Hillman for matrices brought me to the following question. Given $\mathbb{F}_{p^k}$ the finite field with $p^k$ elements when can we find non-trivial solutions to $\begin{...

Closely related to this question and extending comment of R. van Dobben de Bruyn. Working over $\mathbb{F}_p$ and all matrices of square $n \times n$. Alice chooses invertible $X_A$ and non-...