I'm experimenting with some rudimentary ideas for data encryption (I've never formally taken a cryptology class). An idea that I had for an encryption was to use matrices. So I treat a data set as vector and apply a matrix (non-singular of course) to the vector.
So my question is two-fold:
First of all, how would someone go about finding the encryption matrix from the image and the pre-image? Like given $\vec{v}=A\vec{u}$, where only $\vec{v}$ and $\vec{u}$ are known, could one find $A$?
Secondly, how easily could such a code be broken programmatically? I presume it would be fairly difficult because the hacker would not only need to know the matrix, but would also need to know the matrix itself (or there could even be a set of matrices alternating between vectors).
If matrix A is $n\times n$, you need at least $n$ linealry independent pairs of $(\vec u, \vec v)$ to reconstruct $A$. I hope this replies to both of your questions.