Let $A$ be a randomly generated matrix. Let $I$ be the identity matrix. $\times$ is the matrix multiplication operation, $/$ is matrix division (multiplying the first matrix by the inverse of the second). $$ I \times A \times A = B $$
Provide $B$ and $I$ to the recipient. To create encrypted message $E$ from unencrypted message $M$: $$ E = M \times A \times A $$
Send $E$ to the recipient. The recipient will solve for $M$ using: $$ M = E / ( B / I) $$ My question is:
Will the recipient be able to decode the message?
If an attacker knows $E$ and $I$, can they efficiently solve for $M$?
Is there a simple way to make it nonlinear?
I accepted an answer but am still waiting for #3.