The Matrix Reloaded

Useful Sage documentation link about the syntax for matrices. We are given a somewhat similar to a Diffie-Hellman key-exchange, a secret $s$ is picked out, then $H = G * s$ is calculated. They also generate a random vector $v$ in the matrix space. The product of $H \times v = w$ is calculated. Given the two vectors $v, w$, we have to derive the value of the secret $s$ to obtain the decryption key....