Ideally it should work like this:
Supercomputer (more or less expensive), dedicated to Matrix (and other, including Ciphers) Calculations, with Simple Web Service Interface.
This way users can either login (with simple client) and manually upload data to be calculated, then wait and acquire results they paid for. Or they can automate leasing of computing power and resources with their own tools (programs will automatically order such calculations when needed).
This can be useful for Mathematicians to relieve them of simplest, menial tasks.