This is a great question - the Hitron datasheet on the CODA-4582 (link) doesn't indicate the CPU type. I will reach out to my contacts and report back if I get any news!
EDIT: I remember hitron indicating that the CODA-4582 would use the "Intel Puma 7" SoC (system-on-a-chip)...but that was in 2015. Will report back when I hear something.
It's using the Intel Puma 7 (Cougar Mountain) / CE2700 chip, similar to a consumer Intel Atom.
However, it's irrelevant since Hitron doesn't do any proper privilege separation to begin with, and there's no straightforward way to run code on it like a web browser. Any code execution is probably going to give you root anyway, no need for fancy CPU attacks.