I was also going to suggest that... But I imagine that the Ethernet port or antennae wire (and necessary battery to power antennae) would dwarf the size of that MCU. But thinking again, I suppose if the rules permit the MCU to be directly wired to the Ethernet cable, then could bitbang an early Ethernet standard with this MCU's pins...
An RSA key is 4kB by itself, so TLS is out of the picture.