Yes. Though sometimes LEO satellites use standard hardware. Otherwise, rad hard electronics are quite behind the state of the art. A ~100 MHz 32-bit machine with a few dozen megabytes of RAM is typical of recent low-end rad hard space hardware. Still, even that is quite capable of modern public key encryption.
You don't normally use public key encryption in satellites, it is some sort of block crypto. CCSDS (a bunch of standards for space applications that is quite popular in the industry) recommends AES-HMAC for authentication and AES-GCM for both authentication and encryption.
My experience with a LEON processor ~100 MHz is that it is hard to get much throughput out of an AES implementation.
