(that can take many forms, but that general idea is how most software updates currently work)
Yes, EdDSA is faster, with 64 byte signatures. Recommended.
https://en.wikipedia.org/wiki/EdDSA
1. Hashing the incoming data
2. Decrypting an attached signature
3. Verifying the decrypted and calculated hash are the same
Even though Step 2 would involve RSA or ECC, wouldn't Step 1 be the most expensive part regardless?