The CPU is not directly involved in a transfer, as it does not do a calculation for every bit.
The CPU is used more for encrypting/decrypting the data you are streaming. That would indeed be a problem if you used a really long, oldschool RSA key, rather than a new, more efficient, short elliptic curves key, that requires fewer calculations. Then your CPU may not be able to handle gigabit transfer with a singlecore decryption/encryption process.
But that is taken care of behind the scenes. Ciphers are always evolving to become more efficient.
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