The key in your CPU would be the public key, not the private key. The public key can only be used to verify existing signatures, not create new ones. It may be

The key in your CPU would be the public key, not the private key. The public key can only be used to verify existing signatures, not create new ones. It may be possible through power fault injection to flip the bits of the public key such that you could get it to accept microcode signed with your own private key, but I would be very surprised if the public key weren't burned into the structure of the CPU itself in a manner that renders it immune to such attacks. Of course, power fault injection may still allow you to bypass the verification routine altogether instead of modifying the key it verifies with.