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Your Wii then signs the file on the SD card with its private (ECC) key. This is to prevent anyone from modifying the save file while it is on the SD card.
 
Your Wii then signs the file on the SD card with its private (ECC) key. This is to prevent anyone from modifying the save file while it is on the SD card.
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If I then give you a copy of my savefile, your Wii can decrypt it because it knows the SD-key. However, it has no way of checking your Wii's signature, because it doesn't know my console's public key. To solve this problem, the savegame also contains a copy of my Wii's public key -- the one that matches the private key it used to sign the savefile.  (This copy my Wii's public key is called a 'certificate'.)
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If I then give you a copy of my savefile, your Wii can decrypt it because it knows the SD-key. However, it has no way of checking your Wii's signature, because it doesn't know my console's public key. To solve this problem, the savegame also contains a copy of my Wii's public key -- the one that matches the private key it used to sign the savefile.  (This copy of my Wii's public key is called a 'certificate'.)
    
Now your Wii can verify that my Wii signed the file, but it has no way of knowing whether it was really a real Wii that signed it, or if I just made up a new random ECC key to try to fool it. To solve this problem, the certificate stored inside of the savegame is then signed with Nintendo's private key. All Wiis have Nintendo's public key stored in their firmware; your Wii can use that key to verify the signature on the certificate.  If the certificate is valid, it can verify the signature on the savegame against my Wii's signature.
 
Now your Wii can verify that my Wii signed the file, but it has no way of knowing whether it was really a real Wii that signed it, or if I just made up a new random ECC key to try to fool it. To solve this problem, the certificate stored inside of the savegame is then signed with Nintendo's private key. All Wiis have Nintendo's public key stored in their firmware; your Wii can use that key to verify the signature on the certificate.  If the certificate is valid, it can verify the signature on the savegame against my Wii's signature.
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