the algorithm for how the signing process has already been figured out.. that is why xbedump can re-sign xbe's with patched keys (so if you softmod your xbox and mod your key you can sign xbe's with the new key and they will match up).
BenJeremy: I'm pretty sure your wrong about the DVD's public key being on the DVD. They're all signed with the same key, and that key is on the xbox. Otherwise a publisher could sign with their own private key and then put their public key on the DVD and the algorithm would succeed. In reality this can't happen because ALL xbe's must be signed with the MS key (.. unless you've softmodded or something along that line to change your public key...) Don't say that "the format of the DVDs is a MS special system and that's their protection" because that would in reality be very weak compared to the system they are using, which is the public key encryption. It only works if the signed DVD is independent of the key that checks it. However there is in the XBE header a media check flag, which is why without a modchip/resigning the game you can't run a game from the hard drive or a burnt copy or anything like that.
now, in the same light.. when you copy an xbox dash from one xbox to another, what error message do you get? Is it error 21? If not, then it's some other error: not a key issue. My main point being, the public key IS the same to all the xboxes. There are other unique identifiers to each xbox (MAC, HD key) and maybe these are being used in each dash copy, but it's not the public key. The public key is the same for all xboxes. Otherwise you couldn't all play games.