Quiz: The Playstation 3 Hack
aka The Nonce Reuse Attack
Very very secure.
Sony uses a private key, typically stored (in an HSM?) at the company's HQ, to mark their Playstation firmwares as valid and unmodified. The PS3 only needs a public key to verify that the signature came from Sony. Normally, this is considered safe; but Sony did a rookie mistake in the implementation of their signing algorithm - they used the same random number to sign everything.

Recall how the (public parameter)
in the signature is generated from a (secret) random number
, using the formula
kG=RkG = R
being the x-coordinate of the point
Given two signatures that use the same
, prove how you can extract the private key used for signing. Use the signature formula in the ECDSA section. You'll need pen and paper for this.
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