Quiz: The Playstation 3 Hack

aka The Nonce Reuse Attack

Last updated 1 year ago

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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.

Quiz time

Recall how the (public parameter) $r$ in the signature is generated from a (secret) random number $k$ , using the formula $kG = R$ , $r$ being the x-coordinate of the point $R$ .

Given two signatures that use the same $k$ , 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.

Recall how the (public parameter) $r$ in the signature is generated from a (secret) random number $k$ , using the formula $kG = R$ , $r$ being the x-coordinate of the point $R$ .

Given two signatures that use the same $k$ , 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.