He's saying you can derive the private key from a single signature made using a known nonce value (the "bad random"). You can also derive the private key from two signatures made using the same nonce value. In both cases the solution just requires trivial algebra.

That's what we did to get the PS3 signing keys. Accidentally became a bit of a citation in the ECDSA world for that one too; who knew Sony would unwittingly earn the title of "canonical example of how to screw up ECDSA in a consumer product"? :-)

It's also how lots of Bitcoin have been taken away when transactions are signed using broken random number generators. These days people are running bots to spot those keypairs and automatically take the bitcoin.