At the time of this writing, the subtitle of the submission here on HN is

  recovering the signing keys for US driver's license barcodes

Notably, this subtitle doesn't appear on the blog post.

Anyway. I only see claims that the public key can be determined from license barcodes, not that a signing key can be determined. What am I missing or misunderstanding?

To head off one potential retort: While it's true that one can use a public key to encrypt data for the recipient that has the private half of that key or verify that data has been signed by the possessor of the private half of that key, I'm almost 100% certain that it's not possible to use that public key to sign data would validate to other folks as being signed by the private half of that key. It has been more than a decade since I've thought about any of this, but isn't the entire point of public-key cryptography that the public part can be distributed to your worst enemy without causing you any trouble at all?