Does your bank encrypt the PDFs? Some of mine do (Europe). Some combo of bank account and birthday to open them - they state this in the email - so trivial to open by others that know you, but not strangers. Better than nothing I guess.
(And encryption is NOT a signature. Anyone who knows the password can forge an encrypted file with the same password. So the PDFs would still be worthless.)
Encryption involves using signing key and universally uniquely identifying something.
That's exactly what it is. In fact encryption is even more secure than a normal written signature.
I can sign a piece of text put it here -- sign it with my private key -- put it on HN with my public key and everyone can be sure I wrote it.
With asymetric encryption you have a sort of signature because only the sender has the encryption key, so forging somemthing that opens with the same decryption key is hard. But I have yet to see somebody encrypt pdfs with an asymetric method.
No, certainly not.
The biggest issue is that you're conflating a human concept of a signature and the cryptographic one. This is obvious from your second paragraph.
> I can sign a piece of text put it here -- sign it with my private key -- put it on HN with my public key and everyone can be sure I wrote it.
Cryptographically maybe, legally no. We lack crucial information about who can use your keys, there's nothing that says you can't share a random keypair that has no legal backing. We also don't know if your keys are valid at all, maybe you're underaged? Do we know if your keys were valid during the time of signing, maybe you were underaged?
It's way more complex than Sign(text).
As far as signatures in PDFs goes, when have you ever needed them? What’s the real world scenario? I think most recipients would be incapable of validating the signature properly (including verifying ownership of the public key corresponding to the private key that signed it). Ie same flaws of any Cert based system.
How would I prove to a court that I do have money if I only have easily forge-able unsigned PDFs?
Now before you say this is unlikely, ask yourself this:
Would you lend thousands of dollars to a regular person without ANY signed document from them which says they owe you the money?
No, right?
Then why would I do that with a bank?
If they get that much money from me they ought to at least give me a kind-of unforgeable document which says the money is mine.