You can prove that you possess a digital signature from some authority over a statement that says that you are 18 or that you have $1,000,000. However, you don'

You can prove that you possess a digital signature from some authority over a statement that says that you are 18 or that you have $1,000,000. However, you don't have to reveal that actual statement or signature. Typically, that would be because the statement contains your offline identity and you don't want to reveal that to the verifier. This setting is generally "proof of attribute" or "proof of group membership" although in practice it is most often more like "proof of possession of a credential". An interesting example demonstrated a few years ago is that you could prove that you possess a passport from a certain country without revealing anything else about your identity (as the passports are digitally signed by their issuing authorities using publicly-known keys). You could then have, for example, an online forum or poll that only allows participation of people with a certain credential, yet the forum or poll operator never learns the offline identities of the members or participants. There are some logistical issues with this depending on the purpose for which the verifier is relying on the statement, including what happens if a prover submits the same credential twice, and what happens if a prover borrows a credential from someone else. In some settings this is OK or unlikely, while in other settings it might effectively blow up the whole application!