Bulletproofs range proof of value provided from trusted third party I'm really interested in range proofs, and bulletproof seems to be the most effective range proof.

I saw an example of usage of bulletproofs range proof: You can generate a proof that your age is greater than 18 without revealing your exact age.

That sounds cool, but what I don't understand is how I can prove that my age is verified. Say I'm 12, but while I generate a proof, I pretend that I'm 20 and generate a proof for 20 years. Clearly, I need a third trusted party to verify that my age is really greater than 18. How it can be done?

Maybe I should generate a proof, and then a trusted third party - for example my government - signs that it to make it a valid proof? Is there a better approach?
I think the example that you saw was just a simple example of how a range proof would work in theory.

Range proofs could be used for encrypting transactions in cryptocurrencies, specifically the amount of the transaction.

A very simplified mathematical notation would look like this:

$\text{E}(a) - \text{E}(b) = 0$

where $a$ is the amount of coins you "spend" and $b$ is the amount the receiver gets. $\text{E}$ indicates that the values are encrypted. This simple calculation here only indicates, that $a$ and $b$ are equal, so you didn't somehow create coins out of thin air.

Bulletproofs are a new addition to range proofs, they basically prove the same thing but bulletproofs can prove something with less overhead than a normal range proof, which again makes them desirable for cryptocurrencies. You can find more information in this PDF of the published paper.



Now to your actual question:

You can't really prove that your age is a certain number without a trusted party. Range proofs (and bulletproofs) just prove that the encrypted input is equal to the encrypted output.

You technically could do this with your government as you suggested. You would need to create a commitment. The commitment comes from anyone who is trusted by the verifier. So to prove your age, this value would have to come from a government issued ID.