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I recently got a FIDO U2F key (AKA a Yubikey). I currently only use it across a range of services, but could this be a security risk in any way?

For example, if I use my U2F key to authenticate on a shady and/or insecure and/or malicious website, could my U2F key somehow be compromised?

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No, you are safe

Even if you entered it inside a malicious computer, your key could not be compromised. It uses the same security as a credit card; meaning a smart card. This smart card contains a private key that is not disclosed unless you physically open the smart card. This is the reason why credit cards with a smart card are so much better than credit cards with a magnetic stripe. The stripe can be copied just by scanning it while it's impossible to copy the smart card just by using it.

How it works?

It's basically a challenge-response mechanism. The smart card has a private key and it's the only entity that know this private key. When you authenticate, you receive a challenge; usually a random number or something like that. Then, when you press the gold symbol on your usb, the challenge is sent to the smart card that encrypt it using it's private key and then return the encrypted challenge. This encrypted challenge is then send back to the server which contain all the public keys matching the private keys that are stored on the usb. The server then decrypt the encrypted challenge with the right public key and verify that it matches the challenge.

About phishing

Phishing protection in U2F is top-notch it seems. See this excellent answer :

How secure are the FIDO U2F tokens

Still, beware of compromised computers

Even if your usb key cannot be compromised, you, as a user, are still vulnerable if you use a compromised computer. On a compromised computer, you cannot trust anything that you see. Even if everything looks good, url in browser, certificate, etc. You just cannot trust anything. I could present you a login page but I would in fact be using that login information to change your password for that site.

Conclusion

Your usb key is safe. You it's another story. At some point, you are the only one that can save you from using it on a machine infected with virus.

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    U2F is fortunately credentials phishing safe - it is tied to your browser's SSL session with the server, so replays of the challenge will always fail when repeated within another SSL session, so your attacker will be unable to either get an answer at all (pretends to be the same server but sending a challenge not linked to the session) or will be unable to use the answer to authenticate (pretends to be a similarly named server). – Natanael Oct 30 '15 at 18:19

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