OATH is an organization that specifies two open authentication standards: TOTP and HOTP.
To authenticate using TOTP, the user enters a 6-8 digit code that changes every 30 seconds. It can look like this:
The code is generated using
HMAC(sharedSecret, timestamp), where timestamp changes every 30 seconds. The shared secret is often provisioned as a QR-code or preprogrammed into a hardware token.
The website twofactorauth.org lists common websites that supports TOTP.
HOTP works just like TOTP, except that an authentication counter is used instead of a timestamp. The advantage of this is that HOTP devices requires no clock.
HOTP is susceptible to losing counter sync. That is, if the user generates an OTP without authenticating with it, the device counter will no longer match the server counter. This can be mitigated on the server by testing several subequent counter values. This can not happen with Yubico OTP since its counter is encrypted (as opposed to hashed).
When using OATH with a YubiKey, the shared secrets are stored and processed in the YubiKey’s secure element. This has two advantages over storing secrets on a phone:
The secrets always stay within the YubiKey. A phone can get stolen, sold, infected by malware, have its storage read by a connected computer, etc.
You can display OATH codes on more than one phone or computer. If your phone runs out of battery, you can get a code using a friend’s phone or your computer.
A YubiKey can emit a HOTP code when its button is pressed. This is configured using Yubikey Personalization GUI. For TOTP you need an application that can read OATH codes from YubiKeys, since YubiKeys does not have an internal clock.