Enabling two-factor authentication is one of the best ways to improve the security of your online accounts. Most websites that offer two-factor authentication have opted to use either the Time-based One-time Password Algorithm (TOTP) or HMAC-based One-time Password Algorithm (HOTP), which are used in conjunction with an application such as Authy or Google Authenticator to generate temporary one-time passwords.
Twitter, however, decided to go its own route and tie two-factor authentication to its Android and iOS apps. This had two limitations. First, it required users to install the official Twitter application, which was a waste of space for those who prefer third-party applications or the web interface. Second, it required a unique phone number so you could only enable two-factor authentication for one account. Recently, without telling anybody, Twitter decided to enable standard application-based two-factor authentication.
However, Twitter only solved one of the two above mentioned limitations. A unique phone number still needs to be tied to an account to enable two-factor authentication, so this change doesn’t allow you to enable two-factor authentication on multiple accounts unless you also have multiple phone numbers. But it does let you use a standard two-factor authentication app such as Authy or Google Authenticator.