The system is OATH/TOTP 6 digit 30 second authenticator codes, set up by QR code. We have TRNGs we use for seeds that are 320 bits long.
On the accounts system we have gone for some flexibility. Option to SMS codes instead, but configurable, and configurable trust level to decide when to ask for a code. It is also a seed we hold so staff can ask for a code to check you are who you say you are (a useful feature on phone, irc, web chart, etc).
On the control pages (and the internal staff A&A systems) we have gone for encrypted TOTP seed and no SMS option. The seed is binary data, XOR'd with a stretched Argon2 hash of the password and a seed set for that purpose (i.e. the seed also has a random seed for its encryption), so no way to check you have right answer other than doing the Argon2 hash and checking an authenticator code, so not a shortcut to crack the password hash.
This means that on control pages the password change needs old password if you have 2FA set up, and expects an authenticator code as well. Some staff can override, but they will also look at account settings as part of deciding you are you!
I think, overall, we are doing well. Hashed passwords and 2FA with encrypted 2FA seeds.
There is always more to do, and more security to add, but this is an ongoing process.
Customers can now set up 2FA on A&A accounts and control pages if they wish - have fun.
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