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Multi-factor authentication (MFA) is a method of confirming a user's claimed identity in which a user is granted access only after successfully presenting 2 or more pieces of evidence (or factors) to an authentication mechanism: knowledge (something they and only they know), possession (something they and only they have), and inherence (something they and only they are).
Two-factor authentication (also known as 2FA) is a type (subset) of multi-factor authentication. It is a method of confirming a user's claimed identity by utilizing a combination of two different factors: 1) something they know, 2) something they have, or 3) something they are.
A good example of two-factor authentication is the withdrawing of money from a ATM; only the correct combination of a bank card (something that the user possesses) and a PIN (personal identification number, something that the user knows) allows the transaction to be carried out.
Two-step verification or two-step authentication is a method of confirming a user's claimed identity by utilizing something they know (password) and a second factor other than something they have or something they are. An example of a second step is the user repeating back something that was sent to them through an out-of-band mechanism. Or the second step might be a 6 digit number generated by an app that is common to the user and the authentication system. 
The use of multiple authentication factors to prove one's identity is based on the premise that an unauthorized actor is unlikely to be able to supply the factors required for access. If, in an authentication attempt, at least one of the components is missing or supplied incorrectly, the user's identity is not established with sufficient certainty and access to the asset (e.g., a building, or data) being protected by multi-factor authentication then remains blocked. The authentication factors of a multi-factor authentication scheme may include:
Knowledge factors are the most commonly used form of authentication. In this form, the user is required to prove knowledge of a secret in order to authenticate.
A password is a secret word or string of characters that is used for user authentication. This is the most commonly used mechanism of authentication. Many multi-factor authentication techniques rely on password as one factor of authentication. Variations include both longer ones formed from multiple words (a passphrase) and the shorter, purely numeric, personal identification number (PIN) commonly used for ATM access. Traditionally, passwords are expected to be memorized.
Many secret questions such as "Where were you born?" are poor examples of a knowledge factor because they may be known to a wide group of people, or be able to be researched.
Possession factors ("something the user and only the user has") have been used for authentication for centuries, in the form of a key to a lock. The basic principle is that the key embodies a secret which is shared between the lock and the key, and the same principle underlies possession factor authentication in computer systems. A security token is an example of a possession factor.
Disconnected tokens have no connections to the client computer. They typically use a built-in screen to display the generated authentication data, which is manually typed in by the user.
Connected tokens are devices that are physically connected to the computer to be used. Those devices transmit data automatically. There are a number of different types, including card readers, wireless tags and USB tokens.
These are factors associated with the user, and are usually bio-metric methods, including fingerprint readers, retina scanners or voice recognition.
Mobile-phone apps, SMS, and direct push notifications, etc., are not considered "something you have" and thus are not considered in the multi-factor/two-factor equation. Mobile-phone two-step authentication is more secure than single-factor password protection but suffers some security concerns. Phones can be cloned and apps can run on several phones; cell-phone maintenance personnel can read SMS texts. Not least, cell phones can be compromised in general, meaning the phone is no longer something you and only you have.
The major drawback of authentication including something that the user possesses is that the user must carry around the physical token (the USB stick, the bank card, the key or similar), practically at all times. Loss and theft are a risk. Many organizations forbid carrying USB and electronic devices in or out of premises owing to malware and data theft-risks, and most important machines do not have USB ports for the same reason. Physical tokens usually do not scale, typically requiring a new token for each new account and system. Procuring and subsequently replacing tokens of this kind involves costs. In addition, there are inherent conflicts and unavoidable trade-offs between usability and security.
Mobile-phone two-step authentication involving devices such as mobile phones and smartphones was developed[by whom?] to provide an alternative method that would avoid such issues. To authenticate themselves, people can use their personal access-codes to the device (i.e. something that only the individual user knows) plus a one-time-valid, dynamic passcode, typically consisting of 4 to 6 digits. The passcode can be sent to their mobile device by SMS or push notification or can be generated by a one-time-passcode-generator (app). In all three cases, the advantage of using a mobile phone is that there is no need for an additional dedicated token, as users tend to carry their mobile devices around at all times.
As of 2018[update] SMS is the most broadly-adopted multi-factor authentication method for consumer-facing accounts, though in 2016 and 2017 respectively, both Google and Apple started offering user two-step authentication with push notification as an alternative method, although this method is not out-of-band. Notwithstanding the popularity of SMS verification, the United States NIST has condemned it as a form of authentication and many[quantify] security advocates have publicly criticized it. As such, SMS verification is no longer considered[by whom?] verification.
Advantages of mobile-phone two-step authentication
Disadvantages of mobile-phone two-step authentication
Advances in research of two-factor authentication for mobile devices consider different methods in which a second factor can be implemented while not posing a hindrance to the user. With the continued use and improvements in the accuracy of mobile hardware such as GPS, microphone, and gyro/acceleromoter, the ability to use them as a second factor of authentication is becoming more trustworthy. For example, by recording the ambient noise of the user's location from a mobile device and comparing it with the recording of the ambient noise from the computer in the same room in which the user is trying to authenticate, one is able to have an effective second factor of authentication. This also reduces the amount of time and effort needed to complete the process.
The Payment Card Industry (PCI) Data Security Standard, requirement 8.3, requires the use of MFA for all remote network access that originates from outside the network to a Card Data Environment (CDE). Beginning with PCI-DSS version 3.2, the use of MFA is required for all administrative access to the CDE, even if the user is within a trusted network.
Details for authentication in the USA are defined with the Homeland Security Presidential Directive 12 (HSPD-12).
Existing authentication methodologies involve the explained three types of basic "factors". Authentication methods that depend on more than one factor are more difficult to compromise than single-factor methods.
IT regulatory standards for access to Federal Government systems require the use of multi-factor authentication to access sensitive IT resources, for example when logging on to network devices to perform administrative tasks and when accessing any computer using a privileged login.
In 2005, the United States' Federal Financial Institutions Examination Council issued guidance for financial institutions recommending financial institutions conduct risk-based assessments, evaluate customer awareness programs, and develop security measures to reliably authenticate customers remotely accessing online financial services, officially recommending the use of authentication methods that depend on more than one factor (specifically, what a user knows, has, and is) to determine the user's identity. In response to the publication, numerous authentication vendors began improperly promoting challenge-questions, secret images, and other knowledge-based methods as "multi-factor" authentication. Due to the resulting confusion and widespread adoption of such methods, on August 15, 2006, the FFIEC published supplemental guidelines—which states that by definition, a "true" multi-factor authentication system must use distinct instances of the three factors of authentication it had defined, and not just use multiple instances of a single factor.
According to proponents, multi-factor authentication could drastically reduce the incidence of online identity theft and other online fraud, because the victim's password would no longer be enough to give a thief permanent access to their information. However, many multi-factor authentication approaches remain vulnerable to phishing, man-in-the-browser, and man-in-the-middle attacks.
Multi-factor authentication may be ineffective against modern threats, like ATM skimming, phishing, and malware.
In May 2017 O2 Telefónica, a German mobile service provider, confirmed that cybercriminals had exploited SS7 vulnerabilities to bypass SMS based two-step authentication to do unauthorized withdrawals from users bank accounts. The criminals first infected the account holder's computers in an attempt to steal their bank account credentials and phone numbers. Then the attackers purchased access to a fake telecom provider and set-up a redirect for the victim's phone number to a handset controlled by them. Finally the attackers logged into victims' online bank accounts and requested for the money on the accounts to be withdrawn to accounts owned by the criminals. SMS passcodes were routed to phone numbers controlled by the attackers and the criminals transferred the money out.
Many multi-factor authentication products require users to deploy client software to make multi-factor authentication systems work. Some vendors have created separate installation packages for network login, Web access credentials and VPN connection credentials. For such products, there may be four or five different software packages to push down to the client PC in order to make use of the token or smart card. This translates to four or five packages on which version control has to be performed, and four or five packages to check for conflicts with business applications. If access can be operated using web pages, it is possible to limit the overheads outlined above to a single application. With other multi-factor authentication solutions, such as "virtual" tokens and some hardware token products, no software must be installed by end users.
There are drawbacks to multi-factor authentication that are keeping many approaches from becoming widespread. Some consumers have difficulty keeping track of a hardware token or USB plug. Many consumers do not have the technical skills needed to install a client-side software certificate by themselves. Generally, multi-factor solutions require additional investment for implementation and costs for maintenance. Most hardware token-based systems are proprietary and some vendors charge an annual fee per user. Deployment of hardware tokens is logistically challenging. Hardware tokens may get damaged or lost and issuance of tokens in large industries such as banking or even within large enterprises needs to be managed. In addition to deployment costs, multi-factor authentication often carries significant additional support costs. A 2008 survey of over 120 U.S. credit unions by the Credit Union Journal reported on the support costs associated with two-factor authentication. In their report, software certificates and software toolbar approaches were reported to have the highest support costs.
Several popular web services employ multi-factor authentication, usually as an optional feature that is deactivated by default.