Multifactor Authentication
4.3. Proposed MFA Solution for V2X Applications
4.3.1. Factor Mismatch
Assuming that the number of factors in our system is 
the system secret 
can be represented in a simplified way as a group of
![S \leftarrow\left[\begin{array}{llll} F_{1} & F_{2} & F_{3} & F_{4} \end{array}\right]](https://learn.saylor.org/filter/tex/pix.php/6a58626db91026d395a555e3b68e9065.svg "S \leftarrow\left[\begin{array}{llll} F_{1} & F_{2} & F_{3} & F_{4} \end{array}\right]")
Here, if any of 
are modified-the secret recovery mechanism would fail. An improvement to this algorithm is delivered by providing separate system solutions 
for a lower number of factors collected. Basically, for 
the number of possible combinations of factors with one missing is equal to four, as follows
![\begin{array}{l} \overline{S_{1}} \leftarrow\left[\begin{array}{lll} F_{1} & F_{2} & F_{3} \end{array}\right] \\ \overline{S_{2}} \leftarrow\left[\begin{array}{lll} F_{1} & F_{3} & F_{4} \end{array}\right] \\ \overline{S_{3}} \leftarrow\left[\begin{array}{lll}
F_{1} & F_{2} & F_{4} \end{array}\right] \\ \overline{S_{3}} \leftarrow\left[\begin{array}{lll} F_{2} & F_{3} & F_{4} \end{array}\right] \end{array}](https://learn.saylor.org/filter/tex/pix.php/6b6b562b3555be1c5d319ed0a8406aa6.svg "\begin{array}{l} \overline{S_{1}} \leftarrow\left[\begin{array}{lll} F_{1} & F_{2} & F_{3} \end{array}\right] \\ \overline{S_{2}} \leftarrow\left[\begin{array}{lll} F_{1} & F_{3} & F_{4} \end{array}\right] \\ \overline{S_{3}} \leftarrow\left[\begin{array}{lll}
F_{1} & F_{2} & F_{4} \end{array}\right] \\ \overline{S_{3}} \leftarrow\left[\begin{array}{lll} F_{2} & F_{3} & F_{4} \end{array}\right] \end{array}")
The device may thus grant access based on a predefined risk function policy. As the second benefit, it can inform the user (or the authority) that a particular factor 
has to be updated based on the failed combination. Indeed, this
modification brings only marginal transmission overheads, but, on the other hand, enables higher flexibility in authentication and missing factor validation.