## Multifactor Authentication

Authentication can be accomplished with one factor, two factors, or multiple factors. Which one is the weakest level of authentication and which is the most secure and why? When would a more secure system be required? Be able to explain these multifactor authentication methods: password protection, token presence, voice biometrics, facial recognition, ocular-based methodology, hand geometry, vein recognition, fingerprint scanner, thermal image recognition, and geographical location. What are some challenges of multiple factor authentication when using biometrics? There is a lot of interesting information covered in this article that you do not need to memorize, but that you should be aware of.

### 4.3. Proposed MFA Solution for V2X Applications

#### 4.4.3. Evaluation

In this work, we consider a more general case of the probabilistic decision-making methodology, while a combination of the measurement results for the individual sensors is made similarly to the previous works by using the Bayes estimator. Since the outcomes of measurements have a probabilistic nature, the decision function is suitable for the maximum a posteriori probability solution.

In more detail, the decision function may be described as follows. At the input, it requires a conditional probability of the measured value from each sensor $P\left(z_{i} \mid H_{0}\right)$ and $P\left(z_{i} \mid H_{1}\right)$ together with a priori probabilities of the hypotheses $P\left(H_{0}\right)$ and $P\left(H_{1}\right)$. The latter values could be a part of the company's risk policy as they determine the degree of confidence for specific users. Then, the decision function evaluates the a posteriori probability of the hypothesis $P\left(H_{1} \mid Z\right)$ and validates that the corresponding probability is higher than a given threshold $P_{T H}$

The measurement-related conditional probabilities can be considered as independent random variables; hence, the general conditional probability is as follows:

$P\left(Z \mid H_{J}\right)=\prod_{z_{i} \in Z} P\left(z_{i} \mid H_{J}\right), J \in\{0 ; 1\}$

Further, the total probability $P(Z)$ is calculated as

$P(Z)=\prod_{z_{1} \in Z} P\left(z_{i} \mid H_{0}\right) P\left(H_{0}\right)+\prod_{z_{1} \in Z} P\left(z_{i} \mid H_{1}\right) P\left(H_{1}\right)$

where $P\left(z_{i} \mid H_{J}\right), J \in\{0 ; 1\}$ are known from the sensor characteristics, while $P\left(H_{0}\right)$ and $P\left(H_{1}\right)$ are a priori probabilities of the hypotheses (a part of the company's risk policy).

Based on the obtained results, the posterior probability for each hypothesis $H_{J}, J \in\{0 ; 1\}$ can be produced as

$P\left(H_{1} \mid Z\right)=\frac{\prod_{z_{1} \in Z} P\left(z_{i} \mid H_{1}\right) P\left(H_{1}\right)}{P(Z)}$

For a comprehensive decision over the entire set of sensors, the following rule applies

$P\left(H_{1} \mid Z\right)>P_{T H} \Rightarrow\{\text {Accept}\}, \text { else }\{\text {Reject}\}$

As a result, the decision may be correct or may lead to an error. The FAR and FRR values could then be utilized for selecting the appropriate threshold $P_{T H}$ based on all of the involved sensors.