So in this video, let's do an overview of information entropy and to find some of the variables that we will use. So information entropy and we will use capital N to denote information entropy. Information entropy depends on two factors. The first one is the number of possible outcomes, and we will use capital N to denote that. The second factor is the probability distribution of the outcomes, and we will use Pᵢ to denote that, where I is the index of the outcomes. Going back to the previous example with the coin flipping, coin flipping has two possible outcomes: head or tail. Because it has two possible outcomes, capital N=2. Now because it's an unbiased coin, P₁ which is equal to the probability of head is equal to 1/2 P₂ to the second event corresponds to that event of tail, and this is also 1/2. We would also want the information entropy so that the entropy increases with the number of independent events. So H increases linearly with the number of independent events. Again revisiting the coin flipping example, so we want information entropy H to be proportional with the number of coin flips. So in the next couple of videos and in the rest of the lesson, we will look at how the information entropy depends on the number of possible outcomes N and the probability distribution of the outcomes Pᵢs. Before we do that in this lesson, let's look at the applications of information entropy. The applications of information entropy actually expands beyond that of cryptography. One popular use of information entropy is an image processing. For example for data compression, information entropy gives you the lowest number of bits, the smallest number of bits that are required for data compression in a lossless manner. Another popular use of information entropy is for anomaly detection. For example, if a node receives a packet and if the packet is displaying unusually large entropy, then it can contain malicious software like a hidden software, such as a malware. Another popular use of information entropy is in traffic analysis. If there is a high entropy in traffic analysis then that can be used for anomaly detection. Also, information entropy can be used to quantify the key strength in cryptography, and our focus in this course is this last application. Again, the attacker does not know the value of the key and the key looks random to the attacker. The more random it looks to the attacker, the higher the security strength.