So we're going to focus on symmetric key encryption. So in our general model, we encrypt plain text with a key. We get ciphertext. We send the ciphertext to user B and they decrypt using a key to get the original plain text. Metric key encryption, both A and B, use the same key. We call a shared secret key. It's shared amongst the two users and it must be secret. Only those two users must know that key. If anyone else discovers the key, they can also decrypt. So with symmetric key encryption for confidentiality, we use some encryption algorithm. And we're going to talk about some of those algorithms shortly. We take the plain text and we apply the algorithm on that plain text. The other input is the shared secret key and we get ciphertext's output. And that's what we send across our network or that's what we save on the disk. We want to encrypt a file. And the receiver, you want to decrypt the file or decrypt the message that you received. You use the same key and you apply a decryption algorithm on that ciphertext and you'll get the original plain text, the exact same message that the source started with out. That's if the cipher or the algorithms are designed correctly, we must get the original plain text out. An attacker, assuming that they know the algorithm used, so they know what you used to encrypt and decrypt, what the steps you used, they know the ciphertext, they can intercept the ciphertext, then their goal then is to find the plain text or the key. If they find the plain text, then we don't have the service of confidentiality. We've defeated the service from the attacker's perspective. If we find the key, also we can easily find the plain text. If somehow I can find the key k, if I'm the attacker, then I can easily decrypt because I know the algorithm, I know the ciphertext and the key, then I simply apply the decryption algorithm on the ciphertext and I get the plain text. So the attacker aims to find the key or the plain text. They are given the ciphertext and the algorithms. They are not given the key. We assume they don't have it. For this to work, for encryption to be used for confidentiality, we need strong algorithms. So what we're going to do is work through starting from some very old and weak algorithms, but look at the principles they use to build the encryption algorithms and arrive eventually at some of the common techniques used today, the common algorithms. We need a strong algorithm so that the attacker, even if they have the ciphertext, they cannot work backwards and find the plain text or find the key. And in fact, in practice, even if the attacker has the ciphertext and some old plain text, they know in the past you encrypted this plain text and you got this ciphertext. They have a pair of plain text ciphertext, but they don't have the key. It still should be hard for the attacker to find the plain text or key. If it's easy, then we say this is not a strong algorithm. And the other thing that's important, because we have shared secret keys, the way in which that key is shared is important. How does B get the key K from A? Somehow we have to give B the key, or the way in which we distribute that key is very important. It must be done in a secure manner. And we'll talk about that with some examples as we go through. So we assume for now that the key is distributed in a secure manner. So we said that what are the encryption and decryption algorithms? Well, they use two main operations. The algorithms use two main steps, substitution and transposition. So I'll use some of the old ciphers to demonstrate those steps. Substitution ciphers and transposition ciphers. So we'll go through some examples. And then after going through some examples, we'll introduce some different attacks. We'll jump through to the substitution technique, starting from one of the very first known ciphers. So how do we encrypt? Remember substitution? We take one element of our plain text and replace it with another possible value. Well, what are our elements? What are our possible values? In our examples and the classical ciphers that we're going to go through, they are operating, we assume, on the English alphabet. So the possible values of the plain text to keep our examples simple will normally be A to Z, 26 possible values, lower case only. So sometimes I'll write answers or ciphertext in uppercase just to distinguish between plain text and ciphertext, but the set of possible letters are only the lower case letters that we are operating. So we assume the plain text is made up just of the 26 English lower case letters. We could extend the algorithms to operate on different character sets. We can include uppercase, lower case, we could add punctuation, or we could use a different language. The same principles will apply. So substitution ciphers take one letter in the plain text and replace that letter with another possible letter of the 26 possible values. Now we can also extend this to operate on a binary form. That is, it doesn't have to be just on English letters. We can think of a letter using the ASCII encoding maps to a sequence of bits so we could convert to binary if needed. Let's start with English language examples. The first cipher we'll start with is the Caesar cipher named after Julius Caesar, a Roman emperor or general. It's about 2,000 years old, so this is a very old cipher and supposedly was used by Julius Caesar to send secret messages to other people. And it's a very simple cipher. The rule is take your plain text letter, so you have a plain text message you want to send, a set of letters. For each letter you take it and you replace it with the letter three positions to the right in the alphabet. So if your first letter of your plain text is A, then the output cipher text letter will be D. It's three positions, one, two, three to the right of A. If the second letter of your plain text is T, then the output cipher text, the second letter, will be three positions to the right will be W and this just shows the direct output in two lines. And if you get a letter Z as input, then three positions to the right we wrap around back to the start. So three positions to the right of Z is C. So we move one, two, three. So we wrap around so we can handle any possible letter. So that's the algorithm for encryption. It's a substitution. We substitute one letter of our plain text with one of the other 26 letters, which one will define by the rule the one which is three positions to the right in your alphabet. Now this could be extended to other character sets quite easily. It doesn't have to be 26 letters. We could have uppercase and lowercase. We could have a different language and so on. Let's have an example. What will we start with? The cipher text that I'll give you is... Let's start with... That's a D. There's the cipher text. And so you're the attacker in this case. You've intercepted a message sent from A to B and this is what you've intercepted. P, R, Q, G, D, B. And we assume the attacker knows the algorithm that the two users are using. Some other way that they've realized are they're using the cipher... Caesar cipher as the algorithm. So in all our analysis and attacks, we'll assume that the attacker does know the algorithm. In practice, how could they know the algorithm that two people are using? Usually the algorithms used for encryption are standardized. So the algorithm that your computer uses to encrypt files, it maybe comes as part of the operating system or it's a standard for the network protocol. So it's known in advance what algorithms are used for encryption. So it's not hard for the attacker to find out which algorithm you're using. So it's not kept secret. So we know it was performed using the Caesar cipher. Find the plain text. You're the attacker. What's the plain text? The cipher is the Caesar cipher in this case. What's the plain text? Calculate it for yourself. Decrypt. And if you look on the lecture slide, you'll see that the amount of letters help you quickly work backwards to find out what the original plain text was. What's the first letter of the plain text? Z. Now, in all of the examples we'll go through, the plain text will make sense. And we'll see that's one way that will perform a tax. If you get a plain text message in the exam or a quiz answer that doesn't make sense to you, it's usually not English, then you've done something wrong. So make sure you get a plain text that makes sense as a hint. Monday today, yes, but what's the plain text? That's the plain text. Right, I think you'll find that if you go backwards, you get M as the first letter. Why? Decryption. No, decryption is the opposite process of encryption. When we encrypted, we take, say, the letter M, if that was our plain text letter, and we'll get the cipher text letter P. When we decrypt, we must get the original plain text back. So the decryption algorithm is not the same as the encryption algorithm. It should do the opposite. So if we have the cipher text letter P to decrypt with the Caesar cipher, we move the left three positions. And we should get the original plain text letter M. Encrypt, move to the right three positions. To get the original plain text, you must move to the left three positions. So we have the cipher text letter P. We move to the left three positions. We get M. The second cipher text letter was Q, I think. No. What was the second cipher text letter? I'll have a look. R. So the second letter was R. We move to the left three positions and we get O. And then we had Q. Where's Q? To the left, one, two, three, we get N. G. YG. Have I written down the wrong thing? D. Ah, G, sorry, not Q. G goes back to D. P becomes M. R goes to N. O, Q goes to N. And we get our plain text. So we shift to the left. So when you look at decryption algorithms, we'll often only mention the encryption algorithm. The decryption should be the opposite such that we get the original plain text out. This Caesar cipher takes plain text, shifts to the right three positions to get the cipher text. We said in our general model that we, just jumping back to our picture, our ciphers take plain text, encrypt to get cipher text, but we said that there's a key. In this case, we didn't mention a key with our Caesar cipher. But if we generalize that Caesar cipher, which said shift three positions to the right, we could say, well, shift N positions to the right. Where the number of positions we shift to the right could be a parameter that the users choose, and that can become the key. So a generalized Caesar cipher shift K positions to the right to encrypt where K is the key. And to decrypt, shift K positions to the left. So we can think, in this case, the key for this example is three, in that we shifted three positions to the right. And with our letters, how many letters do we have? 26 letters, we'll usually talk about them if we can write this as an algorithm. We can think of them as numbers from zero to 25. A is zero, B is one, is two, D is our key three. I'll just list them. So what we'll often do when we're talking about ciphers to think of them in a numerical form, we can map those letters to numbers, starting from zero. So when I say the key is three, sometimes we'll say the key is D, the letter D. Because D is the fourth letter, if we start at zero, is key number three. So the key may be given either as a number or a letter. And that will become useful when we talk about some other ciphers that are built on Caesar cipher. So there's our very first cipher, very simple, and it substitutes one letter in plaintext with one of the other 26 letters, which one was defined by the key and this algorithm, shift to the right. Unfortunately, you or most of you found the plaintext without knowing the key. In fact, the key is built into this algorithm, three positions. Let's consider another example when we have a different value of the key. A different example where the cipher text, I'll give you another one. It's still using the Caesar cipher, but I'm not going to give you the key in this case. Find the plaintext. So in this general Caesar cipher, the key can be one of 26 possible values. Instead of shifting three positions to the right, I shifted k positions to the right where you don't know what k is. So what I did is I took my plaintext, shifted k positions to the right, and I got ABMDM. You don't know what k is. Because you're the attacker, you don't know the key. What's the plaintext? Or more importantly, what approach would you use to find the plaintext? Brute force. What does brute force mean? Try all possible keys. So if we don't know the key, I'm the attacker, I know the ciphertext, I know it was a Caesar cipher, but I don't know the number of positions shifted to the right, well let's try them all and see if one of them gives us a plaintext message that makes sense. Because we expect that the plaintext message should make sense. And to be English. So let's try some of them. As the attacker, let's say, let's go in order, the key of zero, which corresponds to the letter A. If we label the letters A is zero, B is one and so on, the key of zero means a key of A. And what do we do? We decrypt and we get plaintext, I'll write here, plaintext P, if we decrypt with key zero, what do we get? Decrypt, move K positions to the left. Move zero positions to the left, we get the exact same message. Does this message make sense? Is it an English word or phrase that you recognise? Probably not. So this is the first thing, that the attacker needs some way in this attack to recognise does this potential plaintext make sense? Is it correct or not? And we'll use the structure of the intended message, or say the language, to do that detection in this case. I don't know of any words called Abdomenum. And I can't see if it makes a phrase, so I'm going to assume that this doesn't make any sense. That is, I'm going to assume that this is the wrong key, because it gives me a plaintext that doesn't make sense. So as the attacker, I now try a different key. Let's go in order. K of one or equivalent to B. Just remember. That is, I'll assume that the user encrypted by shifting one position to the right, therefore to decrypt, I'll move one position to the left. What's the letter before to the left of A? That is, the letter to the left of A by one position is in fact Z. So the plaintext will be Z. And to the left of B is A, and so on, L, C, L. So I try this key as the attacker, and I get this plaintext. Does it make sense? No, it doesn't look obvious to me. So I try another key. And we keep going. What keys can I try in worst case? 26 letters. And the way that we... Caesar Cypher works is we move K positions to the right to encrypt, or K positions to the left to decrypt. If we... We saw if we move zero positions, then we get the same input as output. If we move 26 positions, it'd be the same. It would wrap around. 26 to the positions to the right of A is the same as zero positions to the right of A. We wrap around. If we move 25 positions, then A becomes Z. But if we move 26 positions, then A becomes A, which is the same as moving zero positions. If we move 52 positions to the right, it's the same as moving zero or 26 positions. So in fact, there are only 26 possible variations that we can have. There are 26 possible keys, zero to 25. So the attacker in this brute force attack, in the worst case, needs to try all possible keys. So one way we'd go through is we keep trying, and I'm not going to write them down. And we'd find some plain text and whatever it was. I think you'll find that that doesn't make sense. And you keep trying. And anyone know the key? Eight. Eight. We get to eight. Let's see what happens, which is the letter I in our alphabet. The plain text, what do we get with eight? First letter? Well, A lifted... The letter A shifted eight positions to the left, brings us to S. The letter B shifted eight positions to the left, will bring you to T. M, eight positions to the left. One, two, three, four, five, six, seven, eight. Gives you E. And then you may see the plain text. The letter D, eight positions to the left, will go to V. And M, mapped to E. So another M, also mapped to E. Now you guess, ah, this is a message or this is something that makes sense. It's the lecturer's name. So that's probably the correct plain text. And indeed it was. So this is the steps of a brute force attack that a hacker can do. To try and find the plain text and the key, they can try all possible keys. Well, in this case, we only needed to try nine before we got something that matched. We could keep trying those just to confirm. You could try all 26. But what you do, you'll see, I think, none of them make sense. Now, this becomes more accurate for the attacker to identify what makes sense as the message gets longer. The longer the message, the less chance of getting two that make sense when you try different keys. And most plain text messages we're trying to decrypt are not just five characters, usually they're much longer. In this case, we took nine attempts to find the correct plain text. The attack, we had to decrypt nine times and then we got something we recognized. In this example, the actual attempts, we had nine decrypts. That is, the attacker decrypted the ciphertext nine times before they got something they recognized. What's the best case from the attacker's perspective? Let's say it doesn't go in order or it just randomly guesses keys. What's the best case it could achieve? Well, the best case I choose the key first time, the correct key. I randomly choose a key and it is indeed the correct key. So the best case is one decrypt. It takes me one attempt. What's the worst case? 26, I need to try all possible keys. This is from the attacker's perspective. What's the average number of attempts? If we can assume that for a different plain text so maybe a different key was used. So we need to do this many times and we need to guess the key. On average, how many attempts would it take the attacker to guess the key? The correct key. Sometimes we'll get the best case. Sometimes we'll get the worst case. Sometimes we'll take two attempts. Sometimes 25 attempts. On average, how many attempts would it take to get the key? We've got 26 to choose from. Take us... Sometimes we get one attempt. Sometimes we get two attempts. Sometimes it takes three attempts. Sometimes it takes 25 attempts or 26 attempts. On average, it would take half of 26 or 13 attempts. If we want to guess a number from all we're doing here is guessing the key. We know it's from 0 to 25 or 26 possible values. If you randomly guess, on average, it would take you 13 attempts to get the right one. So we can now talk a little bit about the performance of this brute force attack. From the attacker's perspective... Right, sometimes it would be easy. Sometimes it would take... The worst case, it would take all possible keys to try. On average, it would take half of the possible keys. The number of possible keys, 26 divided by 2. Alright, in this particular case, it took 9, better than the average case. But if we had another plain text and we tried again, it may take more than 13. So, in general, for a brute force attack, a brute force attack in the worst case, try every possible key. On the average case, try half of the keys. Here, the 26, we try 13. And it applies to other cyphers as well. How do we stop the attacker from doing a brute force attack? Or how do we make it hard for them to do a brute force attack? Assuming I give you a computer, so you don't have to do it on paper even to calculate, I give you some software to decrypt with the Caesar Cypher. So if it does one decryption very fast, then how can I prevent or stop you from doing a brute force attack? On the Caesar Cypher, is it possible to stop a brute force attack? No, 26 attempts with the computer is going to take less than a second every time. So this key problem with the Caesar Cypher is the number of possible keys. There's only 26 possible keys. So if we have more possible keys, a thousand possible keys, a million possible keys or more, then maybe that leads to more attempts that the attacker needs to take. So the number of possible keys is going to be an important design parameter of our cyphers. We need to have a key space such that a brute force attack is not possible, or it will take too long. We'll return to that, what is a good size after we go through with a few more examples of cyphers. I'll give you another example of Caesar Cypher, but with a computer, so we save some time.  I have a Cypher text message. There it is. I just squeeze it on the screen. This is the Cypher text. I've intercepted. I'm the attacker. I know the Caesar Cypher was used, but I don't know the key. Then what I would do as the attacker is to decrypt that Cypher text message with every possible key. I can try the keys in order, or I can just try them randomly. Assuming the users, when they chose a key, they chose one randomly, it's sufficient that I choose either randomly or in order. So I will not do it on paper. I just have some software that will do it for us. That's the Cypher text. I just have some simple software that will use the Caesar Cypher and decrypt that long Cypher text. So that was the Cypher text. Don't be too concerned about how the software works. I decrypted the Cypher text using the key 0. Now the key 0 is not a good one to use if you encrypt, because this plain text and the Cypher text will be the same. So it's a possible key, but not a smart one to use if you encrypt, because nothing changes. But I don't make any sense of this plain text, so as the attacker I'll try the next key. Key 1. Does it make sense? And I keep trying keys. And I keep going until I get a message that makes sense. And I'll not do them here, but I've done them before, if I can bring it up. Here they are. That is the 26 possible plain text messages. Hard to read, I know, but with key 0 or A I got this. With key 1 I got DROY. 26 possible plain text messages. Which one's the correct key?  And all the rest are random characters. So we can easily detect which is the correct key by detecting the plain text that makes sense. When you have large enough or even reasonable sized plain text messages like this one, it turns out that if you use the wrong key you'll get effectively random characters or characters that don't form an English phrase or message. If you use the right key you'll get a message that does form an English phrase or message. So that's one part of the brute force attack or any attack. The attacker needs some way to recognise is this plain text the correct one or not. And when we have a large enough key space and we use a normal language, that will almost always be true. The attacker can simply look at them, not just look at them and read them but apply some software on them to determine of these 26, this one's correct. So it can automate the detection of the correct plain text. So Caesar Cypher is not good from a brute force attack perspective. There are only 26 possible keys. It doesn't take us long to try them all and find the correct plain text. But there are other possible attacks. Let's try maybe a slightly more intelligent attack on the Caesar Cypher. Let me find another example. I'll give you another example where we know the Cypher text and we know it was encrypted with the Caesar Cypher. So there it is, that's the Cypher text that we've intercepted longer again. We could do a brute force attack. I could try all 26 possible keys. Take me 26 attempts and I would find the correct plain text, fine. But we can do another smarter attack. We can do analysis based upon our knowledge of the algorithm and the language that's being used here. Let's assume the user was using English as the language. The plain text is in English. Therefore we expect that the plain text message has some structure. That is some letters occur more frequently than others. What's the most frequent letter in English? Well, if you look at a large set of texts, you go to a website and download many documents and then count all the letters of them. You could do some analysis. I've downloaded a book just as one example. It's just a book, I don't know how long, but hundreds of thousands of characters. It's just an old book. And what I'm going to do is count the letters in that book. The software we're using to count doesn't matter. Remember, count the letters in our book and that's sought by the percent. And it tells me of all the letters in that book ignoring the punctuation and spaces and so on, the most frequent letter is E. It occurs about 12% of the time. The next most frequent letter is T. It occurs about 9% of the time. And I've only listed the first, I think, 10 or so. If you look at all of them, I think you'll find Q and Z and X are the least frequent letters. And that holds commonly in other texts. It'll be different, but E, T, A, O are usually the most frequent letter in English texts. If you look at other languages, you would see other characteristics, but some characters will be more frequent than others. So we expect, let's assume, that I expect the most frequent letter in my plain text that I'm trying to find is E. But so if E is the most frequent letter, then if I look at my ciphertext, let's look at some statistics. Let's count the letters in our ciphertext as the attacker. I count the letters in my ciphertext, which is shorter, and I see the most frequent letter is J, about 13% of the time. Why about 9%? You'll see that these numbers are similar to the ones we saw before, but of course the letters are different. We had E and T. Here the most frequent letter is J. Remember, Caesar cipher is a substitution cipher. We substitute one letter of plain text with another possible letter of our alphabet, and it's quite a simple cipher in that some letter is mapped or substituted with a letter J. What letter do you think was substituted to get J? Most likely it was E, because if E was the most frequent letter in the plain text and we substitute that with one other and J ends up the most frequent letter in the ciphertext, then it's most likely that E and J map to each other. That is, E is the plain text, J is the ciphertext. If that was true, what would the key be? E moves right five positions to get J, so we would assume that the key is five in that case. Let's try it. Let's decrypt, decrypt our plain text, our ciphertext, which is in a file in this case, with a key five, and it's a file in this case. So I'm going to use a key five. This is my first decryption attempt as the attacker. It's slow because my software is very poorly implemented. It's not. And do we get it correct? We get a plain text that makes sense. What's the point here? The point is the attacker in this attack used one decrypt to get the correct plain text. With a brute force attack, the worst case, I'd use 26 decrypts on average 13 decrypts. So I've sped up my attack by using some knowledge of the algorithm. I know that the cipher maps one letter to one other and I know something about the characteristics of the English language. The letter E is the most frequent. Therefore I guessed the most frequent letter in my ciphertext corresponds to the letter E in the plain text. And once I know that, I know the mapping, the key is five. I try it and it works. It may not have worked. That is, even though E is the most frequent letter in our book, it may not be the most frequent letter in our plain text. But commonly it will be close. And if it's not E, I would have tried T, the second most frequent letter. This is called frequency analysis. We analyse the plain text and ciphertext based upon the frequency of letters. And it's a simple way to do an attack on the cipher. So we've got two problems with the cipher. The key is too short. The key space, there's only 26 possible keys. A brute force attack is possible. But also it's quite weak. Even if we don't do a brute force attack, we can use some analysis of the frequency of letters to find the key quite quickly. Any questions on cipher so far? Just to make it more interesting, we can represent the cipher as an equation. We map our letters to numbers. A is zero, B is one, C is two and so on. The shifting to the right is equivalent to doing addition of our key. The ciphertext is obtained by taking the plain text p letter, the letter of the plain text p and the key value k. We take the plain text value, add the key and the concept of wrapping around, we can implement using mod. Mod of 26. So we'll often look at ciphers from an algorithmic perspective and here we can implement it as a simple equation. Let's just confirm that. Let's just see if it works on our previous example where we map our ciphertext to numbers. Same ciphertext, just to show you the idea of that equation. Let's map those to numbers. A is the number zero. If you can't remember your alphabet, start remembering it. We're just mapping the letters to numbers. B is one, M is 12 and so on. So our ciphertext numbers are 0, 1, 12, 3 and 12. Our key in this case, we found the key to be 8 or i. To encrypt, we take our plain text and add the value of key mod by 26. To decrypt, we take the ciphertext and subtract the value of the key and mod by 26. So we do that on each letter. That is, we take 0, the value of the ciphertext, subtract the key and we get minus 8 and we do it for the others. The second letter, 1. Well, we'll stay on this one. So this is the value of c, the ciphertext, 0. The key is 8, so c minus k is minus 8. What's c minus k mod 26? What's minus 8 mod 26? The same. The same as what? Minus 8 mod 26. Here we have a bit of a problem. What does mod mean? Well, there are in fact two different variations of mod. Here we'll use mod which only returns a positive number 0 to 25 when we mod by 26. Sometimes in different implementations of mod, you can get a negative number. So you may think, what, minus 8? No, here when we write mod, it means the answer must be in the set 0 to 25. And the way to think of it, the meaning of mod in this case is the remainder, I think people understand. The mod we think is the remainder. Well, the idea is some integer times by 26 plus a remainder equals minus 8. So what values can we put here in the spaces such that we get minus 8? Where the remainder is positive. Some integer, positive or negative, times 26, y times 26, we're modding by 26. We understand mod as meaning the remainder when we divide by 26. So that what's left over? So some integer times 26 plus something equals minus 8. What values can we put in there? 18 for the second one and the first value, minus 1. Minus 1 times 26 is minus 26 plus 18 gives us minus 8. The point is the answer is 18. Mod 26, minus 8 mod 26 is 18. It's the remainder when we divide by 26. So be careful with mod here and other places I use it in the course. The answer is always positive. It's between 0 and the modulus, 26. 0 and 25 in this case. What is the letter 18 in our alphabet? It's the 19th letter, which is s. 18 is s. And you can do the same for the other characters. 1 minus 8 is minus 7 minus 7 mod 26 you'll find is 19. In fact, the mod implements the wrap around. The ciphertext value minus the key of 8 4 mod 26, that's an easy one. And 4 is the letter e. Minus 5 mod 26, 21. So if this sees a cipher, we think of shifting letters, we can implement or as an equation in this case, both encryption and decryption. And then you can apply it to any alphabet. If you order the set of characters, then you mod by 26. If we wanted to have 27 letters in our alphabet, include the space as the 27th character. So z is 25, the space character is 26, then we could have the Caesar cipher, but it would be mod by 27. There'd be 27 characters in our character set. Remember that characteristic of the mod that we use in this course. We always end up with a positive number. Alright, let's try a better cipher then. Caesar cipher, the key space is too small. There are only 26 possible keys. Therefore brute force attack is possible. On average, it would take 13 attempts. With a computer, that takes zero time. Very fast. Also, another problem, even if we don't do a brute force attack, the way that the Caesar cipher maps one letter to one other letter makes it easy to do this analysis using the frequency of letters. That is, we see it here. The ciphertext M corresponds to the plaintext E. Whenever we have an M in the ciphertext, it will be the same letter in the plaintext. And from that, based on the frequency of characters expected in the plaintext, we can use that by counting the frequency of characters in the ciphertext to guess the key. And that's quite successful. So how do we improve? Well, how do we improve against brute force? Well, one way is to make the attacker guess what algorithm it uses. Don't tell them that we use the Caesar cipher. But in practice, that's hard because A, there's not many algorithms that they need to try. And B, usually we know the implementation. Again, it's hard to hide the implementation of the operating system or from the encryption software. So usually it's assumed that it's known the algorithm, or it's easy to find. Another thing could be compress the message before we encrypt so that the frequency of characters changes. But again, if the attacker can guess the compression algorithm, ZIP, RA, or Z7Z, or whatever, different compression algorithms, then they can try that into a brute force attack. Use a different language, same problems occur. There's not many languages we could try. Even if there are 100,000 different languages that we could try, a brute force attack increases from average 13 attempts up to 1.3 million attempts. But with a computer, 1.3 million attempts won't take long. So the main way to deter against a brute force attack makes sure that the key space is large. Increase the number of possible keys. So let's see a variation what's called just generally a mono-alphabetic substitution cipher. And instead of doing a shift by K positions in our alphabet, we define which letter maps to which other letter in advance and tell the other side that mapping and then encrypt in the same way. For example, I list my 26 plain text letters and as the user A, the encryptor, I define that every time I encrypt a letter A it will become as D. Every time I encrypt the letter B it will come out as ciphertext Z and C come out as G. And I can choose a random mapping here. I cannot reuse the letters, so there will be the 26 letters in the output. Then when I want to encrypt a plain text message like bad, B-A-D, B-A-D would become Z-D-L. So with the Caesar cipher it defined that the output ciphertext letters must be in the same order. Here we allow it to be in any order. We're to be chosen by the user. Let's consider that. A different example. So the concept of using this cipher, we have our user A, our two users, user A will choose a mapping. That is, think that there's all the letters I will not write them all, but we'll define a mapping and we will choose our own mapping. A can map to any of the 26 possible values in our English alphabet and the user will choose a value randomly. Anyone want to choose a value? L. I just chose a random character. How many values could I choose from? There were 26 possible letters I could choose. Normally I choose to map to L. It could have been one of the 26 possible letters. I just record that. When I chose this letter L, I could choose from 26 possible values. And now I choose a letter that B can map to. And I choose a letter randomly, but I cannot reuse L. This is what we mean by mono-alphabetic cipher. We use just the one instance of that alphabet. So I choose... It doesn't matter for the example. I choose H, for example. The point is that the number of letters I could choose from was 25. Because I couldn't choose L. It was already chosen before. And in C, I mapped to one of the other 24 characters and I could have chosen from 24. And you start to see the pattern and how it's useful. And when it gets down to the last three characters, there's not many to choose from. So there's three remaining. I haven't used the letters T, A and Q. So for X, I'll choose T. There were three to choose from. For Y, I've got A and Q left over. Let's just use A. There were two to choose from. And for Z, there's only one to choose from. The last remaining letter in alphabet. So before I encrypt, this is not encryption. This is defining the mapping from plain text to ciphertext. The user defines this mapping in advance and tells user B what the mapping is. They share this mapping. So the mapping is in fact the key. And they share it to user B saying whenever you get ciphertext I, it really means plain text E. So user B also knows the mapping. When they want to send a plain text message, they'd simply use that mapping. And since I don't have all 26, let's say if the plain text was the word dead, then the ciphertext for this particular mapping, D would become R, E, I, A, L, and D, R. And I would send this ciphertext to user B. User B, which also knows the mapping, sees R is D, I is E, L is A, and R is D. They get the plain text back. That's how it's used. The comparisons of the Caesar cipher, an important point here is how many possible keys can we choose from? Well, I can use this mapping or I could have chosen a different mapping which would give us a different ciphertext which is equivalent to a different key. How many possible mappings are there? How many possible combinations do we have here? What's the answer? 26 factorial. 26 times 25 times 24. That is, for the first letter I can choose from 26 values. For the second letter, 25. So the number of possible combinations there are 26 times 25. For the next letter, 24. So the number of possible mappings, you just multiply all those numbers together, which is 26 factorial, which is a big number. So this is the number of mappings I have possible. Let's ignore this plain text. We'll use this particular mapping for all of my plain text. So I have a long message like my book that I want to encrypt. Then I would most likely use all of the letters in that case, and therefore the entire mapping would be used. If I have a different plain text, then I would use that same mapping all the time. So all I care about at this stage is how many possible mappings I could choose from. Because what the attacker has to do, in this case in a brute force attack, if we have a large plain text, is try all possible mappings. How many possible mappings are there? 26 factorial. Caesar's cipher had 26 possible mappings. Shift to the left, or shift to the right by 0 positions, or 1 position, or 2 positions. This mono-alphabetic cipher has 26 factorial possible mappings. And a brute force attack, if you're going to try all possible mappings, has 26 factorial worst case performance, 26 factorial divided by 2 average case, which is the average brute force. All of them were on average, you only have to try half, which is about 26 factorial. Let's see what my calculator does. It's about 4 by 10 to the power of 26. That's just a coincidence that it's 10 to the power of 26 divided by 2, 2 by 10 to the power of 26. That is, on average, a brute force attack, if we're going to try all possible substitutions, would take us 2 by 10 to the power of 26 decrypt operations. How fast is your computer? Maybe a tablet or a laptop or a PC. How many decrypt operations could your computer do per second? Let's have a guess. I don't know how fast it is with this mapping, but let's say it's very fast. Let's put a number to it and say that my computer could try, I don't know, 10 to the power of 12, which is a million billion decrypts per second. That is, what, a clock rate 1 gigahertz is 10 to the power of 9. Let's say it could do 1,000 decrypts per clock cycle on your CPU, which is unlikely, but you have many CPUs just as an example. Then how long would the brute force attack take? Let's get our calculator. How many seconds? 26 factorial divided by 2 divided by 10 to the power of 12. 10 to the power of 14 seconds. Convert to minutes. Convert to hours. Convert to days. Convert to years. Convert to centuries. Alright, 63,941 centuries. The point is that with this large key space, our brute force attack is no longer possible because it would take so much time to try all those possible keys. Well, you say my computer is slow, or why not try more computers? Well, let's say I have a computer like at this speed, but I have access to a million of those computers. I use computers from other people. If we speed up by a factor of a million, then the time decreases by a factor of one million. Is it six years or something? I think it becomes 6.3 years. If we speed up by another factor of 1,000, then maybe we can bring it down to days. But now we've exceeded all the possible computers, maybe that we can get access to. So it's very easy to stop a brute force attack, make the key very large, the key space very large. When we look at the real ciphers, we'll return and we'll give some numbers of what's a good key size, such that a brute force attack today is not possible. Caesar cipher, brute force attack, 26 keys. This mono-alphabetic cipher, 26 factorial keys. So secure from that perspective. But it's still easy to break if we look at the frequency of letters. And I cannot go through an example in the class, but we have one on the website which is worth reading through because it takes some steps. I'll let you read through. But I have gone through an example where we start out with a cipher text. We can't do brute force because it would take my computer millions of centuries to do it because my computer is quite slow. But what we can do is we can look at the frequency of letters again. And I'll let you read through, but if you count the frequency of letters, t is the most frequent, z is the next most frequent in this cipher text, and compare it to the expected frequency in the plain text, e being the most frequent and so on. And also, you don't have to just look at the frequency of letters, you can look at the frequency of pairs of letters in English called diagrams. In English, the most frequent pairs of letters are things like t-h-a-n-o-n and so on. The letters q followed by x are very infrequent in English. So the frequency of diagrams in the cipher text and expected frequency in the plain text can also be used to start to guess what is the mapping. And I go through an example which is too hard to go through in class that starts with our cipher text and with a few guesses, you can start trying some letters and replacing them and if it doesn't work, you can go back and try a different letter and after a few attempts, it eventually gets to the plain text, the correct plain text. This example on paper may take a couple of hours. With a computer, it would take a few seconds if you could automate the process. So a brute force attack would take hundreds of centuries but a frequency analysis attack on a mono-alphabetic cipher is possible in terms of seconds. So this cipher is still not secure. What I'll leave for homework is I'll maybe, once I add everyone to the course list, I'll send out an email summarizing some homework, unassessed homework in this case, but read the course website and from it you'll find a link to this example and make sure that you understand the Caesar cipher and mono-alphabetic cipher. Your first quiz will give you some test about them but that first quiz may not be until later in the second week.


Welcome to the Art of Charm podcast. We have a very special toolbox episode set up for you guys today. And this was inspired through a conversation that AJ and I had with our guest, Connor Beaton on why young men are opting out of the dating market. And we're going to put that interview in the show notes for those of you who want more contacts on this subject that have an opportunity to listen to it. And that conversation was spawned due to a study that it was, was brought up. Yes, this was actually a Pew research study and it found that among men under 30 years old, over 60% are single. And that's almost double of women in that same age bracket. And it's pretty shocking to hear that studies have been making the rounds online and there's a number of other studies now around what's going on with young men, an increase in loneliness. And we're also seeing it inside of our X Factor accelerator program that more and more men are coming to us for dating help. Because they're feeling challenged in the current dating market. And we've talked in the past about the rise of online dating and technology and AI, and there are a number of factors that are making us less attractive to the opposite sex. So a big goal for today's show is to explain how we work with our clients and how you, the listener, can unlock your X Factor to be more successful in dating, to attract more of the opposite sex in your life, but then also just attract amazing, interesting, awesome people into your life.   And when you master these traits, you're going to see that everything becomes a lot easier. So you're not fretting over the first message. You're not fretting over how do I have to use AI and chat GPT to make my profile more interesting? And how do I go approach that person instead? It's actually going to create a funnel into your life of attractive partners, amazing friends and a vibrant social life and making life so much more fun in the first place. Just to set up some context for this conversation that this is just not a problem that we're seeing here in America. This is a problem that all advanced technological cultures are facing. We're seeing it in the East. We're seeing it in Europe. We're seeing it in Canada. And so it's safe to say that due to all this technology that is supposed to be connecting us in certain areas, it has the direct opposite effect. And this technology is also stifling the three major areas that allow us to be attractive. And those are the areas that we're going to be discussing today. And they are about developing our personality, developing our confidence and developing and building out our network. All of those have a direct correlation to what makes us attractive. And as young adults in the past, we had been out developing all of these areas in our lives through socialization, because that socialization is what enhances us and makes us attractive to others.  The neighborhood was full. When I call home now and talk to my dad about the neighborhood and what's going on, there's no kids outside. There's no kids playing ball, riding bikes. And the children that are there in that town, they're at home. They're on their computers. They're playing video games. And how has this changed over the last 20 years? Like I remember as a kid of the 80s, when I got my first computer, when I got this Amiga 500, this was a new world and then came the PC and then came the internet and it offered so many opportunities, so much fun, so many games, so many internet forums to chat with and who could have foreseen where this was leading us in the long term. Now this is the normal thing to do. We sit at our computer, we chat on our phones. We play a game. We watch something. We stream something on the laptop. And this epidemic of loneliness is so pervasive across the globe. Just like you said, Johnny, there was a very recent study done by Beretto and his team, and they analyzed the frequency of loneliness that was reported by over 46,000 people between 16 and 99 years old across almost 240 countries. And this study is best summarized with one of their closing remarks. And that is, I quote, we found the most vulnerable to loneliness were younger men living in individualistic cultures. Younger men were more lonely than middle aged men and middle aged men were more lonely than senior citizens. That's the epidemic of loneliness. And it hits those of us that grew up with all that amazing technology. This is affecting all of us, right? So I'm slightly older. I'm Gen X. And when we were making plans with our friends, when we were younger or we wanted to make plans, we had to check to see if our plans interrupted our television programming. Right? It's like, on Thursday, it's my block of shows. I can't be bothered. I watch these every week and I'm hooked. Well, those block of shows on Thursday, right, with the internet, we don't I don't have to wait for those shows to come up. Now I fill my schedule with all of the shows that emotionally stimulate me 24 seven. And if we don't take heed of that and acknowledge that, then all of a sudden we become consumed by all of the stimulus that technology offers us. We're in the past. If I wanted to be stimulated, I would have to make plans with my friends. If I wasn't getting that stimulation from television. And there was a phenomenon growing up where even if we were online or even if we were playing video games, we were inviting friends over to participate in that with us. Yeah. You know, we had multiple controllers. We weren't streaming online in different places and in different locations from our friends. I remember crowding around the 56 K modem waiting for AOL to go to their friends to pile in a chat room, but not just to date ourselves. There's something else that we talked about with Connor that I want to bring up here that's very present for a lot of our clients. And that is this pressure on our career and this pressure to succeed in this individualistic and capitalistic culture. So many young men are forced to focus solely on their career waiting and prolonging the dating, the hoping that buying nice things, buying a house, buying the fancy car, buying the watch will then overcome all of these issues that they're having in their dating life to make them more attractive. And unfortunately, so we're talking about a lack of socialization. We're also talking about putting most of our focus and energy around our career. And for many men, that involves exercising your analytical mind. Yeah, exactly. So your analytical mind is running on overdrive. Well, guess what? That analytical mind doesn't help with building out that personality and being more charismatic. It doesn't help with that inner critic and your confidence. And your analytical mind is not helpful when trying to make connections and connect with people on an emotional level. So we've hypermasculinized our analytical mind and focused on developing that out for career success, to the detriment of our personality, to the detriment of our confidence and to the detriment of our connections and relationships in our life. And I want to add to that as well. We will double down on the skills that have gotten us to a certain degree in our life. So as AJ was saying, we're doing a lot of this analytical thingy because we're focusing on our career. If focusing on our career puts food on our table, a roof over our head and clothes on our back, well, then we're going to double down on that skill that has provided so much for us. And this is where we start to run into problems because the only skill that was developed was this analytical problem solution oriented mindset that our personality traits weren't able to be developed. Our imagination wasn't being able to be developed. Our connection skills were not able to be developed like they were in the past. So this creates the gap that we are looking to close. This is the gap that our programs are designed to close. This is the gap that this show is designed to close. And we're going to show you three areas where this technology has hindered and created a gap that is keeping us from not only that connection and that warmth, but also a lot of meaning in our lives and a lot of purpose in our lives because we are finding ourselves distanced from other people and that need is allows us with the feels good. At our core, we are herd animals and all herd animals need three things in order to feel good, attention, approval and acceptance. Attention, approval and acceptance allows us as herd animals to know that we are safe, that that we can relax. Without feeling those three things, our anxiety goes higher because we're not feeling protected. So when we think about personality, what we're talking about here is how do you go from ordinary or average? So if you've been listening to the show, you've heard us ask time and time again of our guests, what makes you extraordinary? What is your X factor? How do you stand out? Your personality is one way that you stand out. That makes you extraordinary. And that personality could take many shapes or forms. It could be your creativity. It could be your music inclination. It could be your ability to use your imagination to build video games or to play Dungeons and Dragons or to master board games. But that personality has to be developed outside of your career. It has to be showcased to other people to stand out from the crowd. And what we see time and time again, a roadblock or a pitfall that our clients are facing around showcasing their personality is being in their head overthinking everything and worried about what to say next. And oftentimes they'll join the X factor asking the exact words, AJ, what do you say in this situation? What do you say, Johnny, in this situation? Well, your personality is different than my personality. My personality is different than Johnny's personality. And if I worried about what I should say to be more like Johnny or to be more like Michael, well, I'm overthinking and I'm not going to be present and I'm not going to be charismatic. And in the moment that attracts people's attention that wins people over and keeps them wanting more of my personality around them. So for the analytical driven mind, I'm going to connect us together and then we're going to give the solution to this. So when you're out at social engagements, if you feel that you are in your head and these symptoms to that are you're going to be at a loss for words, having a lot of anxiety going on, your mind just blanks out. This is due to not being socialized in an area where you are using your personality to connect and draw people in. Now, what's cool about this is now that we've identified the gap in the problem, it's OK, what is the solution to then being able to build out our personality? And what's so awesome about this is that we've been doing this for 17 years. This is a skill that you can develop at any point in your life. It just needs a bit of attention. And for you analytically driven mindset, folks, a few simple frameworks will allow you to feel good in developing this out to give you an area, a place where you can follow a few simple rules and begin to develop this. Now, we had recently just did an episode about improv and improv is working on this very thing, being present in the moment, connecting with with other people. And this is what's fun about that is we went through this that whole episode talking about all the skills that can be developed and through improv. And there is so many of us who feel that these are skills that we're supposed to be have have developed earlier in life. Well, they're going to they're going to develop at any point that you put in the effort and the attention it deserves. Let's be honest, for a lot of us in our career, it's not a great place to work on our sense of humor. No, no one wants to walk in the doctor's office and hear your monologue. No one wants to come to the law office and hear you crack in jokes about the bone in the case. So oftentimes we've neglected our sense of humor and showcasing it because our career has demanded that we be serious and that we focus on the task at hand. So are you creating opportunities in your life to build out and to strengthen that sense of humor? Are you creating opportunities in your life to share a bit more of your story? So if someone was to ask me at a cocktail party, hey, what do you do for a living, AJ? I could say I host a podcast. I coach emotional intelligence. I work with the military, or I could say, you know what, 16 years ago, I fell in love with human dynamics. I was struggling myself with some imposter syndrome and really connecting with others after I graduated from college. And I just went on this journey of self development to figure out how to unlock my personality and be a more charismatic conversationalist. And through that journey, I started a podcast and that turned into a coaching company and now we work with clients worldwide. Which of those two answers at the cocktail party is going to stand out? It's going to draw a crowd over is going to lead to that woman standing across the room, taking interest, the podcast host or the storyteller who shares a journey of not only what he does, but how he fell into that line of work and what you love about your career.  And storytelling is such a creative art form when we talk about being creative. We think about painting, making music, playing an instrument. But what about telling stories? And I don't mean writing a novel, which is certainly an art form, but also giving an answer like that where someone asked you, hey, AJ, what do you do? And instead of the facts, there comes this art form that is called storytelling that's not a novel, but it's 30 seconds of letting people into AJ's life, showing them the world through your eyes, bringing in a little bit of vulnerability as well, which speaks to your confidence of being able to bring this out into the world and not worrying about what people might think or say about. And we'll talk about confidence in a bit, but these are such important parts of connecting to another human being, whether that is a social event where you don't know anyone or whether this is maybe at work in the coffee kitchen, getting a warm beverage or it is at a date. I mean, how boring would a date become for everyone involved if we only threw facts around? I can Google that stuff. I don't need, you know, I can look that up on your LinkedIn. I want to talk to you.  And when we think about charisma, it's not just what you're saying, but it's also how you're listening and what you're picking up on what others are sharing in conversation and that ability to actively listen to a conversation, to showcase empathy, to recognize and validate emotional bids, that creates the spark. That creates the attraction that we're looking for, that we're craving on that first date, that we're craving from a romantic partner. And I know, Michael, there's a great study about just the importance of listening and empathy in our romantic relationships. Yeah, and this was done by Davis and Othout in 1987. So this is a little bit age, but it's still very much up to date. It's called maintenance of satisfaction in romantic relationships, empathy and relational competence. And they interviewed heterosexual romantic couples. And what they found was that empathy, so active listening is a core part of being empathetic, was positively associated with satisfaction in romantic relationships. So now we need to maybe talk just very briefly about what empathy is for those that are shaking their head and scratching their chin. It's like, what are they talking about? So empathy in a nutshell is your ability to understand and share the feelings of others. And that increases the connection in a relationship. And I'm going to argue that this is not only true for romantic relationships. This is just the part where the rubber really hits the road because now you're married to someone, now you have kids with someone. So those relationships are really important. But empathy and active listening also kicks in in fostering those social relationships, the friends, the dates, the coworkers. Because by being empathetic, you show that you are attuned to the other person's needs. And that is important for trust, because if I'm talking with Johnny and I don't feel like he understands my needs, I don't feel he understands where what I'm talking about, why I feel this way. What is the likelihood that I'm going to trust Johnny, right? But or I talk to Johnny and when I talk about a struggle or when I talk about a victory, Johnny is there to support to high five me on a victory and to lend an ear in the shoulder. When I talk about a struggle, it's like, OK, this person gets me. I've just met him. I've just talked to him for two minutes. But this person gets me why, because we're showing empathy. And again, it's not about what is it that we're going to say to remedy this. It's what are the actions that we're going to do that we're convey that actions are always going to speak louder than words. And this is where a lot of analytical mindsets get you in trouble because you're looking now for the right answer for what has just being said. When if if it's empathy, it is how you're conveying that empathy through your body language, through nonverbal communication. Now, these three areas, your sense of humor, your ability to actively listen, showcase empathy and your storytelling. Are skills that you can build. So if you think right now, I'm boring, I don't have much personality outside of my work. I don't have much going on in my life. How do I stand out? How do I become extraordinary? Well, you work on these three areas to build out that exciting, fun personality. And I'm going to let you in on a secret. Chat, GPT, Google Bard, they can't do this for you. They're not going to solve this personality issue in your dating life. But you know what will you chasing after a passion, working on these areas and creating environments for you to practice these skills, which is why we have implementation sessions in the X factor accelerator, working on these exact three things you're listening, your storytelling and your ability to showcase your sense of humor. And when those three in combination come together, you become charismatic, you become memorable. And that first date turns into a second date. And it turns into her being excited to tell her friends at brunch about meeting you and connecting with you and having an opportunity to see you again. Now, the second factor that we're going to talk about here, confidence, right? The first step to unlocking your X factor with dating is to grow your charisma, become someone who can showcase personality effortlessly. Your second step is actually overcoming that inner critic and building confidence in yourself, not only to speak your mind, but to take action in areas that are attractive to actually move that relationship forward from just a first date or a great conversation or some flirty text messaging to someone who is action oriented and is liberated from their inner critic to showcase themselves, to find their voice and communicate who they are with the opposite sex. So AJ, this is something really interesting that we see every time when we do our implementation workshop on vulnerability, where everyone just shares a little bit as much as they're comfortable doing. And this 90 minute workshop, when we're done, no one wants to leave because they're like, Hey, we opened up this. I want to hear more about that. I want to hear more about that. And the participants are like, but I shared something that I'm a little bit embarrassed about. I'm shared, I shared something that my inner critic was speaking up about. But by doing exactly that and showing that human part, everyone else is like, no, I want to hear more about that. Tell me more about that trip. I really want to hear how this played out. And it's amazing to see how conversations just keep rolling and no one's asking, what's the next thing I should say? What's the next question I should ask? Like the moment this vulnerability enters the playing field, the conversation just goes. So the second attraction trigger that we wanted to discuss here is confidence and confidence is something that has to be built, maintained and strengthened as you grow older. As time moves on, it is something that you are actively working on. Confidence is something that you gain, that you just turn on and now you have it, it is fleeting. And so it needs to be worked on continuously. And it needs to have daily attention. If you were to build a skyscraper and leave it go, after years, nature itself, gravity and nature will deteriorate that building and will bring it down. It will come back to earth. Your confidence is just like that building where it needs to have that attention, reinforcement and maintenance in order to stay with you. And this is what makes it difficult because if you're not out regularly in social situations, you will not be able to build that confidence. If all the work that you were going to put in to developing out your personality, it needs that continuous work in order for you to get stronger in it without it, then we lose those skills, the atrophy. Part of that is to navigate your inner critic and to be able to no matter what is going on upstairs in your mind, that you continue to put one foot in front of the other and gaining that confidence. I think one of the because this is the strikes me so many times and I have to try my best not to not to smile when I hear it yet again is that people try to think their way into confidence. Yes, I can make a plan. I can read another book. I can do another video course and then I will be confident and then I'm stepping out into the world.  And it's it's easy. Like building up confidence is something that happens surprisingly fast, if you know exactly what you're doing and you have the right guidance and you can't think your way into confidence. It will actually backfire because your mind is going to ask you, well, if that's true, why aren't you outside? Why didn't you say something? Why didn't you say hi? Why didn't you make a joke? And it just backfires all the time. It's a muscle that needs to be trained. And when you create high expectations of yourself, you've run the risk of feeling never good enough. And if that is the inner critic voice going on in your head, it's going to be very hard to approach someone that's attractive to you. It's going to be very hard for you to navigate and manage the lulls in conversation to introduce yourself to that next opportunity. And I mean, ask any woman she will tell you that confidence is sexy. Confidence is attractive and the science backs it up. Yes. So let's talk about sex here, because I think the amount of sexual encounters can be loosely seen as a good benchmark for for confidence, at least according to the study done by Bailey and team in the year 2000, called do individual differences in social sexuality, represent genetic or environmentally contingent strategies? Now, that's a mouthful. What they found was that confidence as part of a larger personality factor known as extroversion was positively related to sociosexuality, which means having sexual encounters outside of a committed relationship, romantic partner or being in a marriage. So the higher confidence, more sex, more sexual partners. And what they also found is that this extra level of confidence leads to being more outgoing and more assertive and leading to more opportunities for sexual relationships. But on the other side, if we put sex to the side for just half a second, there's another study that showed that confidence also helps in maintaining relationships because it brings about behavior like better conflict resolution, more positive emotional states and and also resilience when there are difficulties in relationships and that that confidence then allows you to say, let's sit down. Let's talk about this instead of blowing up instead of retreating instead of taking out your phone and staring at it, having the confidence to say, no, you know what, I'm fine with this. Let's sit down. Let's make a cup of coffee. Let's chat. Let's chat about this and find a solution. And that's what makes those relationships bloom and last for a really long time and experience builds confidence. So like you were saying earlier, Michael, thinking your way to being more confident versus acting your way to facing life's challenges, to overcoming hurdles, to picking up new skills, to putting yourself in the arena creates the fertile ground for that confidence to grow and blossom as well as gives you tons of things to talk about on the first eight tons of conversational opportunities. So I have I have the perfect example for this because I was just talking with Brian just two hours before we were recording this. And Brian is an American, US American, who moved to China and primarily to learn the language. He wanted to learn Mandarin. And so he got in touch to work with me because he said, look, I don't have the confidence I all my only friends are the people in my language learning group. I don't do anything. I just come home after work. What I really want to do with my life is I want to have a vibrant social circle. I want my calendar to be so full that every evening is filled with something and I'm meeting new people and I'm way too scared to start talking with someone. And like like like we talked about, confidence doesn't mean that you think your way out of it. And it doesn't mean that you start with the most difficult things out there. You built this up like a muscle.  Why don't you go to a park, put in headphones and just dance for 30 seconds? Make a little bit of a fool out of yourself. Be there in the park, dance a little bit. The next week, I told him to go to a park and to just lie down on the sidewalk, as if he's this weird person who's just sunbathing in a park on a Tuesday afternoon. And two weeks into this, he said, Michael, if I can dance all by myself in a park, people looking at me, if I can lie down on the sidewalk with people looking at me, I can talk to people like that is nothing compared to what I've done before. And that's what he started doing. And then he did this really amazing thing that brought both a smile to my face and tears into my eyes where he sent me this text message after we've stopped working together. He sent this text message and he said, Michael was my mom's birthday and I wanted to send her a video. But I thought instead of me recording myself, I'm going to go out and I'm going to ask strangers that I meet in the park or in the shopping mall to wish my mom a happy birthday. And then he sends me this beautifully edited one minute video where like every five seconds, a new person comes into the camera, wishes his mom a happy birthday. I guess that's what they said. It was Mandarin. I'm not familiar with the language, but it was just so amazing to see how he was smiling in the video and the people that he approached. They're like, well, what's happening here? I'm in the presence of a really confident person. And that just took us seven weeks. And that was it from a complete 180 degree turn from I can't talk to strangers to, hey, look at me. Fifty people have wished my mom a happy birthday. Seven weeks if you just know what you're doing. So the thing with confidence is while it's fairly easy to build, you need to know why you want to have it. And I invite you to ask yourself, why do I want to be confident? How will it change my life if I'm confident? And maybe even more importantly, what am I going to lose out on if I don't work on this? Because if you don't work on this today, if you wait another five years before you start working on this, there are five years that you've lost where you're not doing the things that you want to do, where you're still falling back to old behaviors. And the fact is no one can force you to train up your confidence. That's up to you. So I would really invite you to ask yourself, what am I going to gain? And if I work on this, and what am I going to lose if I don't? And what's key here is many of our clients are contextually confident in their career in other areas of their life. But this lacking in social confidence is an impediment to their romantic success. If you can't approach someone you're interested in, if you can't strike up a conversation and flirt with someone that is attractive to you, confidence is at the root of it.  So as we talked about in the first step of unlocking your X factor in dating, we have to showcase our personality and become charismatic. The second step is we have to take action. We have to start approaching people. We have to not just rely on dating apps and rely on Chad GPT to come up with the next response. The third piece, and this is typically after the first date, where there's challenges, is we have to have a vibrant social life. We have to have connections in a network in our life in order to maintain the attraction, in order to actually showcase the preselection that's necessary for that partner to want to be with you, to want to stay around. And I know for many you might be feeling, hey, I'm a bit of a lone wolf. I like going out on my own. I like doing things on my own. I don't need friends. I have a career that I love, but I don't need to have a crazy weekend to be successful. And then I'm just going to hop on the apps and I'm just going to start messaging people and going on dates. And that's going to be my way to success. In every relationship that I've ever been in, upon meeting the woman that I'm going to be dating, eventually there is always a moment where they want to meet your friends.  There's part of birds to a feather, right? It's like you're gaining a larger context of who this person is. But also, are you selected by other people? Do other people trust you? Do other people feel good around you? Do other people talk good about you? All of these are actions and behaviors that send signals out to your prospective girlfriend. And there's also a danger that she needs to check for, which is do I need to take care of this dude? Because a lot of guys, when they're looking for a romantic partner, it's like, yeah, if I have a romantic partner, my evenings are filled. There's going to be sex, I'm going to meet her friends. She's going to take me to parties, she's going to introduce me to hobbies.  Well, guess what kind of burden that puts on the lady? It's like she doesn't want to drag you everywhere. She doesn't want to drag you to Pilates class and then drag you to her girl's night and then bring you here and there.  And that's what she's also checking for when she asked to meet your friends. And there's also this piece where she is going to be betting on you. You may not be the person that she wants to marry yet, but she needs to gain some insight if you are going to turn into that person that she wants to be married. Your friends, your peer group will help determine that. Is your peer group high value that has a lot of inspiration and motivation and aspiration within that peer group? Because she knows those are selective pressures that will push you into a certain direction. If there is none of those things there. Well, there's nothing that is motivating you to be better. There is nothing motivating you into shaping and changing into the person that she is betting on that you will become.   There's nothing less attractive than putting all of that on a partner. And you don't want to wait until you've had the first date and find yourself then chasing friends for that opportunity when she's interested in meeting who's in your life, who is in your network. And this is why so many of our X Factor participants find success in their dating life because they're learning the social skills that create a high value network. They're not just focusing on attraction triggers and how do I get this one woman, this one specific attractive partner in my life. They're looking at it more holistically of how do I become extraordinary by attracting amazing people into my life, not just women. There's yet another powerful thing that a peer group does for you. And that has to do with compliance and conformity. And this is a study done by Kildini and Goldstein. And if the name Kildini rings a bell, that's the author of influence and persuasion, some amazing bestselling books that have a lot of wisdom in them. Anyway, in their review paper on compliance and conformity, they in very short say that when times are uncertain, when situations are uncertain, humans do what the herd does. So how does that apply to you at a social event? Imagine you're coming into a social event and no one knows you. You have to prove yourself.  And if I know you listener, you're going to clutch your beer and you're going to hold it really close to your chest and you're going to just look at your phone a lot. Now let's replay, let's rewind this and say that at the social event, you know a couple of people.  It's like, oh, there's AJ, there's Johnny. They walk over to you. They give you a high five. They give you a hug. They take you to the bar. They buy you a drink. This is the uncertainty they were talking about. People don't know you, but now they are a few influencers.  They appreciate you. They want you to be there. And the rest of the herd does what the leader is doing. Everyone else is thinking, oh, there's AJ, there's Johnny. They must be cool dudes if they are being welcomed like this by their friends. I need to meet them because this is someone, you know, I want to have in my life as well.  So Brad started X Factor After Divorce that basically cut him out of his entire social circle. His ex-wife was very extroverted. He found himself very introverted, working in a high-stakes security job. And he didn't really share much, didn't really get super vulnerable with his social circle. And when he lost his wife, he lost his friends. He was starting over and the first thing he did was fire up his online dating profile. And he started to get some dates, went on a couple first dates, thought he had a great conversation, but never really got the second date and was really struggling to understand why. And one thing that we found in his communication, especially on that first date was he was incredibly available. He was like, Hey, this was great. You want to hang out on Saturday? Oh, you don't want to hang out on Saturday? Well, let's hang out on Monday. Oh, Tuesday look good for you. And this availability created neediness that was picked up on with these women that he had great first dates with. Why is this guy so available? What's going on here that he doesn't have more in his life? So we started talking about finding a social circle through your passions and one passion that he had neglected was dancing. His ex-wife wasn't really into dancing and he wanted to go to lessons, wanted to go to classes, but never really found the opportunity. So we encouraged him to take some dance lessons, put himself out there to find some people who enjoyed dancing. And in the salsa class, not only was he having some fun dancing, but he actually met a few guys in the class and they invited him to check out some other music venues. And all of a sudden his passion for dance led to building a bit of a social circle. After class, he went for drinks to some of his classmates and they started making plans together. Low and behold, fast forward a month later and we checked in on his dating life. Not only was he going on second dates and third dates with some online dating opportunities, but he actually met someone in his dance class. So when you actually understand that having this pre-selection, this third attraction trigger working in your favor, you unlock your ex-factor in dating. You become extraordinary.  I think this is not to get too sentimental here, but this is what I love most about my job. And whenever we have our coaching calls and I joke that it's my time here in Austria, it's 8 p.m. on a Saturday and I don't mind at all because I love working with these people, seeing this change happening. Just to put together a summary of what we talked about today, due to technology, all of us, including you sitting there listening to the show, have allowed certain aspects that make you attractive to be stifled due to all the stimulus and work that we've been putting into our careers. The three main areas that are being neglected are our personality, building our social confidence, and connecting to our network. It is also those three areas that allow us to be incredibly attractive to the opposite sex. And by developing those areas, that makes us a better person. And by developing those areas and making us a better person, it makes us a more attractive person. You go from ordinary to extraordinary.