Hey everyone, Mr. Gibson here with your next lesson in cryptography and today we're going to be looking at cracking the kid RSA cipher.  So why was it secure in theory at least for now? And the short answer is that multiplication is easy to do for us in computers but factoring is hard. For example, generating the public and private keys only involved multiplication, a little bit of addition and subtraction and that was really easy for us to do. But trying to determine D, the decryption key, when you know E, the public encryption key and N, the modules you're working in, that's hard. We did not have a good way to factor those two numbers, meaning finding the product of E and D that resulted in one when we mod by N and one because that's the sign that we actually have multiplicative inverses, their product is equivalent to one. And that's really the basis for any public key crypto system. It's easy to go one way. It's easy to encrypt messages, multiplication, it's easy to generate keys, multiplication, but it's really hard to take the public key and get the private key because the reverse operation is very challenging. So multiplication easy, factoring hard. And we can see that brute forcing is actually pretty good. We can actually crack this as a technique for a little while until the values of Ns get too big. So I've created a table here that show you some samples as randomly generated public keys for kid RSA. So that's the first column. I've bolded the value for N because that's the one that really determines how many potential brute forcing we're going to have to do to determine the correct value for D. A typical thing in public key cryptography is to measure the size of your modulus or N based on how many bits you need to represent it in binary. So that first key has a size of 22 bits. And then it took, you know, .0069977 seconds, so almost no time for my computer to brute force the value of D based off of E and M, but as we increase the size of the key, so we increase the value of N to be bigger and bigger and bigger, we see the length of time it takes to brute force the value of D from E gets longer and longer. And just a 42 bit key now is over a thousand seconds. So we're talking, you know, minutes and minutes to do. And in practice, N is thousands of bits in size and, you know, 4096 is becoming the new standard at this point in time for a public key encryption. And so you can kind of scale this out and realize we're talking hundreds of years of time, maybe thousands of years of time of computation time to actually brute force a public key with this system. So why don't we use it? Well we mentioned at the end of the last lesson that there's an algorithm that's far more efficient than just trying all the possible values of D, multiplying it against E and C if you get one. And that algorithm is called the Euclidean algorithm and it's actually the extended Euclidean algorithm. And this algorithm can be used to quickly determine the multiplicative inverse of any number in a given modulus assuming that such a number exists. And we're going to use this table approach to kind of make a compact representation of a system of equations. So we're going to take our N and we're going to put it in the top row and then to the right of it we're going to put our value for E. And then in that first column we're going to put N and then E again and then some ones and zeros. And here's what this all means. That first row is basically saying that in order to compute the value of N you're going to need one factor of N and zero factors of E and the second row is saying to compute the value of E you'll need zero factors of N and one factor of E and then sum them up. And here's the plan. We're going to use this representation to create new equations by subtracting multiples from the lowest or the last row in this table from the row above it with the goal of trying to reduce the value on the left hand side all the way down to one to eventually obtaining an equation that's in this form one equals X times N so X factors of N plus Y times E so Y factors of E. So in the table that would look like one on the in that first column with the numbers X and then Y in the same row. If we can do that then it turns out that that value in the table for Y ends up being the multiplicative inverse for E in the modulus of N. This is all kind of hard to wrap our heads around with these kind of variables in place. Let's work through an example that uses real numbers. So here's an example of the extended Euclidean algorithm will abbreviate that with EA and we're going to use the public key two thousand two hundred forty nine comma twenty nine thousand five hundred and sixty one. So those are the values for E and N and let's go ahead and set up our table. So we put the twenty nine five sixty one in the top row and then to the right of that the twenty two forty nine and then going down the first column again you put twenty nine five sixty one and twenty two forty nine with the one the zero the zero and the one and again that's just shorthand for this system of equations that we have on the right. I'm going to show all of these systems of equations as we're learning about this algorithm but it's very common that once you get used to it that you only need the table with the shorthand representation you're welcome to use either one but I think once you get the hang of this you'll really only need the representation on the left. So our first step is we want to take this bottom row equation and determine what multiple could I subtract from of this equation from the row above. And the way that we're going to do that is we're going to take the value on the left hand side of this twenty two forty nine and determine well how many times does that divide evenly into twenty nine thousand five hundred and sixty one meaning if I were to divide that what's the whole part of of the quotient ignoring the decimal and it turns out that twenty two forty nine goes in thirteen times with a remainder but it goes in thirteen times. So we're going to multiply every element in this equation so basically multiply the whole equation by the value of thirteen to obtain this new value I'm going to temporarily put this in the table it doesn't really go there as we'll see in a second but it's going to help for our calculation next. So we've created a new equation that's equivalent to the old equation we've just scaled it up by a factor of thirteen and now we're going to subtract off this new equation from the top row to create yet one more new equation. So we can do twenty nine five sixty one minus twenty nine two thirty seven to get three hundred and twenty four. We could also do one minus zero to get one. And we can do zero minus thirteen to get negative thirteen in our table. And I've written the corresponding equation to the right. And we'll go ahead and put back that original value in the second row. So we used some multiples of the second row subtracted off from the values in the first row to generate these new values in the third row. And the third row is still a true statement three hundred and twenty four is equal to one times twenty nine thousand five hundred and sixty one plus negative thirteen times twenty two forty nine. That's true. We don't know why that's helpful yet but we're going to see we're going to get there in just a moment. We're going to do the same thing. We want to think about now focusing on the new bottom row in the table. How many times can I multiply this equation by to generate a new equation where the product on the left is less than twenty two forty nine. So we can take twenty two forty nine divided by three hundred and twenty four. And we see that that goes in six times with the remainder. But that means we're going to scale this up by a factor of six. So I'll show that here now. Again, we'll take our bottom row of the table and subtract it from the previous row. So twenty two forty nine minus nineteen forty four gives us three oh five zero minus six gives us negative six and one minus negative seventy eight gives us seventy nine. And that gives us a new bottom row in the table. And again, you can check that that calculation is true. Three oh five is in fact equal to negative six times twenty two five sixty one plus seventy nine times twenty two forty nine. Again, this is not helpful for us yet, but we're getting there. Remember, the goal is that we want that left hand number in the table, whether in the shorthand version or in the elongated equation. We want that value to be one. It started at twenty two five sixty one. We've got it down to three oh five and we're going to keep working. OK, how many times does this equation go into the one above it? Well, three oh five only goes in one time cleanly, which means that we could just subtract this equation as is to get our next row. Three twenty four minus three oh five is nineteen. One minus negative six gives us the seven negative thirteen minus seventy nine gives us the negative ninety two. And again, there's the long version right up next to it. We're getting close. We want to figure out how many times does nineteen go into three oh five? It goes in sixteen times. And when you do that, multiply this up, subtract the bottom row from the second to last row. And here we are. We've got our equation we were looking for one negative one eighteen one five five one. And this is the equation that gives us the private key. That private key is at fifteen fifty one. So we'll verify that in just a moment. But if you were to encrypt a message using the public key of twenty two forty nine with a mod of twenty two twenty nine five sixty one, you now know that the decryption key on the other end is fifteen fifty one. They are inverses of each other. We've just found somebody's private key with only the public information. That's not what we want if we're going to use this system. Let's verify real quick that these two are inverses of each other. And to do that, we're going to use this long form equation, not the last row on the table, but the corresponding equation for the last row on the table. So let's take a look at it. This is going to be helpful for us. Here's why. If we take the factor that includes the twenty nine five sixty one. So that negative one eighteen times twenty nine five sixty one. And we add that term to the other side. So now we've got one plus one hundred and eighteen times twenty nine five sixty one. We know that's equal to fifteen fifty one times twenty two forty nine. That's the private key times the public key. At least that's what we believe to be true. Let's see why that actually is known to be true. If we take this equation and we reduce it mod twenty nine five sixty one. That left hand side is going to just boil down to one. Now, why is that? Let's take a look at that left hand side on the previous row. One plus some multiple of twenty nine five sixty one. Modded by twenty nine five sixty one. The larger numbers make it hard to think about, but let's take it down smaller. Let's imagine that was one plus twenty six. And we modded by twenty six. It shouldn't be a stretch for us to think about. Well, twenty seven mod twenty six is back to one. And if we did one plus two times twenty six, which would be fifty two. It's not hard for us to compute that. Yeah, one plus fifty two mod twenty six is back down the one and so on. So in that small scale system, one plus any multiple of twenty six. Once we mod by twenty six goes back to one. Same thing here is true. One plus any multiple of twenty nine five sixty one modded by twenty nine five sixty one is going to yield us back the number one. So now we have this statement. We didn't do the calculation on the right yet, but we can see on the left. It's going to be equivalent to one. And what is it equivalent to the product of fifteen fifty one, the private key in twenty two forty nine, the public key modded by twenty nine five sixty one. We have just shown that those two numbers are in fact multiplicative inverses in the given mod, and that is the only requirement for a key pairing in this system. So what we've shown is that we have an efficient way now to determine the private key from the public key. And that is made kid RSA insecure. And our next lesson we're going to look at how can we adapt the kid RSA algorithm to make it secure? We're going to need to do better, I guess, than trying to just rely on that it's hard to calculate multiplicative inverses. So you can take a minute and think about how could you make that more complicated? But that's it for now. Thanks for watching. We'll catch you in the next one.


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Like, I was just constantly putting the book down and just going... AHHHHH! Hi friends, welcome back to my channel. I hope you're well. Today we have a vlog which I have been so excited about for so long. I have three cats. And in my themed weekly vlogs, I typically read through books, so... See, I'm telling you, I have the mind of a mastermind. What's that? I don't know, but I'm so creative like that. What I decided to do is I'm gonna have my cats pick my TBR. So I have three cats, I've got three separate categories, and they're each gonna have three books to choose from. And so out of nine books, we're gonna be reading three because my cats have picked them. My cats all have very different personalities and vibes, so I've tried to match the book category to them. So first is Lux. And Lux is the laziest of all my cats. He sleeps constantly. I've never known a cat to just sleep all day.  He loves his mum, who is one of our other cats, and he also loves the kitten, youngest cat we have. Lux is just flamboyant, he loves having fun, but he also loves to sleep. And so because he's always dreaming, I thought I would get him to pick fantasy books. Because we have no idea what that boy is dreaming. But I like to think he's got some vivid fantasy plot line going on in his head. I'm gonna be getting him to pick between The Poppy War by L.F. Quang, The Never-Totting World by Rin Chipeco, and The Raven Boys by Maggie Stevewater. One, two, three. Is he blind? Gone for that one. He might make you wanna read some more. Do you like to be in front of the camera? He does. Why do you have to make one? Next is Rora, who is our oldest cat. She's the mum of Lux. Now Rora is vicious.  She's beautiful, but she's deadly. She's literally the most vicious.  So for that reason, I've gone with thriller. Because if Rora was a human, she would be living a life of crime. So for that, I'm getting her to pick between No Exit by Taylor Adams, The Family Upstairs by Lisa Jewel, and The Death of Mrs. Westaway by Ruth Ware. Hey, Rora. How you doing?  Can you see that? Treats. Rora, come on then. She's having a good think about what her favourite book is. Yeah. It's like it's between No Exit and The Family Up. Ooh. Ooh. She's gone for No Exit. So lastly is Miko. Miko is our youngest cat. We've had him for just over a year now. He's about a year old. Miko is a lot of fun. He loves playing. He loves just being a good boy. But he's not a good boy when it turns to night because this cat refuses to come in from the garden. He will hide. He will run. It is an Olympic sport. Trying to get Miko to come back inside. So I see him as the most wildly educated of all the cats because the other two just stay inside and sleep all day. Whereas Miko is out there learning, living his best life. So I've chosen non-fiction for Miko because although he or two are older I think he probably knows the most about the world. So I'm gonna be getting him to pick between Biased by Jennifer Eberhardt, Forgotten Women the Leaders by Zing Sheng and I'll Be Gone in the Dark by Michelle Mackinomara. Hey Miko. He smells cheesy. Nice. Look. Can you see the treats? No. Miko, go back. He's the smartest one. So quickly just to recap what was chosen. First Lux Chosen Every Tilting World by Rin Chepeko. I've heard so many people loving this recently. It's about a world that has stopped tilting and so half the world is permanently in the sun and so is like a desert and the other half is permanently stuck in darkness and is all ice and cold. And I think two sisters or goddesses play a role in this as well but I'm not completely sure but I'm very excited to get this one. I've recently hauled and I think it's always good to get to a book when you've just bought it because the excitement is still really fresh. Then for Thriller, Rora chose No Exit by Taylor Adams. So this is about a girl who pulls into like this kind of service station or stop during this snowstorm and she's stuck with I think four strangers and she goes out and she sees that one of the vans has a girl tied up in it. There's obviously been abducted or something similar and so she's trying to figure out which of these people she's with. She can't trust. And I think it's a very action-packed, fast-moving thriller. I think this is going to be the one I read first just because this has been one of my most anticipated books for the longest time. And I've been in a bit of a reading sub lately and so I just really in the mood for a thriller. And then lastly, Miko chose Forgotten Women the Leaders by Zing Sheng. This is when I've spoken loads about my channel but never actually read it. It's always in those like I need to read this book video but this is a series of books and this is the leaders and it has all this amazing artwork in it. What I love about this is that it has women of all colours of all different nationalities. It's a really, I think, hopefully I haven't read it but from just looking through it I think it's a really global look at the Forgotten Women Throughout History. I love learning about women's history and the women who have made an impact on the world throughout time that like have kind of been forgotten because our history curriculum, what we're taught in schools and what we know about history is so just focused on men. I'm going to cooperate. I'm so stressed. I'm so stressed out by this book. I can't do it! I can't. You are stressing me out. I can't do it. It's not a who done it. You find out pretty early on who the main suspect is. The question is whether she can defeat the evil, whether she can trust everyone else who's at the rest stop, whether she can be ingenuative enough. This has been ingenuative so far. I've got to say, she's been, you know, pulling out the bag so far. My heart rate feels like it's at an all-time high. I have a feeling it's only going to get worse. That's the thing as well. Like, things are just starting to turn. It seemed like I was 100 pages in and I was like, right, she's got this. She's fine. She's going to do it. And then, Curveball just came. Plot twist. Oh, guys, I'm stressed. I am so stressed. It's only going to get worse. It's only going to get more stressful. Like, we were hopeful. We were hopeful. We've crested the tip. And it's only going to, I just like it's only going to go downhill from here. I'm not ready. It's such a page turner. So if, like me, you're in a slump, this is the perfect book to just come and like rip you out of that slump. I'm so happy that Aurora picked this. Aurora obviously has taste. Never have I read a book and been so stressed out. I was at, for most of this, like a stress level 10, a danger level 10.  And then about 200 pages in, we went up to a stress 11. And then we went up to stress 15. I think I've actually been getting chest pains and irregular heart patterns from this book. The past two days, like my heart has been hurting. I've been getting heart palpitations. Just thinking about this book. It was so good. Aurora pulled through. So we all gag nation on this. The pacing in this book, absolutely incredible. The things that Darby is able to do, the trick she pulls out the bag, the sacrifice she makes, the heroic she pulls girl I could never. Oh my God, this book. I have been so stressed out while reading it because sometimes with other thrillers, or at least with other thrillers I have read, you have moments of respite, right? There's like periods of not normalcy but not high stakes, high action moments. But in this, you're constantly, constantly on the move, on the go fighting. Like it's so quick and so full on and so extreme and so life or death throughout the whole book. At times I couldn't take it. Like I was just constantly putting the book down and just going, like that. Just constantly. Every three pages. I'm talking about Megan right now and I'm like, oh my God, look what's happening. And he's like, Megan, it's not real. I'm like, I don't care. They're living rent free in my head. But my emotion, and I was just in so much trauma. I was in a shock trauma as well. All the shock, it was like delayed shock. Oh my God. The way it looks at male entitlement as well, I found was a really interesting theme that we got to explore particularly towards the end. The ending, I almost cried. Like I almost cried. I actually think this has raised my blood pressure. I don't even know what that means, but I think it's right. I love, I love in thrillers isolation. I love it. I love when we have a select cast of characters. We are stuck in this place together. We know I love that. All the thrillers I love have that element. Oh my God, my God. It's like you are at 100 miles per hour the entire book. Darby. I want to call my kid Darby now. I'm not even joking. I'm trying to figure out how I'm going to broach the subject with Tom that we've got to call any daughter we have Darby because of what this girl did. Is that weird? She is one of my favourite protagonists now. So Nina's to say I'm giving it five stars. So I've started Lux's Pick, which was The Never-Torting World by Rinchepeko. I'm just over a hundred pages in, so I'm just under a quarter. I've only read that much. I'm like not into it yet. Is that true? It's very true. Which is really sad, I thought it would be the kind of thing that I'd be into straight away. So we have the two worlds, not the two worlds, the two kind of lands, and we're following two perspectives in each of them, so four in total. So essentially you have this world that's been split in half, and a goddess rules each, and each of those has a daughter. And so two perspectives are each of those daughters, and we have two other perspectives as well.  And then the other one is a kind of, she's a kind of like a healer to the goddess now, and they had been meeting up and like going on dates, but she didn't know she was the goddess. She thought she was just like a normal girl. I'm just an ordinary girl. And we're like cycling through them. So we're going like one, two, three, four. One, two, three, four. At least that's what's happening at the moment. So I'm on, I'm just about to start chapter seven, which will be the third perspective for the second time. But what that means to me is like, I'm just not getting particularly connected to the world or any of the characters. There's so many characters in this. And I enjoy when a book is ambitious and has a ton of characters, but they've all just been thrust upon me. But I feel like I'm getting a different sense of world building throughout each character's eyes, if that makes any kind of sense. And I also feel like I can't imagine at some moments what is going on. Like I can't picture it in my head. That's so upsetting. I will say that when I pick it up, I feel like it's quite readable. I'm just like not fully into it in the way that I want to be. However, I need to get into it because I need to finish both of these books by tomorrow night to finish this and Miko's pick, which was Forgotten Room and the Leaders. You pick this book out. What do you think of it? Yeah, you still like it, don't you? So I had to come inside. I was reading outside. Lois on my knee, but it's already every talking to myself. In terms of the never tilting world by Rinchpeco, I am just over halfway and on page 270, so I've got this much left to read, which considering it's like 2 o'clock in the afternoon, I think that's pretty good. I'm still not obsessed with it. I'm still not completely in love with it. I have a few problems, and then we'll get into the things I like. We have those four perspectives that I spoke about and two of the perspectives are together in the half of the world. So it's a continuous story. You're just switching perspectives between the two. So it meant that we were coming back to that plot for quite a while. But it was until about page, I say 120, maybe even a little bit further in that the other two plots met up. So until then, we were following kind of separate stories. And although it was interesting to learn about these two individuals, it just meant that I wasn't connected to their side. They're in the sunny, deserty part. And I felt like that was a subplot to the other two perspectives, which I still kind of feel like in a way. And in terms of the two perspectives that I was enjoying more, they knew each other and were in a relationship before the book started. And then their plot in this one is kind of them, there's a lot of tension between them. There's been a lot of lies in that relationship.  And they're putting a situation which is really difficult for them. But it means that we haven't seen them happy together, which is kind of like, I just stop arguing. It just feels like I have read 270 pages and they haven't made any kind of progress in their relationship and in terms of liking each other again. There's a lot of monsters. Monsters constantly appear and we fight them, but it's like overly fast. And another problem that I have with this is that I just can't picture it. Usually that's a sign of a bad book and I don't think this is a bad book. There's just something about the writing style that means at times, particularly in the really high conflict in the fight scenes, I sometimes am struggling to picture it. At one point, I felt like the plot was very similar to Kendall and Kylie Jenner's book, which I'd hate it. And obviously, Rinchpeco is a wonderful author and it's not Kendall and Kylie Jenner. This is awkward. But like that time has passed, but I had to be upfront. And at one point I was like, this is just the plot of Kendall and Kylie Jenner, but it's not. We've moved past that. But things I am enjoying, I do really, really like the writing, even though I'm struggling at times to connect and to visualise, I enjoy the writing for what it is, if that makes sense. I can see why someone else would love it. I'm just sad that I'm not loving it as much. However, there is a plot twist coming. I think that if it happens, I will live for. I will absolutely live for it. It's a spoiler, so I can't say. And I will just be obsessed if that happens. It will be like a stroke of genius if what I think is going to happen happens. Keep saying it. Just keep saying it. Keep saying it out loud. And maybe you will convince hope. I have also started Forgotten Women the Ludas. I think this is quite a good thing for me to pick up when I'm like a bit fed up of this. I love this already. Learning about these women and their lives and about these women that I've never heard about before is just wonderful. And did you know that women only make up half a percent of history? I just finished The Never-Tilting World by Ren Chepeko. I'm going to give this three stars. Gah! Gah! Gah! Gah! Gah! My issues that I'd already spoken about just continued throughout the book for me. The thing that I wanted to happen, I was like, oh, I'll be so happy if that happens, did happen. But not quite to the extent that I wanted it to. It kind of backtracked right at the end from the direction I was hoping it would go. And I just felt like it was a bit of a wimp move. Like I think we should have just gone all the way. I would say I think she's really good at writing romance and like steamy scenes.  Maybe one of them was a sex scene, but it's very tame. Like it's not vivid. This is YA. But she's good at writing that romantic relationship. And it meant, through the romantic relationship, particularly with the characters, I said I didn't connect to as much. I connected to them much more towards the end. Actually I ended up preferring them in some ways, which was interesting. The main thing that I have discovered from this is that I don't like books when it's split between two different storylines. I was thinking about it, and I didn't like it in Next Year in Havana, which I just didn't like that because of a whole, but I think that was a reason as to why I didn't like it. And although I gave it five stars, I really didn't like it in Obsidio. Obsidio's the third in the Illuminae files, and that's one of my favourite series, but Obsidio is probably my least favourite from that series. So I've just come to the conclusion that I don't like books where we are half and half between two different storylines. I just think I struggle to connect to the characters in the way that I want to. I struggle to connect to the storylines. I struggle to keep engaged. I just like a continuous narrative, whereas when it's like this, it feels so broken up to me that's going back and forth. And so me giving this three stars, I always rate based on personal enjoyment. And so I think this is a really good YA fantasy. If you don't mind that, but I think I've noticed a pattern and I think that's something I really don't like in books. So I just shouldn't pick up anything with that stylistic feature. That's right. Although I'm giving this three stars, that's not me saying it's a bad book. I would really be interested in reading anything that else that Rintpeco's written. And so now I am going to finish Forgotten Women, The Leaders. It's currently just past nine, but I am 56 pages into this and it is 200 pages. So that means I've got 150 pages left. But as we know, there's a lot of pages where the whole page is taken up by an illustration. So at the moment, I'm not too worried about finishing this. For me, this is like the perfect nighttime book. I was so excited to read this tonight because I often fall asleep watching history videos. It's so weird. We are going to pretend we didn't hear that. I've spoken before how much I love this channel by a woman called Lindsay Holiday. And like when you watch it, it's the cheesiest, weirdest history. But Lindsay Holiday is a queen in my opinion and that's often the video I put on when I'm about to go to sleep because it's just easy. Like her voice, it just sends me to sleep. But this was Miko's pick. And he's been hanging around in my room the whole day and he's just left. He's like, Bitch, I've been waiting for you to read my pick. I'm leaving now. Give it up. When little does he know I'm about to re-get into it. Linda's this morning and I'm going to give it four stars. I really, really enjoyed this and I would definitely recommend it if you're looking to learn about women from all over the world in so many different time periods. I just loved this. I think though I couldn't give it five stars because there were some stories I was just more engaged with than others. I think non-fiction it's always very difficult to give it five stars especially something that isn't giving you a message necessarily. This is just like history. I just loved learning about these women. There were some women that I had some knowledge about already and there were a lot that I had no idea about and it was good I think to have that mix where some of them I was able to draw on previous knowledge and then others were completely new to me and I was learning about this woman that I'd never heard before. Miko picked a good one. I really enjoyed it and yeah I would really recommend it if you want to learn more about the women the history has forgotten and the art throughout all of this was just incredible like the art was amazing and a real highlight. I mean like isn't that so pretty. So thank you so much for watching this video I hope you enjoyed it hopefully maybe I'll do it again soon. My cats will pick what I read again but yeah it was just a bit of fun and I liked filming them even though they didn't like it they really didn't like me taking a thumbnail for this video they were like this ain't it not this not this I hope you enjoyed the video I will see you very very soon with another one bye


Hello, fellow fragrance lovers. It's Hila here on Age Loves Fragrance. So today I'm so excited to be doing a tag video from one of my most favorite perfume YouTube channels, Clare Smith. And the tag is called Matching Perfumes to Dresses. I first saw it when she released the video three weeks ago and it looked like so much fun. And if you haven't checked out Clare Smith, do go check out her channel. She's amazing, so knowledgeable about perfumes and she does a lot of fun and interesting videos. So, I decided to do this. At first I was initially hesitant because I do make my own clothes. I very rarely actually buy any clothes now. I've been sewing my own clothes for the past seven years. But you know what? I thought even if I can't reference Max & Spencer's or Bowden or any of those other fancy places, I still can talk about the perfumes and what I like to wear with them. So let's jump straight into it. I have five perfumes and five outfits to share with you. So I'm going to start off with a chilling out cozy Netflix at home kind of outfit. And this is a really oversized, comfortable sweater hoodie that I made for myself using some lovely, really florally fabric. Because I do love florals and I wanted something nice and thick and cozy to wear in winter. And the perfume that I like to wear with this is fancy. Now fancy is such a gorgeous perfume. And even though it starts off super sweet and strong and fruity, give it time because the dry down is much calmer. It's still sweet but in a vanilla dessert kind of way. The heart has a pink floral blend but it is not too distinct. But it is the end where it becomes a woody musk that's laced with caramel and a lingering scent of burnt sugar is absolutely beautiful. And for me this is perfect for just chilling at home, watching Netflix with the kids. So that's fancy from Jessica Simpson and an oversized hooded sweater that is just soft and cuddly. The next outfit that I have is a dark winter floral dress. It's got a fitted bodice and a gathered skirt. And I love the style of dress. I have made about 10 of these types of dresses but using different fabrics. But for winter I love the dark winter floral. And for this look when paired with knee high boots and tights, I love wearing it with Adam Levine for her. Now Adam Levine for her opens up with saffron, citrus, marigolds and spices. Is it a coincidence that I like this fabric as well that has got some oranges to it? I don't know. But the dry down is quite musky sandalwood and it's got jasmine in it. There's a spicy woodiness that is perfect for the cold weather. Even though the longevity is a few hours on me, it is a fragrance that I think is literally impossible to over spray. And I have the opportunity to just really spray loads of it on me. So this is how I see Adam Levine for her that it would be perfect for a lovely dark winter floral dress like this one. The next winter outfit is a little bit more dressier but I love this style. It's got a flare skirt and it's layered with a turtleneck and an off-shoulder top over the top. And I love to wear this with brogues. I love brogues and I've got a huge collection of brogues. And for me this outfit goes really well with la vie belle. I love Lancome's la vie belle. It opens up with a fruity pear and black currant. There's a tonka being mixed with the chocolate praline and jasmine. And let's not forget the orange blossom. I love the orange blossom in it. The dry down has got the patchouli and the chocolate accord. It's gentle. It's warm. It's elegant with poise. And that's how I feel when I'm wearing this particular outfit. So that's la vie belle with this layered skirt look. Up next we've got a midi-lamp A-line flare skirt that I've made in a scuba fabric. And I like to wear it with a black turtleneck. And I feel very elegant in this outfit especially when I wear it with my knee-high boots. And I think Givenchy and Linda Dee is perfect for this outfit. And in fact every time I wear this I do put on Linda Dee. I love Linda Dee for its pear, caramel and vanilla coupled with the freshness of bergamot. And it's got a rich white floral to it that comes from the tuberose. And it has this dark undernodes of vetiver and patchouli. And to me Linda Dee is dark. And I tend to find that I love wearing it with anything that's got a black turtleneck in it. So for this outfit, Linda Dee from Givenchy. For outfit number five which is a sheep dress that I made in a scuba jersey fabric, I chose Sarah Jessica Parker stash. Now I love stash. It is a soft creamy, tranquil fragrance with a really beautiful green note to it. It's sadder and it's got a boozy woodiness with it. Vetiver is in there which gives it a lovely dryness and it is so satisfying to the senses. With notes of grapefruit, black pepper, sage and ginger lily, it is so lovely and it's so perfect for the winter. And I do find that I reach for it a lot especially when I'm wearing this sort of simple style outfit. And I would normally throw on an oversized cardigan. And I just feel really cozy when I am wearing this. So that's Sarah Jessica Parker stash. So those are my outfits matched with perfumes. Thank you so much Claire Smith for creating such a fun tag to do. So this is my winter edition. And again as I say guys, if you haven't checked out Claire Smith's channel, go and check that channel out and subscribe. She is just so much fun to watch. Thank you so much for watching. I appreciate you staying until the end. And I hope that you enjoyed the video. Please do give it a big thumbs up down below. It really helps the channel. And if you're mad about perfumes and you find perfume as much of a never-ending fascination as I do, then please hit that subscribe button and join along the fun. Until I see you next time guys. Take care. Bye.


Israel is deliberately keeping the humanitarian aid, and it's difficult as possible. And we are fighting with time right now. We have a very little time, and we have 1 million people, 50% are in severe danger. So my guess is they are trying to make them leave, but there's no place to leave.


It is common knowledge that FM radio is affected less than AM by the many electrical disturbances that cause interference to radio communication. The technician, however, wants more than common knowledge. He must know why and how. But before studying FM, the fundamentals of AM should be reviewed. You will see why the problem of interference exists in high frequency AM and then learn how FM has reduced it. Let us review in detail the separate actions which take place in an AM transmitter. The information or intelligence to be transmitted starts as sound waves which travel through air. The microphone picks up these waves and transforms them into electrical energy. Now the intelligence travels into the transmitter, taking the form of audio frequency voltages. Audio frequencies in military equipment generally fall within a range of from 300 to 3,000 cycles per second. However, it is not practical to transmit these audio frequencies directly. An oscillator provides a much higher frequency. This radio frequency wave is called a carrier. By means of a modulator and one or more RF amplifiers, the amplitude variations of the audio signal and the radio frequency carrier are combined. Now the radio intelligence takes the form of amplitude variations in the carrier. The amplitude modulated RF carrier is fed to the antenna from which it is radiated through space to the receiving antenna. Once the signal has left the antenna, however, it can be affected by many disturbances. For example, one such disturbance can be lightning. Let's please the signal at the receiver antenna and see what the interference has done to it. Our primary concern is with the amplitude variations, for they carry the intelligence. To a point, the variations are just as we transmitted them and the AM system was working fine, but the lightning has added new variations. These are superimposed upon the variations carrying intelligence. There are many manmade devices and natural elements or occurrences that can affect the amplitude of the RF carrier. Each one adds more hash, more static, more interference. Before considering the AM receiver, notice one fact. The electrical disturbances alter the amplitude of the RF, but they have no effect upon its frequency. An important point to remember is that the distance between each wave is identical. The receiving antenna will pick up both the composite RF waves from the transmitting antenna and the random noises generated by the lightning. These two will combine and distort the amplitude of our desired signal, but the frequency we transmit is unaltered, unaffected by disturbances. Now a partial review of what happens in the AM receiver. The amplitude-modulated RF carrier is picked up by the receiver's antenna. The receiver extracts the intelligence carried by the RF, transforms it back to an audio signal, amplifies it, and feeds it to the speaker. It emerges from the speaker as sound waves, which can be heard and understood by the human ear, unless the intelligence is smothered by interference. To see how interference gets through to the speaker, one of the receiver components, the detector or demodulator, must be examined. The detector receives the RF and transforms its amplitude variations into corresponding audio voltage variations. The detector does its job well, but blindly it cannot think or interpret. Faded an RF signal with constant amplitude and there will be no output signal. Faded a modulated RF and it will provide an audio signal which mirrors the amplitude variations of that RF. Faded an RF signal that has been hashed off by interference and the audio signal will contain an accurate reproduction of that same interference. The audio signal mirrors the interfered RF signal fed into the detector. There you have a major disadvantage of AM radio. It is unable to separate the intelligence from the hash and static that appear when conditions are unfavorable. The FM radio is not a miracle. It was in fact a logical development, a natural step forward in electronic evolution. Now some of the facts about the evenly spaced unmodulated RF carrier observed in our review of AM can be utilized. Interference does not affect the frequency of the RF carrier wave. Therefore, when intelligence causes the frequency of the carrier to change, the problem of hash and static is automatically eliminated. In frequency modulation, the frequency of the carrier is modulated as evidenced by the uneven spacing of the wave rather than the amplitude. An unmodulated carrier would be the same for FM as it is for AM. It has constant frequency and constant amplitude in its unmodulated condition. The carrier frequency which is determined by the oscillator is called the rest frequency. So long as there is no audio signal, the carrier is unaffected. But see what happens when an audio signal is applied starting with the negative half cycle. For this illustration, the negative half cycle causes the carrier to drop below its rest frequency as evidenced by the wider spaced wave. When the positive half cycle of the audio signal is added, it causes the carrier to rise above its rest frequency as evidenced by the narrow space wave. This is an audio signal of one complete cycle with a corresponding frequency modulated RF wave underneath it. A variation of the amplitude in the audio signal is accurately reflected by a frequency variation or modulation in the RF carrier. The negative half cycle of the audio made the carrier drop below rest frequency and the positive half cycle of the audio made the carrier rise above rest frequency. The carrier's ability to reflect the amplitude of the audio signal can be easily visualized. But how will it record changes in the frequency of the audio signal? This question can be answered by changing the frequency of the audio signal and observing the result in the carrier. If the frequency of the audio signal is doubled, then in the same period of time, there will be two complete cycles instead of one. Note that the amplitude of the two cycle audio signal is the same as the amplitude of the single cycle audio signal. Now let's see what this has done to the carrier. As before, the carrier responded to the amplitude of the negative half cycle by dropping below rest frequency. And the carrier responded to the amplitude of the positive half cycle by rising above rest frequency. Thus, the carrier has moved above rest frequency twice as often in the same interval of time. And the carrier has moved below rest frequency twice as often in the same period of time in response to the doubling of the audio signal frequency. But since the amplitude of the audio signal was not changed, the distance above and below rest frequency traveled by the carrier has remained constant. The relationship of the audio signal and its carrier can be observed even more clearly by studying a typical military FM channel. Just where in the radio spectrum are FM channels assigned? The nature of FM normally requires a greater band width than with AM. Therefore, FM communication channels are normally assigned above the medium frequency band. A typical FM channel, 40 megacycles, would be located here. This is the rest frequency of the channel. When the carrier is frequency modulated, it will move above and below its rest frequency. In other words, it will need room on the spectrum to carry its frequency variation. A typical amount of room might be 15 kilosecels above rest and 15 kilosecels below rest. To avoid conflict with adjacent FM channels, 10 kilosecels guard bands are added on each end. This typical channel will allow the carrier a 15 kilosecels deviation above and below its rest frequency. Add to this the 10 kilosecels on each end for guard band and the total band width is 50 kilosecels. The 50 kilosecels band width is not a standard. All FM transmitters do not have the same deviation. It will vary in accordance with the equipment's design and mission, but the principles under study apply to any and all FM transmitters. Ordinarily, an audio frequency wave is visualized horizontally like this. But in order to see more clearly its modulating effect on the carrier, let's shift it about and direct it at the channel. Notice that the amount of deviation above and below rest frequency is determined by the amplitude of the modulating signal. If we raise or lower the frequency of the modulating signal, we increase or decrease only the speed at which the carrier moves above and below its rest frequency. We do not change the extent of its deviation. Only by changing the amplitude of the modulating signal do we change, decrease or increase the extent of deviation above and below rest. FM circuitry is designed so that maximum amplitude of the modulating signal will cause the carrier to deviate to the maximum frequency range assigned to it. Note that this does not include the guard band, or in other words, the carrier will swing as far above and below its rest frequency as it can go. And this brings up another point, percentage of modulation. In FM, 100% modulation is achieved when the carrier reaches full deviation. If the amplitude of the modulating signal is lowered so that the carrier deviates only 25% or one quarter the frequency scale allotted to it, the carrier is said to be modulated 25%. Percentage of modulations in FM, therefore, refers to the amount of carrier deviations in relation to the total frequency range or range of deviation allotted to the particular FM channel. Here you see visualized a voice comprised of different frequencies and amplitudes. In actuality, of course, the actions we are looking at occur in time intervals as small as many millionth of a second. We have slowed them down considerably, and we are not viewing them in their exact ratios, but the principles you see demonstrated here are correct. Now that we are familiar with the basic principles of FM, let's make a quick rundown of the components that make it possible. The transmitter's components are similar in name to their AM equivalent, and they do similar jobs, but in a different way. The audio circuit provides the audio frequency signal, which is fed to the modulator. The action of the modulator is such that the output of the oscillator is a frequency modulated RF wave. The components of the FM receiver are a bit more complex, for they have an additional factor to contend with. The incoming carrier contains intelligence in the form of frequency variations, but it also contains amplitude distortions, hash, and static, these we do not want. Since these distortions are located along the amplitude peaks of the carrier, we can eliminate them by eliminating the peak. This is accomplished by a circuit that clips the peak by limiting the amount of current flow induced by the positive and negative alternations of the carrier. This stage is called a limiter. Its output is a wave that still carries the intelligence in the form of frequency variations, but it no longer includes the extremes of amplitude that carried any interference picked up during transmission. The next step is to extract the intelligence to change the frequency variation back into audio frequency voltage variations, which we can then amplify and feed to a speaker. In an FM receiver, this is the function of the demodulator or discriminator. You might say that the discriminator in FM is the rough equivalent of the detector in an AM receiver. Save the frequency modulated carrier into the discriminator and its output will be an audio frequency voltage. Feed it an RS signal with constant frequency and there will be no output signal. All FM discriminators do the same job, but not all do it the same way for a briefing in the fundamentals of the discriminator. Let's take a simplified look at how this typical discriminator does its job. We are primarily concerned with two things, the wave and the discriminator. In place of the wave, this vertical line will represent the range of input frequencies to the discriminator. This horizontal line represents the frequency range of the carrier. It also will represent rest frequency. This line will represent the maximum deviation above rest frequency, and this line will represent the maximum deviation below rest frequency. On this scale, we will see the frequency of the carrier as it arrives at the discriminator. Now we'll add another scale. This one will measure the voltages of the audio frequency signal coming from the discriminator's output. We'll add three dotted lines. One will represent zero voltage. A second line will represent peak positive voltage, and a third will represent peak negative voltage. When the carrier is at rest frequency, the audio output voltage of the discriminator will be zero, thus an unmodulated carrier results in no audio signal. For this illustration, when the carrier deviates above rest frequency, the circuitry of the discriminator generates a positive voltage. When the carrier drops back down to rest frequency, the positive voltage gradually diminishes. When the carrier deviates below rest frequency, the discriminator responds with a negative voltage at its output. When the carrier moves back up to rest frequency, the negative voltage diminishes to zero. Now watch the continuous action. Note that the amplitude of the audio signal is an accurate reflection of the amount of the carrier's deviation above and below rest frequency. Also note that the frequency of the audio signal is an accurate reflection of the rate or speed at which the carrier registers its deviation. Thus, the audio signal's two characteristics, its amplitude and its frequency, are an accurate reflection of the carrier's amount of deviation and rate of deviation. In this way, we have transformed an RF carrier's frequency variation back into an audio frequency signal. From the discriminator, the audio goes into an audio amplifier and from there to a speaker or headphones. The intelligence has completed the trip from transmitter to receiver. Let's review what we've learned about FM principles by constructing an animated diagram that illustrates those principles in action. Let this vertical line represent the high frequency portion of the radio spectrum. Another point of our FM channel will be at a particular frequency. This is called the carrier's rest frequency. The bandwidth will include an equal amount of frequencies above and below rest frequency. In addition to including a range of frequencies above and below rest, the channel will also include two guard bands on either end for channel separation. The carrier can be deviated above and below its rest frequency. The extent of carrier deviation in kilocycles will depend upon the particular equipment in use and the bandwidth assigned. These factors will vary with the type of equipment and their particular mission. Percentage of modulation is rated on a simple basis. The percentage of modulation is simply the amount of deviation in relation to the total. For example, the carrier might be modulated 25%, 50%, or 100%. 100% modulation occurs when the carrier deviates to the maximum frequency above and below rest. The transmitter audio signal shown here modulates the carrier frequency. The audio signal crosses the frequency to go above and below rest. This same FM signal arrives at the receiver as its peaks clipped by the limiter and its frequency variations changed to an audio frequency signal as shown by the receiver audio signal. Note that the receiver audio is an exact replica of the transmitter audio signal free of interference. The FM principle of radio communication demonstrated here is a practical useful technique. It has made FM radio equipment an important part of the Army's overall communication picture. Due to the frequency at which it is normally operated, FM transmission is primarily utilized for short-range line-of-sight communications. This is just one reason that FM should not be thought of as a miraculous device that will obsolete all other types of communications equipment. FM and AM will both be around for some time to come, for each still has important work to do. The FM radio has limitations as well as capabilities, but for short-range communications in the air and on the ground. For a radio link that can guarantee clarity even when conditions are unfavorable, the FM radio is invaluable. Thank you.