1 00:00:01,230 --> 00:00:06,990 Now, in this video, we are going to talk about this artist and this artist are going to miss a small 2 00:00:06,990 --> 00:00:07,140 talk. 3 00:00:07,230 --> 00:00:13,350 So that means we will use one key for encryption, another key for decryption at encryption. 4 00:00:13,350 --> 00:00:22,740 The Keys, public and private and public debate is used for encryption and private companies for the 5 00:00:22,740 --> 00:00:22,900 group. 6 00:00:23,100 --> 00:00:30,660 So we need to allow us to generate the public and say we need to to the private and the public can be 7 00:00:30,660 --> 00:00:31,620 known to anyone. 8 00:00:31,830 --> 00:00:37,180 And this private key should only be known to the person who is decrypting our ciphertext. 9 00:00:37,620 --> 00:00:40,560 And these algorithms and raising those are the prime numbers. 10 00:00:40,770 --> 00:00:46,350 Standardly, you need to search the large numbers and we will see why you need to sell the numbers. 11 00:00:47,160 --> 00:00:54,340 And if you choose the smartphone and it will be easy to brute force are cracking. 12 00:00:55,470 --> 00:00:58,190 So the algorithm is here just for us. 13 00:00:58,650 --> 00:01:05,430 We need to start two prime numbers and SIPI and keep and we need to find and value be in the clear. 14 00:01:05,790 --> 00:01:08,610 So that is my definition of those two prime numbers. 15 00:01:08,940 --> 00:01:12,180 Next, we need to find that you will push and function that is powerful. 16 00:01:12,540 --> 00:01:15,180 Powerful is defined by B minus one in particular. 17 00:01:15,200 --> 00:01:23,550 And so actually this function Testor, if you find the if you want to find the function of the number, 18 00:01:24,120 --> 00:01:33,210 you need to select only the numbers that are not divisible by that number for a number function is defined 19 00:01:33,700 --> 00:01:39,690 as what we want to find for this in the toilet function is P, Q minus one. 20 00:01:41,320 --> 00:01:48,220 We have to duty and we need to assume undervalue such that DVD of this is no value and profit should 21 00:01:48,220 --> 00:01:54,850 be one that wins British government should be one that means there is there must be no other number 22 00:01:55,120 --> 00:02:01,570 that this isn't offer and which concludes that ENP often should be prime to each other. 23 00:02:02,080 --> 00:02:03,480 So that's what it is. 24 00:02:04,140 --> 00:02:10,630 Assume no such that this prime number and this parliament should be the prime to each other and the 25 00:02:10,630 --> 00:02:11,100 public. 26 00:02:11,110 --> 00:02:13,110 E e come on. 27 00:02:13,120 --> 00:02:14,790 The speed is culpability. 28 00:02:15,490 --> 00:02:22,940 If we assumed the prime number that is in cooperation with Parliament and the public e e come on. 29 00:02:23,320 --> 00:02:26,920 And we need to conclude the presidency, how we get the private comments. 30 00:02:28,000 --> 00:02:30,580 This expression gives us the priority. 31 00:02:31,720 --> 00:02:36,910 We need to set a date such that be into modulars profit is equal to one. 32 00:02:37,120 --> 00:02:39,950 So we have got already the value of it and the payoff. 33 00:02:40,390 --> 00:02:47,950 Now we want the world to play one to find the multiple of such that if you divide it by often, you 34 00:02:47,950 --> 00:02:48,970 should get the one. 35 00:02:51,520 --> 00:02:55,630 All right, then, after getting ready, where do the priorities become when? 36 00:02:58,100 --> 00:03:05,420 So we have got the public and the private, public and private is the government now what we want to 37 00:03:05,420 --> 00:03:08,200 do is to find a ciphertext from the gun prints. 38 00:03:08,570 --> 00:03:16,370 Well, I hope you find this plaintext party, Madison, and and we get the ciphertext that we need to 39 00:03:16,370 --> 00:03:25,340 develop, which is the priority beyond our priority keeper and ciphertext party into Martin, which 40 00:03:25,340 --> 00:03:26,330 gives us a pretext. 41 00:03:26,600 --> 00:03:30,040 So if this seems confusing, let's see an example. 42 00:03:31,280 --> 00:03:35,280 So I'm going to show you what not OK. 43 00:03:35,370 --> 00:03:37,820 My handwriting will be better because I'm using. 44 00:03:39,140 --> 00:03:43,550 So let's take the easy calls to fight. 45 00:03:44,120 --> 00:03:46,170 And Q is equal to seven. 46 00:03:47,450 --> 00:03:48,970 So these two are prime numbers. 47 00:03:48,980 --> 00:03:55,130 I have taken P and you know what you want to find and value how you get and value. 48 00:03:55,130 --> 00:03:58,990 You need to be in the Q five and certainly to Stuttaford. 49 00:04:03,540 --> 00:04:07,740 Now, what we're going to do is we want to find a what is your consent function? 50 00:04:08,900 --> 00:04:10,580 That's a pile of. 51 00:04:13,410 --> 00:04:18,030 Because people are responding, because that means for 26, 24. 52 00:04:20,620 --> 00:04:27,510 So I'm taking the normal lesson on lesson number because I just want to keep the calculation simple 53 00:04:28,660 --> 00:04:31,630 and we have to use to the degree of come up. 54 00:04:31,660 --> 00:04:35,200 Your friend is an artist and your friend should be proud to each other. 55 00:04:35,710 --> 00:04:38,680 Let's say easy calls to what? 56 00:04:38,830 --> 00:04:40,430 A lot of news 24. 57 00:04:41,260 --> 00:04:42,420 So that's. 58 00:04:44,910 --> 00:04:56,220 Equals to five equals to fight scenes in 24 hour around each other, and the greatest commander is for 59 00:04:56,220 --> 00:05:03,630 these numbers will be one because there are no common orders except one. 60 00:05:04,860 --> 00:05:07,160 So we have got our public debate, which is. 61 00:05:14,080 --> 00:05:17,270 It is five Kamahl thirty free. 62 00:05:20,150 --> 00:05:26,080 Now we need to develop and care. 63 00:05:27,240 --> 00:05:29,070 We have already seen be in. 64 00:05:34,930 --> 00:05:39,670 B into E, which is five. 65 00:05:42,780 --> 00:05:54,210 More powerful payoff in values to default rate from default is equal to one, so after this, we get 66 00:05:54,210 --> 00:05:55,160 the debate. 67 00:05:55,170 --> 00:05:56,360 You can do that. 68 00:05:56,370 --> 00:05:59,440 I'm going to use it online tool online. 69 00:05:59,940 --> 00:06:00,290 OK. 70 00:06:03,170 --> 00:06:10,260 So we need to find the inverse MODULA to get the value of the so I'm going to use this website Let's 71 00:06:10,280 --> 00:06:19,300 Dinty that we want to play a serious fight, at least 24, because it's five models from before. 72 00:06:20,360 --> 00:06:23,180 Let's calculate so we get right. 73 00:06:23,510 --> 00:06:26,580 So if you multiply five and fight, we get twenty four. 74 00:06:26,850 --> 00:06:34,490 If you do it with twenty eight, you get if you get down to this fight, if you multiply, fight and 75 00:06:34,490 --> 00:06:35,570 fight, you get quantifier. 76 00:06:35,750 --> 00:06:45,380 If you want to divide it with a good reminder that these models were so our divide, you use fight which 77 00:06:45,380 --> 00:06:52,620 satisfies this equation perfectly because for you to fight, quantify what you're going to want. 78 00:06:53,660 --> 00:06:55,970 So we have got the private key. 79 00:07:00,030 --> 00:07:01,350 So it is Decameron. 80 00:07:02,220 --> 00:07:04,650 So, for example, what is an. 81 00:07:09,810 --> 00:07:17,370 So you can see we got the same Evalu and Disvalue, but in rare cases we get like this. 82 00:07:17,890 --> 00:07:23,650 So in order to calculate the ciphertext, I imagine it's Citizen Stansel ciphertext. 83 00:07:24,090 --> 00:07:31,520 So first I want to let you take a no go Compte for. 84 00:07:32,670 --> 00:07:37,610 OK, let's take a small number for easy calculations that let's take seven. 85 00:07:37,730 --> 00:07:38,830 Here's the plain text I want. 86 00:07:38,850 --> 00:07:41,940 And so in real world, you need to send the message right. 87 00:07:42,270 --> 00:07:44,910 You can encoded into the hex. 88 00:07:45,030 --> 00:07:51,360 You can decode that as kitching into that hex format and then you can convert that into integer. 89 00:07:51,540 --> 00:07:54,320 So we see in it. 90 00:07:55,130 --> 00:07:56,520 And another example. 91 00:07:56,520 --> 00:07:57,190 I like that. 92 00:07:57,530 --> 00:08:00,920 So let's assume that my brain is seven. 93 00:08:01,410 --> 00:08:03,720 So how to convert the prediction. 94 00:08:03,720 --> 00:08:06,140 The ciphertext brain Darkspore Madison. 95 00:08:08,310 --> 00:08:11,700 And seven E, which is five. 96 00:08:13,090 --> 00:08:14,690 My guess and. 97 00:08:16,640 --> 00:08:24,990 It is 35, so I'm going to open this calculator, so we need to find the of it. 98 00:08:25,550 --> 00:08:31,370 Let's listen in to know don't you get seven square again? 99 00:08:31,370 --> 00:08:37,650 If you hit enter, the previous operation will be performed here again here and you'll get 70 sound 100 00:08:37,670 --> 00:08:38,400 powerful song. 101 00:08:38,420 --> 00:08:38,920 Perfect. 102 00:08:39,710 --> 00:08:41,100 So this is perfect. 103 00:08:42,890 --> 00:08:46,990 Let's go with this and did not back. 104 00:08:50,380 --> 00:08:51,410 I want to go into this. 105 00:08:51,450 --> 00:08:59,790 We are going to find out what the Stuttaford so let's click on Water and hope that it gives rise to 106 00:08:59,790 --> 00:09:00,150 seven. 107 00:09:02,660 --> 00:09:09,920 Those I saw ciphertext is seven, we need to get the plane touched so you can send these seven value 108 00:09:09,920 --> 00:09:18,100 as a ciphertext to the receiver and thus I hope to get the predictions. 109 00:09:18,170 --> 00:09:22,070 I would actually ciphertext more into my Madison. 110 00:09:29,660 --> 00:09:33,340 I'm sorry, I should not put that into this. 111 00:09:33,720 --> 00:09:36,890 I'm sorry for this because I would expect to be Martin. 112 00:09:39,030 --> 00:09:48,240 What ciphertext seven and these also White and Marda, and it is 34, so in this case, the body operations 113 00:09:48,240 --> 00:09:51,750 are the same and we get the seven as the plane touched. 114 00:09:54,610 --> 00:10:01,870 So this is how you make the side and the predictions are brutal. 115 00:10:02,230 --> 00:10:09,650 So let's talk about the weakness of artists are so publicly coming is known to everyone. 116 00:10:09,820 --> 00:10:16,120 So I am a I was told this in a notepad or some other expert. 117 00:10:17,740 --> 00:10:19,840 So we have got that and we have got the. 118 00:10:19,840 --> 00:10:23,750 And so how do you keep the ciphertext? 119 00:10:24,070 --> 00:10:26,810 We have already and from this public debate. 120 00:10:27,040 --> 00:10:27,490 Right. 121 00:10:28,900 --> 00:10:34,480 Are you want to do you want to this find the disvalue. 122 00:10:34,660 --> 00:10:43,400 How to find disvalue means you need to find a multiple of such that the payoff is equal to one. 123 00:10:44,470 --> 00:10:52,870 So we got the end value is in the queue right then if you factor is this envelope in the two primes, 124 00:10:53,710 --> 00:10:55,440 then obviously you get powerful. 125 00:10:56,050 --> 00:10:56,440 Right? 126 00:10:57,370 --> 00:11:02,530 So if I take the small print on Macerich, let's see the numbers. 127 00:11:02,530 --> 00:11:03,450 We have taken five. 128 00:11:03,460 --> 00:11:04,530 We have got the 35. 129 00:11:05,110 --> 00:11:12,350 So if you factor is this a value into two primes and you can assume that those problems are used in 130 00:11:12,740 --> 00:11:20,170 the encryption process, if you assume that like that, you can easily get the are the factors of the 131 00:11:20,190 --> 00:11:25,860 default rate and in the fact of the default, one of these pages, five seven. 132 00:11:26,020 --> 00:11:27,240 And these are pretty numbers. 133 00:11:27,490 --> 00:11:34,840 So I can easily factor this value together, uh, factors like five and so and these two are pretty 134 00:11:34,870 --> 00:11:35,230 numbers. 135 00:11:35,230 --> 00:11:42,520 I can check the numbers and I can find this perfect illustration function because we got the P and we 136 00:11:42,520 --> 00:11:49,070 have successfully factories and value and we can calculate this function by using P Es. 137 00:11:50,250 --> 00:11:54,340 So within this one value we got the P Q and I'll see you later. 138 00:11:54,970 --> 00:12:01,060 All you need to do is you need to cover this because we have got the probability. 139 00:12:01,120 --> 00:12:01,450 Right. 140 00:12:02,080 --> 00:12:12,760 So this is because we got these are these values because of this small and value to get larger and value. 141 00:12:13,030 --> 00:12:15,310 It takes so much time to find the factors. 142 00:12:15,550 --> 00:12:18,350 And particularly we need to find the factors of prime numbers. 143 00:12:18,370 --> 00:12:26,860 And that's why it is best to choose the right numbers, because the larger numbers are to produce the 144 00:12:26,860 --> 00:12:27,770 larger number. 145 00:12:28,450 --> 00:12:32,720 That's why even though if occurs is the probability, of course he will. 146 00:12:33,850 --> 00:12:38,820 Anyone can access this publicly and attacker can factor this value. 147 00:12:39,010 --> 00:12:46,110 So in order to make him make the process start to one, you need to take the large numbers. 148 00:12:46,510 --> 00:12:52,030 So the weakness facing these numbers you need to fit is the weak program. 149 00:12:52,270 --> 00:12:57,630 Then your decryption process will be very easy for that way. 150 00:12:57,910 --> 00:13:01,630 It's always the best practice, which is the numbers.