1
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So now let us understand, encrypting with them a fine.

2
00:00:04,350 --> 00:00:11,910
Now, one downside to using the multiplicative cipher is that the letter capitally always maps to letter

3
00:00:11,910 --> 00:00:12,630
capitally.

4
00:00:12,900 --> 00:00:19,770
The reason is that capital is the index number and zero multiplied by anything will be zero.

5
00:00:20,250 --> 00:00:26,310
Now, we can fix this particular issue by adding a second key to perform a single cipher encryption

6
00:00:26,310 --> 00:00:30,800
after the multiplicative ciphers, multiplication and modding is done.

7
00:00:31,260 --> 00:00:36,120
Not this extra step changes the multiplicative cipher into a fine.

8
00:00:36,780 --> 00:00:43,460
Not a fine cipher has to say, for example, key and B not 60.

9
00:00:43,470 --> 00:00:49,910
E is the integer you use to multiply the letters number and multiply the plaintext by eight.

10
00:00:49,920 --> 00:00:55,650
You are key to the product and then you're more the sum by 66 as you did in the original.

11
00:00:56,850 --> 00:01:02,880
So this means that the Afie inside four has six to six times as many possibilities as a multiplicative

12
00:01:02,880 --> 00:01:03,300
cipher.

13
00:01:03,660 --> 00:01:09,030
It also ensures that the letter A. does always encrypt itself.

14
00:01:09,320 --> 00:01:16,260
OK, now if we come to the decrypting with the fine sign now in the Sisa Saiful, you used addition

15
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to encrypt and subtraction to decrypt in the afine side, for you have used multiplication to encrypt.

16
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Naturally, you might think you can divide to decrypt the defined safe, but if you try this, you will

17
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see that it doesn't work to decrypt with your fine cipher, you need to multiply the keys modular involves.

18
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Now this reveals the more operations from the encryption process.

19
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A modular inverse of two numbers is represented by an expression say for example, A multiplied by modulo

20
00:01:49,980 --> 00:01:52,530
M if it's equal to one.

21
00:01:53,080 --> 00:01:58,770
OK, now where the AI is the modular inverse and anima two numbers.

22
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For example, the modular inverse of five more seven would be some number I would fire into.

23
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I am modulo seven is equal to one.

24
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Now you can brute force this calculation for example like one is is in the modular inverse of five more

25
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seven because firing the one modulo seven is five and second is in the modular inverse of five more

26
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seven because firing the two modulo seven constantly.

27
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So three is the modular inverse of five and seven because if you see five in two three modules when

28
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it comes to one.

29
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So although the encryption and the decryption keys for the Caesar cipher part of the offensive four

30
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are the same, the encryption key and the decryption keys for multiplicative side four are two different

31
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encryption keys can be anything you choose as long as it's relatively blind to the size of this Envisat

32
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which in this case is it?

33
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And if you choose the key fifty three for encrypting with the fine for decryption key in the modular

34
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inverse of fifty three more sixty six.

35
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So that in that case you will have to check for in numerical one because say for example if you see

36
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fifty three.

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Multiplied by one more and this whole we would put it in a bracket to Morillo 66.

38
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Now this comes to 53.

39
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So one is not possible.

40
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Similarly, if we just cooperate on this multiple times and just replace this value 53 into two.

41
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Now, this comes to say 40.

42
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If we say 53 into three, and that comes to say twenty seven.

43
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If we say fifty three into four and this comes to say 14.

44
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And here if we say 53 to five, this comes to one.

45
00:03:51,890 --> 00:03:59,220
OK, so now in this case, because now your five is a modular inverse of fifty three and sixty six,

46
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you know that they are fine for decryption keys.

47
00:04:02,200 --> 00:04:09,180
Also five, decrypt a ciphertext letter, multiply that number by five and then model 266.

48
00:04:09,550 --> 00:04:13,610
And the result is the number of original plaintext letters that you have.

49
00:04:14,050 --> 00:04:21,310
So since six to six characters in this set, let's end the war of particular words, the cat using the

50
00:04:21,320 --> 00:04:22,240
key 53.

51
00:04:22,300 --> 00:04:28,880
OK, so if we say over here, OK, now save you capital C will be at the indexical.

52
00:04:29,080 --> 00:04:37,510
OK, so if we say two multiplied by fifty three that will come to say one zero six, which is larger

53
00:04:37,510 --> 00:04:40,210
than this implicit size because the size is sixty six.

54
00:04:40,690 --> 00:04:43,690
So we need two more, one zero six by sixty six.

55
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So if we say one zero six modulo six to six, if this comes to the results for the character of the

56
00:04:52,060 --> 00:04:56,650
index 14, the symbol set that is equal to say zero.

57
00:04:56,860 --> 00:05:00,060
OK, so the symbol C encrypts now.

58
00:05:00,070 --> 00:05:04,690
So if we give you a B, this falls to zero.

59
00:05:05,460 --> 00:05:08,980
I will use the same step for the next letter that is available.

60
00:05:09,340 --> 00:05:16,680
Now this we have done it for C, so if we take a look now the string is at the index number twenty six,

61
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which is equal to twenty six.

62
00:05:18,580 --> 00:05:26,600
And if we say twenty six multiplied by fifty three then modulo sixty six.

63
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Now that comes to say fifty eight and the index at fifty eight is equal to seven.

64
00:05:33,910 --> 00:05:36,970
OK, so we have that eight to seven.

65
00:05:37,580 --> 00:05:42,010
OK now this ring that is being that is Malti.

66
00:05:42,420 --> 00:05:46,960
OK, so over here, this comes at an index of forty five.

67
00:05:47,500 --> 00:05:57,070
So if we see forty five multiplied by fifty three modulo six to see this comes to nine and the index

68
00:05:57,070 --> 00:05:59,990
nine you have the capital G.

69
00:06:00,520 --> 00:06:06,490
So therefore diversity has been encrypted to zero seven right now.

70
00:06:06,520 --> 00:06:14,110
Similarly, if you have to decrypt this zero seven back to the original then we'll have to multiply

71
00:06:14,110 --> 00:06:18,990
the modular inverse that is say fifty three modulo sixty six.

72
00:06:19,330 --> 00:06:21,210
OK, now this comes to five.

73
00:06:21,460 --> 00:06:23,950
So the symbol zero is that the index 40.

74
00:06:24,220 --> 00:06:24,620
Right.

75
00:06:24,850 --> 00:06:29,180
So we say 40 multiplied by five.

76
00:06:29,590 --> 00:06:32,210
Then again modulo sixty six.

77
00:06:32,320 --> 00:06:39,180
And this comes to two which is the index of capital C, symbol seven.

78
00:06:39,430 --> 00:06:40,380
Is that the index.

79
00:06:40,390 --> 00:06:41,110
Fifty eight.

80
00:06:41,500 --> 00:06:47,880
So if we just take it over here, the first one that is we have ok.

81
00:06:48,270 --> 00:06:51,970
OK, so all the index is 40.

82
00:06:52,130 --> 00:06:58,240
OK now the next index is seven seven letters of the index of that is the fifty eight.

83
00:06:58,870 --> 00:07:08,410
So now if we try to do fifty eight multiplied by five modulo sixty six that comes to twenty six.

84
00:07:08,980 --> 00:07:10,590
OK, which is equal to eight.

85
00:07:10,810 --> 00:07:14,590
And then the symbol capital G the index is nine.

86
00:07:14,800 --> 00:07:23,980
OK, and here we say nine multiplied by five modulo sixty six which is equal to forty five, which is

87
00:07:23,980 --> 00:07:32,530
equal to be for the ciphertext zero seven G has encrypted or decrypted back to see eighty with these

88
00:07:32,530 --> 00:07:36,410
capital, which is original plaintext just as expected.

89
00:07:36,920 --> 00:07:37,270
Right.