1 00:00:02,640 --> 00:00:09,850 Welcome to a course on the working principles inapplicability of symmetric and asymmetric ciphers the 2 00:00:09,850 --> 00:00:16,110 module will focus on examining diverse components of cryptographic systems. 3 00:00:16,130 --> 00:00:21,240 Let's begin with a short introduction before we can move on. 4 00:00:21,310 --> 00:00:24,170 We must understand what information theory means. 5 00:00:25,820 --> 00:00:32,260 This field was developed by Claude Shannon who you can see in the picture. 6 00:00:32,450 --> 00:00:38,360 Shannon is the author of two of the most seminal works on information theory a mathematical theory of 7 00:00:38,360 --> 00:00:44,060 cryptography and a mathematical theory of communication which was published soon after the first book 8 00:00:48,310 --> 00:00:55,090 Shannon first coined the word bit a bit is defined as the smallest information unit required to encode 9 00:00:55,090 --> 00:01:05,480 one of the two values zero or one will come back to this later Jether term Shannon and used as entropy. 10 00:01:05,860 --> 00:01:12,960 Entropy is the smallest amount of information needed on the average to encode and invent. 11 00:01:13,110 --> 00:01:19,150 There's a set of probable events for which you need to determine information entropy. 12 00:01:19,200 --> 00:01:23,620 The more improbable or unlikely an event the bigger the entropy is. 13 00:01:25,450 --> 00:01:32,920 If you roll fair dice the entropy of the probability that you will get a 1 is quite small the number 14 00:01:32,920 --> 00:01:36,330 of total outcomes is only 6. 15 00:01:36,390 --> 00:01:44,010 On the other hand in lotto games with the draw results of 5 15:23 and so on the information entropy 16 00:01:44,010 --> 00:01:48,020 is very high because the probability of winning is extremely low. 17 00:01:50,330 --> 00:01:54,270 There was a huge number of possibilities. 18 00:01:54,320 --> 00:01:59,030 Our task in cryptography is to maximize entropy. 19 00:01:59,060 --> 00:02:00,960 Let's start with this simple example. 20 00:02:03,660 --> 00:02:09,620 Let's take a look at a short script that will launch in a moment this short script is designed to calculate 21 00:02:09,620 --> 00:02:13,120 the password entropy in bits. 22 00:02:13,330 --> 00:02:18,650 We'll have to calculate a logarithm from multiplying two values. 23 00:02:18,860 --> 00:02:26,690 The first variable range specifies the range of possibilities determined in the definition. 24 00:02:26,830 --> 00:02:35,380 If a password can for example only be expressed in upper case the range of this will be one to 26. 25 00:02:35,460 --> 00:02:42,910 The second variable number specifies still length of our password since the desired result should be 26 00:02:42,910 --> 00:02:47,770 in bits well divided by the logarithm from two. 27 00:02:47,800 --> 00:02:53,450 Next we'll call the previously mentioned simple function for some of the passwords. 28 00:02:53,500 --> 00:02:57,340 The first password uses 8 uppercase characters. 29 00:02:57,370 --> 00:03:01,500 The range is 1 to 26. 30 00:03:01,520 --> 00:03:04,700 The second case allows passwords to use lower case letters 31 00:03:07,480 --> 00:03:12,110 the third password is again limited to uppercase only password length is doubled 32 00:03:14,900 --> 00:03:20,650 the fourth password uses both upper case and lower case letters and a relatively secure number of characters 33 00:03:21,130 --> 00:03:23,320 16. 34 00:03:23,370 --> 00:03:27,700 Let's now find out the true entropy strength of the individual passwords. 35 00:03:30,040 --> 00:03:39,940 The first password is only 38 bits Strong see entropy as indicative of the secrecy of something the 36 00:03:39,940 --> 00:03:46,370 bigger the entropy the more secret or improbable something is. 37 00:03:46,500 --> 00:03:50,890 Your password should be as secretive as possible for everyone except yourself. 38 00:03:52,210 --> 00:03:54,250 38 bits is not a good strength. 39 00:03:55,640 --> 00:03:58,800 In the second case there are 46 bits. 40 00:03:58,820 --> 00:04:01,460 It's more but the difference is not likely to matter. 41 00:04:02,330 --> 00:04:05,440 8 character letter only passwords are not secure. 42 00:04:07,490 --> 00:04:14,580 16 character uppercase passwords provide security level for modern computer systems that amount to 77 43 00:04:14,600 --> 00:04:17,530 bits of entropy. 44 00:04:17,620 --> 00:04:20,890 The last password is 93 bit strong. 45 00:04:20,890 --> 00:04:25,960 This means that even if you have a 16 bit password that contains both upper case and lower case letters 46 00:04:26,500 --> 00:04:33,480 you still won't get over 100 bits of entropy when we'll be talking about algorithms. 47 00:04:33,710 --> 00:04:38,380 We'll show you that algorithms that make use of a key with a length similar to the result we've got. 48 00:04:38,420 --> 00:04:42,400 Provide no security. 49 00:04:42,450 --> 00:04:44,890 The passwords are not really secure. 50 00:04:45,090 --> 00:04:53,090 There should be more complicated before we move on to discuss algorithms symmetric algorithms in particular 51 00:04:53,360 --> 00:04:57,920 will need to explain two terms. 52 00:04:58,000 --> 00:05:05,740 The first concept is confusion confusion measures a non-linear relationship between the plaintext ciphertext 53 00:05:05,890 --> 00:05:08,310 and the key. 54 00:05:08,390 --> 00:05:14,240 It describes the dissimilarity of the ciphertext in the plaintext and the difficulty of extracting information 55 00:05:14,240 --> 00:05:18,110 about the key from the ciphertext. 56 00:05:18,120 --> 00:05:21,290 This is a vital concept. 57 00:05:21,330 --> 00:05:26,670 The bigger the confusion the more immune to the linear approximation cryptanalysis your cipher will 58 00:05:26,670 --> 00:05:30,700 be. 59 00:05:30,760 --> 00:05:38,120 The second crucial term is diffusion diffusion specifies the distribution or spreading of the plaintext 60 00:05:38,140 --> 00:05:45,160 information in the ciphertext Caesar cipher diffusion was one to one. 61 00:05:45,300 --> 00:05:48,330 The letter A always represented the letter D. 62 00:05:48,890 --> 00:05:55,300 The diffusion was practically non-existent in that case read like the plaintext information not to be 63 00:05:55,300 --> 00:05:59,250 distributed to one fixed position in the cipher text. 64 00:05:59,380 --> 00:06:06,680 Rather it should be spread all over the ciphertext diffusion as measured by the probability of the successful 65 00:06:06,680 --> 00:06:08,720 differential approximation.