1 00:00:02,120 --> 00:00:08,360 Encryption doesn't translate to the ability to prove a message senders identity. 2 00:00:08,400 --> 00:00:14,670 The two factors authenticity and non repudiation are insured by the use of hash functions in digital 3 00:00:14,670 --> 00:00:15,420 signatures 4 00:00:19,830 --> 00:00:22,220 a hash function is a one way function. 5 00:00:22,660 --> 00:00:29,090 You have to find a hash a characteristic fixed length trade of a variable length message 6 00:00:32,370 --> 00:00:37,400 cryptographic hash functions should also guarantee you the maximum possible randomness of the result. 7 00:00:38,310 --> 00:00:43,380 Minimize the risk that the hatch result generated from two different inputs will be the same and make 8 00:00:43,380 --> 00:00:47,440 a hash result from two very similar sets of data dissimilar as possible. 9 00:00:52,350 --> 00:00:59,010 This means that for any text computing the hash should be easy fast efficient and not complex. 10 00:00:59,010 --> 00:01:02,540 While mapping a text to a signature should be very hard to achieve. 11 00:01:05,810 --> 00:01:08,850 Different inputs should also be mapped to different hashes. 12 00:01:10,020 --> 00:01:13,160 The use of hash functions is connected with a serious threat. 13 00:01:13,930 --> 00:01:17,270 The security of symmetric or asymmetric algorithms varies. 14 00:01:17,470 --> 00:01:21,190 You can be certain that the hash functions used today are not secure. 15 00:01:21,190 --> 00:01:26,970 What's the reason for the state. 16 00:01:26,990 --> 00:01:32,040 The first problem that pertains to hash functions is the birthday paradox and the attack that exploits 17 00:01:32,070 --> 00:01:34,990 it. 18 00:01:35,020 --> 00:01:36,690 What is this problem about. 19 00:01:37,090 --> 00:01:42,310 If you get together with a group of 23 people what is the probability that two of the people have the 20 00:01:42,310 --> 00:01:43,380 same birthday. 21 00:01:45,130 --> 00:01:52,120 As it turns out this probability is surprisingly high it's over 50 percent. 22 00:01:52,130 --> 00:01:54,570 There are 365 days in a year. 23 00:01:54,740 --> 00:01:59,480 So 23 people would be enough for the probability of discovering that at least one pair and the group 24 00:01:59,690 --> 00:02:06,120 share the same birthday over 50 percent if seven more people made up. 25 00:02:06,280 --> 00:02:08,150 The group will increase to 30. 26 00:02:08,500 --> 00:02:13,870 The probability of at least two people in the group having the same birthday increases to over 70 percent. 27 00:02:17,940 --> 00:02:19,940 Why is the probability so high. 28 00:02:21,440 --> 00:02:28,790 First since there are 365 days in a year the first collision or match will occur after a give or take 29 00:02:28,790 --> 00:02:39,980 the 19th attempt 19 a square root of 365 in statistics a first match will occur likely soon after the 30 00:02:39,980 --> 00:02:41,870 square root of all possibilities. 31 00:02:44,870 --> 00:02:51,980 In a group of pointone you can create n times and minus one divided by two to one hundred ninety pairs 32 00:02:54,150 --> 00:02:55,150 for each of the pairs. 33 00:02:55,150 --> 00:02:59,470 The probability of having the same birthday is 1 to 365. 34 00:03:02,340 --> 00:03:09,480 You see the data to calculate the probability computing 20 times 20 minus one divided by two times divided 35 00:03:09,480 --> 00:03:18,430 by 365 gives us 380 730 slightly over 50 percent. 36 00:03:18,440 --> 00:03:19,700 Why even mention this 37 00:03:23,010 --> 00:03:32,170 from the birthday paradox you know that the risk of college in structure is quite a bit. 38 00:03:32,380 --> 00:03:34,420 It's certainly bigger than it would seem. 39 00:03:35,470 --> 00:03:37,860 How can you protect yourself against this problem. 40 00:03:39,260 --> 00:03:41,170 How is this shortcoming addressed. 41 00:03:42,380 --> 00:03:52,670 There's one viable solution used hash function results have to be lengthened. 42 00:03:52,720 --> 00:03:57,340 We started with the 128 bit length. 43 00:03:57,350 --> 00:04:04,570 Now there are even hash function results that are 512 bits long what hash functions are there. 44 00:04:09,900 --> 00:04:13,050 The first function is the MDI family message digest 45 00:04:15,570 --> 00:04:24,680 these hash functions were developed by Ron Rivest M.D. 2 was published in 1989 and before in 1990 and 46 00:04:24,700 --> 00:04:35,790 the five in 1991 the function's return 128 bit long outputs for several years now it's been known that 47 00:04:35,790 --> 00:04:42,530 there are a phishing attacks on all versions of the M.D hash function. 48 00:04:42,600 --> 00:04:50,240 For this reason the functions are not considered secure and are not recommended MT 5 is still widely 49 00:04:50,240 --> 00:04:51,120 used though. 50 00:04:51,260 --> 00:04:53,360 For example in Internet Applications 51 00:04:55,910 --> 00:04:59,740 an other option is using the SAHD family of hash functions. 52 00:05:02,600 --> 00:05:05,500 They were developed by the NSA. 53 00:05:05,700 --> 00:05:12,080 The hash that's returned is quite longer at 160 bits. 54 00:05:12,220 --> 00:05:20,440 The first of the S.H. a hash functions as actuates 0 and SH 1 are not secure censor publication they've 55 00:05:20,460 --> 00:05:22,900 been shown to be susceptible to attacks. 56 00:05:24,080 --> 00:05:26,700 The security of the former is 39 bits. 57 00:05:26,720 --> 00:05:32,410 All the security of the latter is 63 bits. 58 00:05:32,570 --> 00:05:42,290 There's also another variation of the hash function to OSHA to create hashes that are 256 or 512 bits 59 00:05:42,290 --> 00:05:45,190 in length. 60 00:05:45,310 --> 00:05:50,080 While some Chinese researchers have announced that they have successfully cracked sh to. 61 00:05:50,390 --> 00:05:52,920 There's no official proof to support this claim.