Ruby Meditation #20 February 17, 2018 Kyiv

1. Cryptography: way to Arkham
Andrii Savchenko

2. Crypto primitives

3. One-way hash functions
Symmetric encryption
Asymmetric encryption
PRNGs
Boring large prime number math
(MOST COMMONLY USED) CRYPTO PRIMITIVES
3

4. ONE WAY HASH FUNCTIONS
4

5. ONE WAY HASH FUNCTIONS – DUMMY EXAMPLE
5
D U C K
4 21 3 11
22450325
1 / 421311 = 0.000002373543534 = 34 = 22
2 / 421311 = 0.000004747087069 = 69 = 45
3 / 421311 = 0.000007120630603 = 03 = 03
4 / 421311 = 0.000009494174137 = 37 = 25

6. ONE WAY HASH FUNCTIONS – DUMMY EXAMPLE
6
F U C K
6 21 3 11
0C192531
1 / 621311 = 0.000001609499912 = 12 = 0C
2 / 621311 = 0.000003218999825 = 25 = 19
3 / 621311 = 0.000004828499737 = 37 = 25
4 / 621311 = 0.000006437999649 = 49 = 31

7. ONE WAY HASH FUNCTIONS – DUMMY EXAMPLE
7
DUCK = 22450325
FUCK = 0C192531

8. ONE WAY HASH FUNCTIONS – DUMMY EXAMPLE
8
ANDRII = 083B2712
ANDRIJ = 0E1C2A38

9. SHA
MD5
BLAKE
ONE WAY HASH FUNCTIONS – REAL WORLD
9

10. SYMMETRIC ENCRYPTION
10

11. Key: Joker
Phrase: Why so serious
SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
11

12. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
12
whysoserious
jokerjokerjo

13. 13

14. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
14
whysoserious
jokerjokerjo

15. 15

16. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
16
whysoserious
jokerjokerjo
f

17. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
17
whysoserious
jokerjokerjo
f

18. 18

19. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
19
whysoserious
jokerjokerjo
fv

20. SYMMETRIC ENCRYPTION – CHIFFRE DE VIGENÈRE
20
whysoserious
jokerjokerjo
fviwfbsbmfdg

21. AES
3DES
RC4
Blowfish
Salsa20
SYMMETRIC ENCRYPTION – REAL WORLD
21

22. ASYMMETRIC ENCRYPTION
22

23. Lets say, we have some magic public key and private key, for example:
ASYMMETRIC ENCRYPTION – SIMPLE RSA
23
Public key: 3
Private key: 7

24. Also, we need another magic number n, for example 33
ASYMMETRIC ENCRYPTION – SIMPLE RSA
24

25. 25

26. So, Harley Quinn want to send message "14" to Joker, knowing only Joker's public key
ASYMMETRIC ENCRYPTION – SIMPLE RSA
26

27. Harley Quinn: encrypted = messagepublic mod n = 143 mod 33 = 5
Joker: encryptedprivate mod n = 57 mod 33 = 14
ASYMMETRIC ENCRYPTION – SIMPLE RSA
27

28. Batman want to know what Harley sent to Joker, but only knows the public key 3, message 5 and
magic number 33, but have no possibility to decipher message without private key 7
ASYMMETRIC ENCRYPTION – SIMPLE RSA
28

29. Not every 3 numbers may give you expected result
PROBLEM 1
29

30. Choose two prime numbers: p and q (in this example: p = 11, q = 3)
Get magic number n = p * q = 33
Get Euler's phi = (p - 1) * (q - 1) = 10 * 2 = 20
Choose public key which should be coprime with phi, p-1 and q-1 and satisfy 1 < public < phi
Find private key where phi divides public * private - 1 (3 * 7 - 1 = 20, 20 / 20 = 1, private = 7)
You are all done! Easy-peasy! Enjoy your public key encryption
GETTING KEY PAIR
30

31. message could not be bigger or equal than n
PROBLEM 2
31

32. Well, latin alphabet is only 25, let's write small Ruby script
PROBLEM 2
32

33. 33
PUB = 3
PRIV = 7
N = 33
DICT = { 'a' => 1, 'b' => 2, 'c' => 3, ... }
RDICT = DICT.invert
def encrypt(message)
message.each_char.map { |letter| DICT[letter] ** PUB % N }
end
def decrypt(array)
array.inject('') { |message, letter| message += RDICT[letter ** PRIV % N] }
end
encrypted = encrypt('batman') # => [8, 1, 14, 19, 1, 5]
decrypt('encrypted') # => 'batman'

34. Protocols

35. Protocol, basically, is a set of crypto primitives
PROTOCOLS
35

36. TLS
IPSec
oAuth
SSH
100500 more…
PROTOCOLS
36

37. Implementing crypto protocols

38. Good mathematicians often makes very bad code
Partial implementations
Incorrect implementations
Outdated protocol versions or crypto primitives
Abandoned projects
Absence of implementation
Fun
WHY?
38

39. PROBLEMS
39

40. HTTPS://VIMEO.COM/52882780
40

41. 41
Secure Remote Password protocol

42. 42
RFC2945

43. 43

44. 44
RFC2945

45. RFC2945
45

46. RFC2945
46

47. 47

48. 48

49. 49

50. 50

51. 51
S = (B - kg^x) ^ (a + ux)

52. 52
S = ((B - kg^x) ^ (a + ux)) mod N

53. 53
S = ((B - kg^x) mod N ^ (a + ux) mod N) mod N

54. 54
S = ((B - kg^x mod N) mod N ^ (a + ux mod N) mod N) mod N

55. 55

56. 56
B = k * v + ((g ** b) % N)

57. 57
B = k * v + ((g ** b) mod N)

58. 58
B / k = v + I

59. 59
B = k * v + ((g ** b) mod N) mod N

60. 60

61. 61

62. 62
One possible way

63. 63
One possible way

64. 64
One possible way

65. 65
One possible way

66. 66
One possible way

67. 67
M = H(A | B | S)
M = H(A | B || K)
M = H(H(N) xor H(g) | H(I) | s | A | B | K)

68. 68
H(A | M | S)
H(A | M | K)

69. 69

70. 70

71. 71
One possible way

72. 72

73. 73
x = H(s | p)
x = H(s | H(I) | H(p))
x = H(s | H(I | ":" | p))
x = KDF(s, p)

74. UTF-8
Binary values representation
Implementation incompatibilities
Ruby limitations
BONUS
74

75. 75
> 3 ** 7 % 33
=> 9
> 3 ** 1234567890 % 33
(pry):62: warning: in a**b, b may be too big
=> NaN

76. 76
> require 'openssl'
=> true
> 3.to_bn.mod_exp(1234567890, 33).to_i
=> 12

77. 77

78. Thank you for attention!
https://github.com/esrp/ruby

79. Andrii Savchenko
@ptico
andrii@aejis.eu
@ptico
My contacts