SeaGL Computational Randomness

Transcript

1. Computational Randomness: Controlled Chaos in an Ordered Machine by @amandasopkin
2. Who am I? @amandasopkin
3. Just a randomness fan @amandasopkin
4. Where are we headed? @amandasopkin
5. History of Cryptography @amandasopkin
6. 1900 BC: Cryptographic hieroglyphics @amandasopkin
8. 100 BC: Julius Caeser @amandasopkin
9. @amandasopkin
10. 1500s: Vignere’s system @amandasopkin
12. Kerchoff’s Principle: secrecy of key @amandasopkin
13. 1800s: Hebern’s system @amandasopkin
14. 1800s: Hebern’s system
15. Letter frequencies Can be used to break a cipher
16. Letter frequencies
17. Letter frequencies Frequency of each letter in cipher Sorted from most common to least
18. Letter frequencies Standard english letter frequencies
19. Letter frequencies Frequencies of letters in cipher
20. Letter frequencies Most frequent letters in cipher are S and O
21. Substitute E and T for S and O
22. Spot instances of “tle”
23. Most common letter is now G, which must be a, i, or o
24. Spot oFe and theF and then Lheet
25. Spot sODVe and OK
26. Sub l for D, v for V, R for K
27. Spot enoQRh
28. Spot EesMge and Nount
29. Few more steps...
30. Solved!
31. 1800s: Hebern’s system
32. WW1: Engima Machine @amandasopkin
34. 1973: IBM’s Luther @amandasopkin
35. Note on block cipher encryption @amandasopkin
37. 2000: Advanced Encryption Standard (Rijndael) @amandasopkin
39. Crypto Wars @amandasopkin
41. Key size restrictions @amandasopkin
42. The end of crypto wars @amandasopkin
43. 1991: PGP (Pretty Good Privacy) @amandasopkin
45. Bread and Butter of cryptography
46. Cipher text: input that has been encrypted Bread and Butter of cryptography
47. Why is randomness important? @amandasopkin
48. We use session keys to encrypt cipher keys @amandasopkin
49. @amandasopkin
50. Randomness Makes processes secure Mathematically/computationally, naturally, philosophically important Difficult to actually achieve @amandasopkin
51. Why do we need randomness today? @amandasopkin
52. 4oio342ip4o24p32o
53. 4fdslf95454
56. Problems with randomness The seed, or starting point The algorithm @amandasopkin
58. 1. Determined that user ids were seeded with restart time 2. Crashed the Hacker News site 3. Predicted restart time 4. Predicted assigned user ids as users logged in 5. Impersonated discovered users @amandasopkin
59. DUAL_EC_DRBG Controversy • 2004: Dual EC PRNG introduced
60. • 08/2007: Shumow and Ferguson present Dual_EC_DRBG flaw at cryptography conference DUAL_EC_DRBG Controversy
61. • 11/2007: Schneier bases article in Wired on their findings DUAL_EC_DRBG Controversy
62. “...would allow NSA to determine the state of the random number generator, and thereby eventually be able to read all data sent over the SSL connection.” DUAL_EC_DRBG Controversy
64. • 09/2013: One of the purposes of Bullrun is described as being "to covertly introduce weaknesses into the encryption standards followed by hardware and software developers around the world." DUAL_EC_DRBG Controversy
65. • NIST recommends removal of the algorithm as a standard DUAL_EC_DRBG Controversy
66. • 2004: Dual EC PRNG introduced • 08/2007: Shumow and Ferguson present Dual_EC_DRBG flaw at cryptography conference • 11/2007: Schneier bases article in Wired on their findings DUAL_EC_DRBG Controversy
67. • 09/2013: One of the purposes of Bullrun is described as being "to covertly introduce weaknesses into the encryption standards followed by hardware and software developers around the world." • 12/2013: Presidential advisory examines encryption standards • 2014: Standard is removed DUAL_EC_DRBG Controversy
68. Years until standard removed... 10!
69. Who did this impact? Microsoft, Google, Apple, McAfee, Docker, IBM, Oracle, Cisco, VMWare, Juniper, HP, Red Hat, Samsung, Toshiba, DELL, Ruckus, F5 Networks, Lenovo, Nokia, the RSA BSAFE libraries for Java and C++ and more....
70. Ok, so you want to create randomness... @amandasopkin
71. An ideal pseudo random number generator should...
72. 1. Pass statistical tests of randomness An ideal pseudo random number generator should... Monobit Distance Poker or Craps Birthday
73. 1. Pass statistical tests of randomness 2. Take a long time before repeating An ideal pseudo random number generator should... Have a long “period”
74. 1. Pass statistical tests of randomness 2. Take a long time before repeating 3. Execute efficiently An ideal pseudo random number generator should... & Quick Low storage
75. 1. Pass statistical tests of randomness 2. Take a long time before repeating 3. Execute efficiently 4. Be repeatable An ideal pseudo random number generator should...
76. 1. Pass statistical tests of randomness 2. Take a long time before repeating 3. Execute efficiently 4. Be repeatable 5. Be portable An ideal pseudo random number generator should... Can be run on any machine or system
77. What are the common ways of generating “randomness”? @amandasopkin
78. Linear congruential generators Linear congruential generators take the form xk = (axk−1 + c) (mod M) where x0 is the seed, the integer M is the largest representable integer, and the period is at most M.
79. Linear combination generators a = 3 c = 9 m = 16 x0 = 4394 def lcg(): xi = x0 for i in range(10): xi = (a*xi + c)%m print(xi)
80. Linear combination generators Algorithm: xi = (a*xi + c)%m 7 14 3 2 15 6 11 10 7
81. Towards a better pseudorandom generator @amandasopkin
82. Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.
83. Mid square method generally Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s Take the middle 4 digits of the result Repeat the sequence
84. Mid square method generally Start with a 4 digit seed 9834
85. Mid square method generally Start with a 4 digit seed Square this value 96707556 9834
86. Mid square method generally Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s 96707556 9834 96707556
87. Mid square method generally Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s Take the middle 4 digits of the result Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s 9834 96707556 96707556 7075
88. Mid square method generally Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s Take the middle 4 digits of the result Repeat the sequence Start with a 4 digit seed Square this value If the result has fewer than 8 digits, add leading 0s 9834 96707556 96707556 7075 50055625
89. Mid square method seed_number = int(input("Please enter a four digit number:\n[####] ")) number = seed_number already_seen = set() counter = 0 while number not in already_seen: counter += 1 already_seen.add(number) number = int(str(number * number).zfill(8)[2:6]) print(f"#{counter}: {number}") print(f"We began with the seed {seed_number}, and" f" we repeated ourselves after {counter} steps" f" with {number}.")
90. Mid square method Please enter a four digit number: [####] 5859 #1: 3278 #2: 7452 #3: 5323 #4: 3343 #5: 1756 #6: 835 #7: 6972 #8: 6087 #9: 515 #10: 2652 ....... #59: 24 #60: 5 #61: 0 #62: 0 We began with the seed 5859, and we repeated ourselves after 62 steps with 0.
91. Issues with mid square method Relatively slow Statistically unsatisfactory Sample of random numbers may be too short
92. Predicting the mid square method Advanced LCG Mid square method
93. Let’s talk cryptography @amandasopkin
94. Most used pseudo random number generator Very long period (the Mersenne prime: 219937 − 1) Not cryptographically secure The Mersenne Twister
95. Predicting the random() module from random import random import matplotlib.pyplot as plt def uni(n, m, a, c, seed): sequence = [] Xn = seed for i in range(n): Xn = ((a*Xn + c) % m) sequence.append(Xn/float(m-1)) return(sequence) x = range(1000) y_1 = uni(1000, 2**32, 11695477, 1, datetime.now().microsecond) y_2 = [random() for i in range(1000)] plt.plot(x, y_1, "o", color="blue") plt.show() plt.plot(x, y_2, "o", color="red") plt.show()
96. Predicting the random() module Advanced LCG Built in Random PRNG
97. Whats wrong with the random module? @amandasopkin
99. Problems with the random module...
100. Problems with the random module...
101. Problems with the random module... ...
102. Introducing...the secrets module! @amandasopkin
103. The Secrets module Is cryptographically secure Includes ready made “batteries” for Users that don’t want to build their own Uses 32 bytes of entropy by default
104. A note on entropy... @amandasopkin
105. @amandasopkin Natural sources of entropy
106. Source code of Secrets module from random import SystemRandom _sysrand = SystemRandom() randbits = _sysrand.getrandbits choice = _sysrand.choice def randbelow(exclusive_upper_bound): return _sysrand._randbelow(exclusive_upper_bound) DEFAULT_ENTROPY = 32 # number of bytes to return by default def token_bytes(nbytes=None): if nbytes is None: nbytes = DEFAULT_ENTROPY return os.urandom(nbytes) def token_hex(nbytes=None): return binascii.hexlify(token_bytes(nbytes)).decode('ascii') def token_urlsafe(nbytes=None): tok = token_bytes(nbytes) return base64.urlsafe_b64encode(tok).rstrip(b'=').decode('ascii')
107. SystemRandom Uses OS as a source of randomness Not available on all systems Does not rely on software states Sequences are not repeatable
108. /dev/random Will block without sufficient entropy Relies on “the kernel entropy pool” Slower than /dev/urandom
109. /dev/urandom Will not block without sufficient entropy Relies on “the kernel entropy pool” Faster than /dev/random Theoretically vulnerable to attack
110. Using the secrets module to get tokens import secrets token1 = secrets.token_hex(16) token2 = secrets.token_hex(10) print(token1) print(token2) d2bdc979d5ecec0dccf67854459c5284 584d93ac921d3c74be9c
111. Using the secrets module for password generation import secrets import string alphabet = string.ascii_letters + string.digits password = ''.join(secrets.choice(alphabet) for i in range(10)) print(password) i3OFMKPr8q
112. The secrets module: not the end all be all. @amandasopkin
113. Popular algorithms • AES • RCA • ECC
114. Popular algorithms • AES: made of three block ciphers: AES-128, AES-192 and AES-256. Each cipher encrypts and decrypts data in blocks of 128 bits using cryptographic keys of 128-, 192- and 256-bits
115. Popular algorithms: AES
116. Popular algorithms • RSA: involves a public key and private key. The public key can be known to everyone; it is used to encrypt messages. Messages encrypted using the public key can only be decrypted with the private key.
117. Popular algorithms: RSA
118. Popular algorithms • ECC: based on the algebraic structure of elliptic curves over finite fields.
119. Popular algorithms: ECC
120. Python’s “nuclear reactor” of Randomness "...folks really are better off learning to use things like cryptography.io for security sensitive software, so this change is just about harm mitigation given that it's inevitable that a non-trivial proportion of the millions of current and future Python developers won't do that."
121. Installation of Cryptography.io $ pip install cryptography
122. Cryptography.io
123. Let’s wrap up... @amandasopkin
124. Is very important for security Difficult to truly achieve Can be simulated Randomness... @amandasopkin
125. Something to say? Amanda Sopkin @amandasopkin
126. Thank you! @amandasopkin
127. Sources: • Icons taken from flaticon.com • https://crypto.stackexchange.com/questions/51232/using- 32-hexadecimal-digits-vs-ascii-equivalent-16-character- password • https://dev.to/walker/pseudo-random-numbers-in-python-f rom-arithmetic-to-probability-distributions • Wired Magazine • The Washington Post • NYT • Dilbert