Alice & Bob: Public key cryptography 101 - PHP|Tek 2012

Transcript

1. Alice & Bob
   PHP|Tek - Chicago - USA
   May 25, 2012
   Public key cryptography 101
   

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2. Joshua Thijssen / Netherlands
   Freelance consultant, developer and
   trainer @ NoxLogic / Techademy
   Development in PHP, Python, Perl,
   C, Java....
   Blog: http://adayinthelifeof.nl
   Email: jthijssen@noxlogic.nl
   Twitter: @jaytaph
   2
   

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3. An introduction into public key cryptography
   3
   

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4. 4
   Without this there would be
   no internet as we know today
   (really)
   

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5. Meet Alice,
   and Bob.
   5
   Hi Bob!
   Hello Alice!
   

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6. “bad” encryption algorithms
   6
   http://www.flickr.com/photos/dpwk/1714014449/in/pool-1621478@N23/
   

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7. ciphertext:
   12, 1, 13, 5
   “algorithm”:
   A = 1, B = 2, C = 3, ...., Z = 26
   =
   L A M E
   ‣ SUBSTITUTION SCHEME
   7
   

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8. 8
   ciphertext:
           
   =
   W I N G D I N G S
   ‣ SUBSTITUTION SCHEME
   

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9. “algorithm”:
   c = m + k mod 26
   ‣ CAESARIAN CIPHER or CAESARIAN SHIFT
   9
   Message: C O D E
   Ciphertext (key=1): D P E F
   Ciphertext (key=2): E Q F G
   Ciphertext (key=-1): B M C D
   Ciphertext (key=0): C O D E
   Ciphertext (key=26): C O D E
   Ciphertext (key=52): C O D E
   http://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Caesar3.svg
   

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10. ➡ Key is too easy to guess.
    ➡ Key has to be send to Bob.
    ➡ Deterministic.
    ➡ Prone to frequency analysis.
    ‣ FLAWS IN THESE CIPHERS
    10
    

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11. ➡ The usage of every letter in the English (or
    any other language) can be represented by
    a percentage.
    ➡ ‘E’ is used 12.7% of the times in english
    texts, the ‘Z’ only 0.074%.
    11
    

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12. http://www.gutenberg.org/cache/epub/14082/pg14082.txt
    Once upon a midnight dreary, while I pondered, weak and weary,
    Over many a quaint and curious volume of forgotten lore—
    While I nodded, nearly napping, suddenly there came a tapping,
    As of some one gently rapping—rapping at my chamber door.
    "'Tis some visitor," I muttered, "tapping at my chamber door—
    Only this and nothing more."
    12
    

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13. A small bit of text can result in differences, but still there are
    some letters we can deduce..
    ‣ “THE RAVEN”, FIRST PARAGRAPH
    13
    

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14. We can deduce almost all letters just without even CARING
    about the crypto algorithm used.
    ‣ “THE RAVEN”, ALL PARAGRAPHS
    14
    

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15. Determinism and the ability to apply
    frequency analysis are “bad things”
    ‣ FLAWS IN THESE CIPHERS
    15
    

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16. ➡ Previous examples were symmetrical encryptions.
    ➡ Same key is used for both encryption and decryption.
    ➡ Good symmetrical encryptions: AES, Blowfish, (3)DES.
    ➡ They are fast and secure.
    ‣ SYMMETRICAL ALGORITHMS
    16
    

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17. Q: How does Alice send over the key securely
    to Bob? Everybody’s listening!
    ‣ THE PROBLEM WITH SYMMETRICAL ALGORITHMS
    17
    

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18. Another encryption system:
    Asymmetrical encryption or public key encryption.
    18
    

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19. Two keys instead of one:
    public key - available for everybody.
    Can be published on your blog.
    private key - For your eyes only!
    19
    

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20. http://upload.wikimedia.org/wikipedia/commons/f/f9/Public_key_encryption.svg
    ‣ USES 2 KEYS INSTEAD OF ONE: A KEYPAIR
    20
    

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21. It is NOT possible to decrypt the message
    with same key that is used to encrypt.
    21
    

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22. Encrypt with public key:
    - only private key (thus Alice) can decrypt.
    - message is only for Alice = encryption
    22
    Encrypt with private key:
    - only public key can decrypt.
    - message is guaranteed coming for Alice = signing
    

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23. Symmetrical
    ✓ quick.
    ✓ not resource intensive.
    ✓ useful for small and large
    messages.
    ✗ need to send over the key
    to the other side.
    Asymmetrical
    ✓ no need to send over the
    (whole) key.
    ✓ can be used for encryption
    and validation (signing).
    ✗ very resource intensive.
    ✗ only useful for small messages.
    23
    

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24. A: Use symmetrical encryption for the (large)
    message and encrypt the key used with an
    asymmetrical encryption method.
    24
    Q: How does Alice send over the key securely
    to Bob? Everybody’s listening!
    

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25. +
    http://www.zastavki.com/pictures/1152x864/2008/Animals_Cats_Small_cat_005241_.jpg
    Hybrid
    ✓ quick
    ✓ not resource intensive
    ✓ useful for small and large messages
    ✓ safely exchange key data
    25
    =
    

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26. But how does it work?
    26
    

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27. RSA
    Ron Rivest, Adi Shamir, Leonard Adleman
    27
    1978
    Pierre de Fermat, Leonard Euler
    17th - 18th century
    

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28. Public key encryption works on the premise that it
    is practically impossible to refactor a large number
    back into 2 separate prime numbers
    Prime number is only divisible by 1 and
    itself: 2, 3, 5, 7, 11, 13, 17, 19 etc...
    28
    

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29. “large” number: 221
    but we cannot calculate its
    prime factors without brute force.
    There is no “formula” (like e=mc2)
    (13 and 17)
    29
    

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30. ➡ There is no proof that it’s impossible to refactor
    quickly (all tough it doesn’t look plausible)
    ➡ Brute-force decrypting is always lurking around
    (quicker machines, better algorithms).
    30
    

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31. 31
    This is mathness!
    No, this is RSAAAA!
    

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32. 32
    ➡ p = (large) prime number
    ➡ q = (large) prime number (but not too close to p)
    ➡ n = p . q (bit length of the RSA key)
    ➡ φ = (p-1) . (q-1) (the φ thingie is called phi)
    ➡ e = gcd(e, φ) = 1
    ➡ d = (d . e) mod φ = 1
    

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33. Step 1: select primes P and Q
    ‣ P = 11
    ‣ Q = 3
    ‣ P = ? | Q = ? | N = ? | Phi = ? | e = ? | d = ? 33
    

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34. ➡ N = P . Q = 11 . 3 = 33
    ➡ φ = (11-1) . (3-1) = 10 . 2 = 20
    Step 2: calculate N and Phi
    ‣ P = 11 | Q = 3 | N = ? | Phi = ? | e = ? | d = ? 34
    33 decimal is 100001 in binary == 6 bit key
    

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35. Step 3: find e
    ‣ e = 3
    ‣ gcd(e, φ) = 1 ==> gcd(3, 20) = 1
    ‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = ? | d = ? 35
    Fermat number: 2 + 1
    2
    n
    Fermat prime: Fermat that is prime: 3, 5, 17, 257, 65537
    Study shows that 98.5% of the time 65537 is used
    

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36. ‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = ?
    Step 4: find d
    ‣ Extended Euclidean Algorithm gives 7
    ‣ brute force: (e.d mod φ = 1)
    3 . 1 = 3 mod 20 = 3
    3 . 2 = 6 mod 20 = 6
    3 . 3 = 9 mod 20 = 9
    3 . 4 = 12 mod 20 = 12
    3 . 5 = 15 mod 20 = 15
    3 . 6 = 18 mod 20 = 18
    3 . 7 = 21 mod 20 = 1
    3 . 8 = 24 mod 20 = 4
    3 . 9 = 27 mod 20 = 7
    3.10 = 30 mod 20 = 10
    36
    

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37. That’s it:
    ➡ public key = (n, e) = (33, 3)
    ➡ private key = (n, d) = (33, 7)
    ‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = 7 37
    

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38. The actual math is much more complex since
    we use very large numbers, but it all comes
    down to these (relatively simple) calculations..
    38
    

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39. 39
    jthijssen@debian-jth:~$ openssl rsa -text -noout -in server.key
    n
    e
    d
    p
    q
    d mod (p-1)
    e mod (q-1)
    (inverse q) mod p
    Private-Key: (256 bit)
    modulus:
    00:c2:d0:c4:1f:6f:78:16:82:d1:0c:dd:5a:af:de:f2:ff:31:c6:
    9b:3b:9f:e8:24:2a:5c:06:56:ea:d7:7c:c6:19
    publicExponent: 65537 (0x10001)
    privateExponent:
    22:8f:fd:2b:82:90:30:96:36:d6:6c:73:09:5e:a9:87:73:6e:
    2d:d4:d5:78:fc:3b:20:ea:0d:02:e5:2b:cb:3d
    prime1:
    00:f0:49:fd:91:18:01:53:92:8f:87:d7:2b:c8:19:7d:17
    prime2:
    00:cf:8d:a1:3b:93:af:61:77:8f:c9:8f:1d:aa:8d:b4:4f
    exponent1:
    00:e1:d8:c9:89:bc:84:52:a6:a8:5d:47:32:91:6a:d3:95
    exponent2:
    5a:88:b1:fa:d5:d9:db:8f:16:a6:5a:0a:1b:ba:42:1b
    coefficient:
    00:99:fa:de:80:d4:ee:f3:69:59:e5:8a:72:ad:e5:30:3d
    

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40. Encrypting a message:
    c = me mod n
    Decrypting a message:
    m = cd mod n
    40
    

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41. Encrypting a message: private key = (n,d) = (33, 7):
    Decrypting a message: public key = (n,e) = (33, 3):
    m = 13, 20, 15, 5
    13^7 mod 33 = 7
    20^7 mod 33 = 26
    15^7 mod 33 = 27
    5^7 mod 33 = 14
    c = 7, 26, 27,14
    41
    c = 7, 26, 27,14
    7^3 mod 33 = 13
    26^3 mod 33 = 20
    27^3 mod 33 = 15
    14^3 mod 33 =5
    m = 13, 20, 15, 5
    

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42. ➡ A message is an “integer”
    ➡ A message must be between 2 and n-1.
    ➡ Deterministic, so we must use a padding
    scheme to make it non-deterministic.
    42
    

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43. ➡ Public Key Cryptography Standard #1
    ➡ Pads data with (random) bytes up to n bits
    in length (v1.5 or OAEP/v2.x).
    ➡ Got it flaws and weaknesses too. Always
    use the latest available version (v2.1)
    43
    

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44. Data = 4E636AF98E40F3ADCFCCB698F4E80B9F
    The encoded message block, EMB, after encoding but before encryption, with random
    padding bytes shown in green:
    0002257F48FD1F1793B7E5E02306F2D3228F5C95ADF5F31566729F132AA12009
    E3FC9B2B475CD6944EF191E3F59545E671E474B555799FE3756099F044964038
    B16B2148E9A2F9C6F44BB5C52E3C6C8061CF694145FAFDB24402AD1819EACEDF
    4A36C6E4D2CD8FC1D62E5A1268F496004E636AF98E40F3ADCFCCB698F4E80B9F
    After RSA encryption, the output is:
    3D2AB25B1EB667A40F504CC4D778EC399A899C8790EDECEF062CD739492C9CE5
    8B92B9ECF32AF4AAC7A61EAEC346449891F49A722378E008EFF0B0A8DBC6E621
    EDC90CEC64CF34C640F5B36C48EE9322808AF8F4A0212B28715C76F3CB99AC7E
    609787ADCE055839829E0142C44B676D218111FFE69F9D41424E177CBA3A435B
    http://www.di-mgt.com.au/rsa_alg.html#pkcs1schemes 44
    

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45. 45
    Practical applications of PKE
    

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46. ➡HTTP encapsulated by TLS (previously SSL).
    ➡More or less: an encryption layer on top of http.
    ➡Hybrid encryption.
    HTTPS
    46
    

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47. ➡Actual encryption methodology is decided by
    the browser and the server (highest possible
    encryption used).
    ➡Symmetric encryption (AES-256, others)
    ➡But both sides needs the same key, so we
    have the same problem as before: how do we
    send over the key?
    HTTPS
    47
    

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48. ➡Key is exchanged in a public/private encrypted
    communication.
    ➡Which public key?
    ➡It is stored inside the server’s SSL certificate
    HTTPS
    48
    

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49. 49
    jthijssen@debian-jth:~$ openssl x509 -text -noout -in github.pem
    Certificate:
    Data:
    Version: 3 (0x2)
    Serial Number:
    0e:77:76:8a:5d:07:f0:e5:79:59:ca:2a:9d:50:82:b5
    Signature Algorithm: sha1WithRSAEncryption
    Issuer: C=US, O=DigiCert Inc, OU=www.digicert.com, CN=DigiCert High Assurance EV CA-1
    Validity
    Not Before: May 27 00:00:00 2011 GMT
    Not After : Jul 29 12:00:00 2013 GMT
    Subject: businessCategory=Private Organization/1.3.6.1.4.1.311.60.2.1.3=US/
    1.3.6.1.4.1.311.60.2.1.2=California/serialNumber=C3268102, C=US, ST=California, L=San Francisco, O=GitHub, Inc.,
    CN=github.com
    Subject Public Key Info:
    Public Key Algorithm: rsaEncryption
    RSA Public Key: (2048 bit)
    Modulus (2048 bit):
    00:ed:d3:89:c3:5d:70:72:09:f3:33:4f:1a:72:74:
    d9:b6:5a:95:50:bb:68:61:9f:f7:fb:1f:19:e1:da:
    04:31:af:15:7c:1a:7f:f9:73:af:1d:e5:43:2b:56:
    09:00:45:69:4a:e8:c4:5b:df:c2:77:52:51:19:5b:
    d1:2b:d9:39:65:36:a0:32:19:1c:41:73:fb:32:b2:
    3d:9f:98:ec:82:5b:0b:37:64:39:2c:b7:10:83:72:
    cd:f0:ea:24:4b:fa:d9:94:2e:c3:85:15:39:a9:3a:
    f6:88:da:f4:27:89:a6:95:4f:84:a2:37:4e:7c:25:
    78:3a:c9:83:6d:02:17:95:78:7d:47:a8:55:83:ee:
    13:c8:19:1a:b3:3c:f1:5f:fe:3b:02:e1:85:fb:11:
    66:ab:09:5d:9f:4c:43:f0:c7:24:5e:29:72:28:ce:
    d4:75:68:4f:24:72:29:ae:39:28:fc:df:8d:4f:4d:
    83:73:74:0c:6f:11:9b:a7:dd:62:de:ff:e2:eb:17:
    e6:ff:0c:bf:c0:2d:31:3b:d6:59:a2:f2:dd:87:4a:
    48:7b:6d:33:11:14:4d:34:9f:32:38:f6:c8:19:9d:
    f1:b6:3d:c5:46:ef:51:0b:8a:c6:33:ed:48:61:c4:
    1d:17:1b:bd:7c:b6:67:e9:39:cf:a5:52:80:0a:f4:
    ea:cd
    Exponent: 65537 (0x10001)
    

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50. ➡Browser sends over its encryption methods.
    ➡Server decides which one to use.
    ➡Server send certificate(s).
    ➡Client sends “session key” encrypted by the
    public key found in the server certificate.
    ➡Server and client uses the “session key” for
    symmetrical encryption.
    HTTPS
    50
    

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51. ➡Thus: Public/private encryption is only used in
    establishing a secondary (better!?) encryption.
    ➡SSL/TLS is a separate talk (it’s way more complex
    as this)
    ➡http://www.moserware.com/2009/06/first-few-
    milliseconds-of-https.html
    HTTPS
    51
    

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52. http://torontoemerg.files.wordpress.com/2010/09/spam.gif
    http://change-your-ip.com/wp-content/uploads/image/nigerian_419_scam.jpg
    52
    

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54. ➡ Did Bill really send this email?
    ➡ Do we know for sure that nobody has read
    this email (before it came to us?)
    ➡ Do we know for sure that the contents of
    the message isn’t tampered with?
    ➡ We use signing!
    Questions:
    54
    

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55. ➡ Signing a message means adding a signature
    that authenticates the validity of a message.
    ➡ Like md5 or sha1, so when the message
    changes, so will the signature.
    ➡ This works on the premise that Alice and
    only Alice has the private key that can
    create the signature.
    Signing a message
    55
    

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56. http://en.wikipedia.org/wiki/File:Digital_Signature_diagram.svg
    Signing a message
    56
    

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57. ➡ GPG / PGP: Application for signing and/or
    encrypting data (or emails).
    ➡ Try it yourself with Thunderbird’s Enigmail
    extension.
    ➡ Public keys can be send / found on PGP-
    servers so you don’t need to send your
    keys to everybody all the time.
    Introduction a pretty-good-privacy
    57
    

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58. ‣ Everybody can send emails that ONLY YOU can read.
    ‣ Everybody can verify that YOU have send the email
    and that it is authentic.
    ‣ Why is this not the standard?
    ‣ No really, why isn’t it the standard?
    58
    

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60. ➡ Public key authentication
    ➡ Because you suck at creating and/or
    remembering passwords
    SSH
    60
    

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61. ➡ Run ssh-keygen
    ➡ copy id_rsa.pub over to server’s ~/.ssh/
    authorized_keys
    ➡ Easy for tools / scripts to connect
    ➡ Easy for you (no remembering passwords)
    ➡ More fine grained security model.
    61
    

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62. ➡ Domain Key Identified Mail
    (spam protection)
    ➡ BitCoin
    ➡ IPSEC / PKI
    ➡ DRM
    62
    

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63. 63
    Some words of wisdom:
    (free of charge)
    

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64. ➡ Don’t “invent” your own encryption. It will
    NOT be secure, and it WILL fail.
    ➡ Encryption is as strong as the weakest link,
    which 9 out of 10 times will be you.
    ➡ Encryptions evolve. Do not use today what
    you used 10 years ago.
    ➡ Every encryption will become obsolete!
    ➡ Always follow the best practices.
    64
    

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65. http://farm1.static.flickr.com/73/163450213_18478d3aa6_d.jpg
    Questions?
    65
    

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66. Please rate my talk on joind.in:
    http://joind.in/6484
    Thank you
    66
    Find me on twitter: @jaytaph
    Find me for development and training: www.noxlogic.nl
    Find me on email: jthijssen@noxlogic.nl
    Find me for blogs: www.adayinthelifeof.nl
    

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