Cryptography: 500 BC to Quantum Computing

Have you always wanted to learn more about cryptography? This high-level survey of crypto takes the audience all the way from Scytales and Caesar ciphers in ancient Greece, to Vigenere Square, to Enigma in World War II, to TLS, and even Post-Quantum Cryptography!

Transcript

1. Cryptography:
   500 BC - Quantum Computing
   

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3. About me
   I’m not a crypto engineer
   I’m a web developer

   who got into

   Security Engineering
   I’ve always been scared

   and fascinated by crypto
   

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4. About this talk
   2700 years in 40 minutes
   Don’t take notes
   Slides are already up at:

   speakerdeck.com/groovecoder
   

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5. 2 “stories” of
   cryptography
   

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6. technology
   

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7. code-makers 

   vs.

   code-breakers
   

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8. Thru-out this talk, I’m going
   to track this with a timeline …
   

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9. “Ages”
   “Code-making”
   “Code-breaking”
   

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10. “Ages” of technology
    Ancient: 7m
    Renaissance: 5m
    Industrial: 7m
    Computing: 12m
    Quantum: 5m
    

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11. Ancient Code-making
    

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12. T
    ranspositional/Permutation

    Ciphers
    Anagrams: move letters around
    

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13. Permutation Cipher
    For example, consider this short sentence
    35 letters
    50,000,000,000,000,000,000,000,000,000,000

    (50 trillion trillion) permutations
    

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14. “Strength” of encryption systems:
    How “easy” or “hard” are they?
    

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15. Time Complexity
    

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16. Permutation Cipher
    EXPERIMENTATIONS FRESH CHORD LOSS
    50,000,000,000,000,000,000,000,000,000,000

    (50 trillion trillion) permutations
    1 check/second =

    1,500,000,000,000,000,000,000,000 years

    (1 trillion billion years)
    

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17. Drawbacks of
    random permutation cipher
    Impossible for intended recipient too
    False positives: which anagram is right?
    Do Not Attack at Midnight
    Attack at Mind: do T
    onight
    

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18. We need a

    deterministic
    way to encrypt & decrypt
    

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19. Algorithms & Keys
    

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20. Rail fence cipher
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    

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21. Rail fence cipher
    key = 4
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    they are attacking from the north
    

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22. Rail fence cipher; k=4
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    they are attacking from the north
    

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23. Rail fence cipher; k=4
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    they are attacking from the north
    TEKOOHRACIRMNREATANFTETYTGHH
    

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24. Rail fence cipher; k=4
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    they are attacking from the north
    TEKOOHRACIRMNREATANFTETYTGHH
    they are attacking from the north
    

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25. Machines for
    cryptography
    

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26. Scytale, ~700 BCE - 120 AD
    Algorithm
    Wrap message around a
    cylinder
    Key
    Diameter of cylinder
    

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27. Ancient
    Scytale
    ~700 BC
    

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28. Cryptanalysis
    Breaking encrypted messages
    

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29. Breaking rail fence cipher
    http://crypto.interactive-maths.com/rail-fence-cipher.html
    “Naive Brute Force” 

    key search:

    T
    ry a bunch of numbers of
    rows by hand
    

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30. Breaking rail fence cipher
    DELEHELFTAAEDSWNT
    2 rows: daealeedhsewlnftt
    3 rows: deslefwtlanaeetdh
    4 rows: detwaheeanellfdts
    5 rows: defend the east wall
    

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31. So, the first cryptanalysis is
    simply “naive brute force” 

    key searching
    

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32. “Key space”
    How many possible keys are there?
    

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33. Breaking a Scytale
    “Naive Brute Force”

    key search:

    T
    ry a bunch of cylinders
    

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34. Ancient
    Scytale
    ~700 BC
    Brute Force
    Key Search
    

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35. Substitutional Cipher
    Change letters into other letters
    

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36. Caesar Cipher, 49 - 44 BC
    Algorithm
    Replace each letter with
    another letter
    Key
    K positions down the
    alphabet
    

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37. Caesar (Shift) Cipher
    Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: DEFGHIJKLMNOPQRSTUVWXZYABC
    

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38. Ancient
    Steganography,

    Scytale
    ~700 BC
    Brute Force
    Key Search
    Caesar Cipher
    ~50 BC
    

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39. Breaking a Caesar Cipher
    “Naive Brute Force” 

    key search:

    26 possible shifts
    

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40. Can we give ourselves a really
    large key space?

    

    So it would take an attacker a
    long time to search them all?
    

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41. Non-shifted Random
    Substitution
    Algorithm
    Replace each letter with another letter
    Key
    Any Cipher Alphabet
    (An anagram of the alphabet! such meta!)
    

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42. Non-shifted Substitutional Cipher
    26 letters to re-arrange
    Key space: 403,291,461,000,000,000,000,000,000

    (403 trillion trillion or ~288)

    possible re-arrangements (English)
    120,000,000,000,000,000,000

    (120 billion billion)

    years at 1 check/s
    

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43. Most crypto-systems
    don’t try to offer
    “perfect” encryption …
    

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44. … most crypto systems try to
    force attackers into 

    key searches that take too
    long to complete
    

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45. Non-shifted Substitutional Cipher
    26 letters to re-arrange
    Key space: 403,291,461,000,000,000,000,000,000

    (403 trillion trillion or ~288)

    possible re-arrangements (English)
    120,000,000,000,000,000,000

    (120 billion billion)

    years at 1 check/s
    

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46. Key:
    XZAVOIDBYGERSPCFHJKLMNQTUW
    

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47. Can we create a

    “pseudo-random”
    key that is easy to memorize?
    

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48. Easy to memorize key
    JULIUS CAESAR

    JULISCAER
    

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49. Easy to memorize key
    Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ
    JULIUS CAESAR

    JULISCAER
    

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50. Easy to memorize key
    Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ
    JULIUS CAESAR

    JULISCAER
    Note: smaller key space
    

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51. “key derivation function”
    Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ
    JULIUS CAESAR
    

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52. Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: JULISCAERTVWXYZBDFGHKMNOPQ
    Defend the East wall
    ISCSYI HES SJGH NJWW
    

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53. Ancient
    Steganography,

    Scytale
    ~700 BC
    Brute Force
    Key Search
    Caesar Cipher
    ~50 BC
    Non-shifted

    Substitution

    Cipher
    

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54. So, we’ve got a simple crypto-
    system that would take decades
    for hundreds of thousands of
    computers to break!
    

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55. npm install
    keyed-substitution-cipher
    git commit -m

    “lulz crypto”
    

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56. Non-shifted Substitution Cipher
    considered un-breakable
    for ~800 years, until …
    

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57. ةامعملا بتكلا جارختسا يف ةلاسر
    (On Decrypting Encrypted Correspondence)
    يدنكلا حاّبصلا قاحسإ نب بوقعي فسوي وبأ

    (Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī)

    Al-Kindi
    801-873 AD
    

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58. Frequency Analysis
    Attack
    

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59. View Slide

60. “PCQ VMJYPD LBYK LYSO KBXBJXWXV BXV
    ZCJPO EYPD KBXBJYUXJ LBJOO KCPK. CP LBO
    LBCMKXPV XPV IYJKL PYDBL, QBOP KBO BXV
    OPVOV LBO LXRO CI SX’XJMI, KBO JCKO XPV
    EYKKOV LBO DJCMPV ZOICJO BYS, KXUYPD:
    “DJOXL EYPD, ICJ X LBCMKXPV XPV CPO
    PYDBLK Y BXNO ZOOP JOACMPLYPD LC UCM
    LBO IXZROK CI FXKL XDOK XPV LBO RODOPVK
    CI XPAYOPL EYPDK. SXU Y SXEO KC ZCRV XK LC
    AJXNO X IXNCMJ CI UCMJ SXGOKLU?”
    –OFYRCDMO, LXROK IJCS LBO LBCMKXPV XPV CPO PYDBLK
    

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61. Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: ??????????????????????????
    

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62. Likeliest plaintext letters
    O = e
    X = t
    P = a
    

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63. English frequency rules
    Vowels appear before and after most other letters
    Consonants avoid many letters
    E.g., ‘e’ appears before/after virtually every other letter; while ’t’
    is rarely seen before or after ‘b’, ‘d’, ‘g’, ‘j’, ‘k’, ‘m’, ‘q’, ‘v’
    “ee” occurs more than “oo” occurs more than other double-vowels
    “a” occurs on its own often - more than “I” on its own
    ‘h’ frequently goes before ‘e’
    but rarely after ‘e’
    

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64. Cipher
    O = e
    X = a
    Y = i
    B = h
    P = t ?
    

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65. “PCQ VMJiPD LhiK LiSe KhahJaWaV haV ZCJPe
    EiPD KhahJiUaJ LhJee KCPK. CP Lhe LhCMKaPV
    aPV IiJKL PiDhL, QheP Khe haV ePVeV Lhe LaRe CI
    Sa’aJMI, Khe JCKe aPV EiKKeV Lhe DJCMPV
    ZeICJe hiS, KaUiPD: “DJeaL EiPD, ICJ a LhCMKaPV
    aPV CPe PiDhLK i haNe ZeeP JeACMPLiPD LC UCM
    Lhe IaZReK CI FaKL aDeK aPV Lhe ReDePVK CI
    aPAiePL EiPDK. SaU i SaEe KC ZCRV aK LC AJaNe
    a IaNCMJ CI UCMJ SaGeKLU?”
    –eFiRCDMe, LaReK IJCS Lhe LhCMKaPV aPV CPe PiDhLK
    

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66. “PCQ VMJiPD LhiK LiSe KhahJaWaV haV ZCJPe
    EiPD KhahJiUaJ LhJee KCPK. CP Lhe LhCMKaPV
    aPV IiJKL PiDhL, QheP Khe haV ePVeV Lhe LaRe CI
    Sa’aJMI, Khe JCKe aPV EiKKeV Lhe DJCMPV
    ZeICJe hiS, KaUiPD: “DJeaL EiPD, ICJ a LhCMKaPV
    aPV CPe PiDhLK i haNe ZeeP JeACMPLiPD LC UCM
    Lhe IaZReK CI FaKL aDeK aPV Lhe ReDePVK CI
    aPAiePL EiPDK. SaU i SaEe KC ZCRV aK LC AJaNe
    a IaNCMJ CI UCMJ SaGeKLU?”
    –eFiRCDMe, LaReK IJCS Lhe LhCMKaPV aPV CPe PiDhLK
    “Lhe” 6 times
    

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67. “Lhe”
    Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: X???O??BY??????????L??????
    “the”
    

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68. “PCQ VMJiPD thiK tiSe KhahJaWaV haV ZCJPe EiPD
    KhahJiUaJ thJee KCPK. CP the thCMKaPV aPV IiJKt
    PiDht, QheP Khe haV ePVeV the taRe CI Sa’aJMI,
    Khe JCKe aPV EiKKeV the DJCMPV ZeICJe hiS,
    KaUiPD: “DJeat EiPD, ICJ a thCMKaPV aPV CPe
    PiDhtK i haNe ZeeP JeACMPtiPD tC UCM the
    IaZReK CI FaKt aDeK aPV the ReDePVK CI aPAiePt
    EiPDK. SaU i SaEe KC ZCRV aK tC AJaNe a IaNCMJ
    CI UCMJ SaGeKtU?”
    –eFiRCDMe, taReK IJCS the thCMKaPV aPV CPe PiDhtK
    “aPV” 5 times
    

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69. “aPV”
    Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: X??VO??BY????P?????L??????
    “and”
    

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71. “now during this time shahra[qxzj]ad had borne king
    shahriyar three sons. on the thousand and first night,
    when she had ended the tale of ma’aruf, she rose and
    kissed the ground before him, saying: “great king, for
    a thousand and one nights i have been recounting to
    you the fables of past ages and the legends of
    ancient kings. may i make so bold as to crave a favour
    of your ma[qxzj]esty?”
    –epilogue, tales from the thousand and one nights
    Plain alphabet: abcdefghijklmnopqrstuvwxyz
    Cipher alphabet: XZAVOIDBY?ERSPCF?JKLMNQ?U?
    

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72. Frequency Analysis:
    An analytical attack faster
    than naive brute force
    key search
    

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73. Ancient
    Steganography,

    Scytale
    ~700 BC
    Brute Force
    Key Search
    Caesar Cipher
    ~50 BC
    Non-shifted

    Substitution

    Cipher
    Frequency

    Analysis

    ~800 AD
    

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74. Frequency Analysis
    considered indefensible
    for ~800 years
    

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75. Code-makers needed a

    crypto-system that wasn’t
    vulnerable to

    Frequency Analysis
    

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76. Leon Battista Alberti
    1404-1472
    “poly-alphabetic”
    cipher
    

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77. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    Poly-alphabetic
    Substitution Cipher
    

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78. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    “R?????”
    Poly-alphabetic
    Substitution Cipher
    

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79. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    “RA????”
    Poly-alphabetic
    Substitution Cipher
    

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80. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    “RAB???”
    Poly-alphabetic
    Substitution Cipher
    

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81. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    “RABH??”
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    Poly-alphabetic
    Substitution Cipher
    

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82. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    “RABHK?”
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    Poly-alphabetic
    Substitution Cipher
    

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83. D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    “secret”
    “RABHKK”
    Poly-alphabetic
    Substitution Cipher
    

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84. False frequencies
    ‘e’ is enciphered as both ‘A’ and ‘K’
    ‘K’ is deciphered as both ‘e’ and ‘t’
    “secret”
    “RABHKK”
    

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85. Ancient
    Steganography,

    Scytale
    Brute Force
    Key Search
    Caesar Shift
    Non-shifted

    Substitution
    Frequency

    Analysis

    ~800 AD
    Homophonic
    Substitution
    Renaissance
    Poly-alphabetic
    Substitution
    ~1450 AD
    

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86. Poly-alphabetic beats
    frequency analysis, but …
    

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87. Poly-alphabetic ciphers
    are complex
    D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    

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88. Keyword

    SECRET
    D M B X K I V A S Z N P L Y F C J O R T E Q H WG U
    Z J D P A I Q H T WL F B G O X N H U K R C Y V S E
    a b c d e f g h i j k l m n o p q r s t u v w x y z
    

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89. Le Chiffre Indéchiffrable
    created by Blaise de Vigenère
    1523 - 1596
    Created new

    poly-alphabetic cipher
    

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90. Vigenère Square
    

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91. a b c d e f g h i j k l m n o p q r s t u v w x y z
    B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
    C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
    D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
    E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
    F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
    G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
    H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
    I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
    J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
    K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
    L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
    O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
    P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
    Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
    R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
    S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
    T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
    U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
    V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
    W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
    X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
    Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
    Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    

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92. Repeat keyword for all of text
    Plaintext: AttackFromTheSouthAtDawn
    Ciphertext: ????????????????????????
    Keyword: SECRETSECRETSECRETSECRET
    

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93. a b c d e f g h i j k l m n o p q r s t u v w x y z
    B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
    C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
    D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
    E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
    F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
    G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
    H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
    I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
    J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
    K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
    L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
    O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
    P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
    Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
    R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
    S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
    T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
    U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
    V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
    W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
    X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
    Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
    Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    Ciphertext: S???????????????????????
    Plaintext: AttackFromTheSouthAtDawn
    Keyword: SECRETSECRETSECRETSECRET
    S
    

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94. a b c d e f g h i j k l m n o p q r s t u v w x y z
    B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
    C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
    D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
    E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
    F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
    G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
    H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
    I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
    J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
    K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
    L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
    O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
    P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
    Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
    R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
    S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
    T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
    U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
    V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
    W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
    X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
    Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
    Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    Ciphertext: SX??????????????????????
    Plaintext: AttackFromTheSouthAtDawn
    Keyword: SECRETSECRETSECRETSECRET
    X
    

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95. a b c d e f g h i j k l m n o p q r s t u v w x y z
    B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
    C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
    D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
    E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
    F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
    G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
    H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
    I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
    J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
    K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
    L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
    O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
    P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
    Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
    R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
    S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
    T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
    U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
    V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
    W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
    X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
    Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
    Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
    Ciphertext: SXV?????????????????????
    Plaintext: AttackFromTheSouthAtDawn
    Keyword: SECRETSECRETSECRETSECRET
    V
    

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96. Plaintext: AttackFromTheSouthAtDawn
    Ciphertext: SXVRGDXVQDXAWWQLXASXFRAG
    Keyword: SECRETSECRETSECRETSECRET
    

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97. Ancient
    Steganography,

    Scytale
    Brute Force
    Key Search
    Caesar Shift
    Non-shifted

    Substitution
    Frequency

    Analysis

    ~800 AD
    Homophonic
    Substitution
    Renaissance
    Poly-alphabetic
    Substitution
    Le Chiffre
    Indéchiffrable
    ~1550 AD
    

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98. Industrial
    Revolution
    ~1760 - 1840
    

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99. “Black Chambers”
    • 1700s
    • “Assembly-line” Cryptanalysis
    • Each European power had one
    • Breaking all mono-alphabetic
    ciphers
    • Encouraged adoption of
    Vigenère Square for

    poly-alphabetic ciphers
    

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100. Ancient
     Steganography,

     Scytale
     Brute Force
     Key Search
     Caesar Shift
     Non-shifted

     Substitution
     Frequency

     Analysis
     Homophonic
     Substitution
     Renaissance
     Poly-alphabetic
     Substitution
     Le Chiffre
     Indéchiffrable
     ~1550 AD
     Assembly-line
     Frequency Analysis
     ~1700’s
     Industrial
     

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101. Charles Babbage
     • 1791 - 1871
     • 1854: Broke Vigenère
     Cipher
     • Without machinery
     

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102. REPEATING KEYWORD
     Plaintext: AttackFromTheSouthAtDawn
     Ciphertext: SXVRGDXVQDXAWWQLXASXFRAG
     Keyword: SECRETSECRETSECRETSECRET
     

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103. False SYMBOL
     frequencies
     • ‘e’ is enciphered as both ‘A’ and ‘K’
     • ‘K’ is deciphered as both ‘e’ and ‘t’
     “secret”
     “RABHKK”
     

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104. Word frequencies
     

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105. Plaintext: thesunandthemaninthemoon
     Ciphertext: DPRYEVNTNBUKWIAOXBUKWWBT
     Keyword: KINGKINGKINGKINGKINGKING
     

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106. Plaintext: thesunandthemaninthemoon
     Ciphertext: DPRYEVNTNBUKWIAOXBUKWWBT
     Keyword: KINGKINGKINGKINGKINGKING
     

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107. Breaking Vigenère
     • Look for repeated sequences
     of letters
     • Measure spacing between
     repetitions
     • Identify most likely length
     of key: L
     

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108. Cipher text
     WUBEFIQLZURMVOFEHMYMWTIXCQTMPIFKRZUPMVOIRQMM
     WOZMPULMBNYVQQQMVMVJLEYMHFEFNZPSDLPPSDLPEVQM
     WCXYMDAVQEEFIQCAYTQOWCXYMWMSEMEFCFWYEYQETRLI
     QYCGMTWCWFBSMYFPLRXTQYEEXMRULUKSGWFPTLRQAERL
     UVPMVYQYCXTWFQLMTELSFJPQEHMOZCIWCIWFPZSLMAEZ
     IQVLQMZVPPXAWCSMZMORVGVVQSZETRLQZPBJAZVQIYXE
     WWOICCGDWHQMMVOWSGNTJPFPPAYBIYBJUTWRLQKLLLMD
     PYVACDCFQNZPIFPPKSDVPTIDGXMQQVEBMQALKEZMGCVK
     UZKIZBZLIUAMMVZ
     

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109. REPETITIONS
     EFIQ, PSDLP, WCXYM, ETRL
     WUBEFIQLZURMVOFEHMYMWTIXCQTMPIFKRZUPMVOIRQMM
     WOZMPULMBNYVQQQMVMVJLEYMHFEFNZPSDLPPSDLPEVQM
     WCXYMDAVQEEFIQCAYTQOWCXYMWMSEMEFCFWYEYQETRLI
     QYCGMTWCWFBSMYFPLRXTQYEEXMRULUKSGWFPTLRQAERL
     UVPMVYQYCXTWFQLMTELSFJPQEHMOZCIWCIWFPZSLMAEZ
     IQVLQMZVPPXAWCSMZMORVGVVQSZETRLQZPBJAZVQIYXE
     WWOICCGDWHQMMVOWSGNTJPFPPAYBIYBJUTWRLQKLLLMD
     PYVACDCFQNZPIFPPKSDVPTIDGXMQQVEBMQALKEZMGCVK
     UZKIZBZLIUAMMVZ
     

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110. spacing between repetitions
     Repetition Spacing
     Possible Length of Key
     2 3 4 5 6 7 8 9 10 11 121314 15 1617181920
     EFIQ 95 ✓ ✓
     PSDLP 5 ✓
     WCXYM 20 ✓ ✓ ✓ ✓ ✓
     ETRL 120 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
     

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111. 5 separate cipher texts
     WIREWQFPROLVVEESSV
     XVITXSCYLGWYXELWRL
     VXLSECWLQPSRQRBQCH
     OTPYWLCNPVGVAMZUZ
     WIREWQFPROLVVEESSV
     XVITXSCYLGWYXELWRL
     VXLSECWLQPSRQRBQCH
     OTPYWLCNPVGVAMZUZ
     WIREWQFPROLVVEESSV
     XVITXSCYLGWYXELWRL
     VXLSECWLQPSRQRBQCH
     OTPYWLCNPVGVAMZUZ
     WIREWQFPROLVVEESSV
     XVITXSCYLGWYXELWRL
     VXLSECWLQPSRQRBQCH
     OTPYWLCNPVGVAMZUZ
     WIREWQFPROLVVEESSV
     XVITXSCYLGWYXELWRL
     VXLSECWLQPSRQRBQCH
     OTPYWLCNPVGVAMZUZ
     Break each with frequency analysis
     

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112. Ancient
     Steganography,

     Scytale
     Brute Force
     Key Search
     Caesar Shift
     Non-shifted

     Substitution
     Frequency

     Analysis

     ~800 AD
     Homophonic
     Substitution
     Renaissance
     Poly-alphabetic
     Substitution
     Le Chiffre
     Indéchiffrable
     ~1550 AD
     Assembly-line
     Frequency Analysis
     ~1700’s
     Industrial
     Babbage
     Frequency
     Analysis
     ~1800’s
     

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113. Electric Telegraphs
     • Buried underground or
     suspended overhead
     • 1844

     60km wire between
     Baltimore & Washington
     DC
     

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114. How can you
     represent letters
     and words as
     electrical signals?
     

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115. Morse Code:
     “Encoding” not “Encryption”
     

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116. I.e., this is still
     “plaintext”
     

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117. Radio, 1899-1901
     • 3,000 km from Cornwall to
     to Newfoundland
     • Transatlantic
     communication
     • Instant military commands
     • All messages reach enemy too
     • Increases need for
     encryption
     

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118. Enigma: Electrical Encryption
     • Arthur Scherbius, 1918
     • Mass Production in 1925
     CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=497329
     

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119. Input
     Keyboard
     Rotors
     Output
     Lampboard
     

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120. By User:RadioFan, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30719651
     

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121. By MesserWoland - Own work based on Image:Enigma-action.pnj by Jeanot; original diagram by Matt Crypto, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1794494
     

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122. 3 rotors of 26 wirings
     26 x 26 x 26
     =
     17,576 Cipher Alphabets
     

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123. 17,576 orientations
     x
     6 arrangements
     =
     105,456 Cipher Alphabets
     

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124. 105,456 possible keys
     • A new key was used every day
     • Assume 1 orientation check per minute
     • (Just type ciphertext and look at plaintext)
     • 96 enigma machines = .75 days to crack
     

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125. Plugboard
     By Bob Lord - German Enigma Machine, uploaded in english wikipedia on 16. Feb. 2005 by en:User:Matt Crypto, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=258976
     Swap up to 6 of 26 letters
     

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126. 100,391,791,500
     Plugboard Settings
     

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127. 10,586,916,711,696
     (10 trillion)
     Total Possible Keys
     

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128. 10,586,916,711,696
     possible keys
     • At 1 check per minute:
     • 38,291,799 enigma machines = 1 day to crack
     

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129. Message Keys
     • Using day key, send a message rotor orientation first. 

     E.g., A, S, D
     • Send it at the beginning, twice for integrity. 

     E.g., ‘asdasd’ = QWERTY
     • Receiver types QWERTY, sees ‘asdasd’
     • Re-orients their rotors to A, S, D for the rest of the
     message
     • Minimizes amount of ciphertext created by day key
     

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130. Is cracking Enigma
     possible?
     • At 1 check per minute:
     • 38,291,799 enigma machines = 1 day to crack 

     

     A SINGLE MESSAGE!
     

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131. Ancient
     Steganography,

     Scytale
     Brute Force
     Key Search
     Caesar Shift
     Non-shifted

     Substitution
     Frequency

     Analysis

     ~800 AD
     Homophonic
     Substitution
     Renaissance
     Poly-alphabetic
     Substitution
     Le Chiffre
     Indéchiffrable
     Assembly-line
     Frequency Analysis
     Industrial
     Babbage
     Frequency
     Analysis
     One-Time
     Pad
     Enigma
     ~1925
     

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132. Cracking Enigma
     

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133. Polish Biuro Szyfrów
     • Established after WWI to
     protect Poland from Russian
     & Germany
     • Received photographs of
     Enigma instruction manual
     from French espionage
     • Deduced rotor wirings
     • Usage of codebook
     A. Jankowski "Warszawa" Publisher:Wydawnictwo Polskie, Poznań, 

     Public Domain, https://commons.wikimedia.org/w/index.php?curid=1514113
     

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134. Marian
     Rejewski
     By Unknown - Rejewski's daughter's private archive,
     CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=216461
     

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135. Found “chain” cycles

     in the first 6 letters
     4th Letter: FQHPLWOGBMVRXUYCZITNJEASDK
     1st Letter: ABCDEFGHIJKLMNOPQRSTUVWXYZ
     3 links: A-F-W-A
     

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136. Found “chain” loops

     in the first 6 letters
     4th Letter: FQHPLWOGBMVRXUYCZITNJEASDK
     1st Letter: ABCDEFGHIJKLMNOPQRSTUVWXYZ
     7 links: C-H-G-O-Y-D-P-C
     

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137. Marian Rejewski
     • Realized the # links in the
     chain were only caused by
     the rotors
     • Could try to break the
     105,456 possible rotor
     settings, not all
     10,000,000,000,000,000
     possible day keys
     • 100,000,000,000 times easier
     By Unknown - Rejewski's daughter's private archive,
     CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=216461
     

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138. Cyclometer
     • Team checked each of
     105,456 possible settings
     on replica Enigma machines
     and recorded which chains
     were generated by each
     rotor setting
     • Took 1 year to complete
     • Could look up rotor settings by
     chains found in first 6
     letters of ciphertext
     http://www.cryptomuseum.com/crypto/cyclometer/index.htm
     

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139. Cyclometer created
     the first
     “Rainbow Table”
     for looking up
     cryptographic keys
     

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140. How to find the plugboard
     settings out of 100,391,791,500?
     • Plugboard: Un-plug all
     • Rotor Arrangement: III, I, II
     • Initial Rotor Orientations: Q, C, W
     • Type in ciphertext, see:
     • “rettew”
     • Swap R/W = Wetter (weather)
     

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141. Polish
     Cryptographic Bombs
     • 6 machines for the 6 possible
     rotor arrangements
     • Each with 6 full Enigma rotor
     sets at top for the 6 characters
     of the repeated message key
     • Given a number of “females”
     to find, Bomba could recover
     settings in less than 2 hours
     

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142. British Bombes
     • 36 rotors arrange in 3 banks
     of 12
     • 210 bombes by the end of
     the war
     • Operated by 2,000
     members of Women’s
     Royal Navy Service
     

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143. Colossus
     • Inspired by Turings ideas
     and his bombe
     • 1,500 electronic valves -
     faster than
     electromechanical relay
     switches
     • Programmable - first
     computers?
     

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144. Ancient
     Steganography,

     Scytale
     Brute Force
     Key Search
     Caesar Shift
     Non-shifted

     Substitution
     Frequency

     Analysis

     ~800 AD
     Homophonic
     Substitution
     Renaissance
     Poly-alphabetic
     Substitution
     Le Chiffre
     Indéchiffrable
     Assembly-line
     Frequency Analysis
     Industrial
     Babbage
     Frequency
     Analysis
     Enigma
     ~1925
     Colossus
     Mark 1
     1943
     Computer
     

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145. Computer Cryptography
     

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146. In the early days of
     computing, electrical
     signals were much
     harder to measure
     and control precisely
     It made more sense
     to only distinguish
     between an “on” state
     and an “off” state
     

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147. Like the telegraph required
     morse to encode messages into
     electrical signals …
     In computers, we need a way to
     encode messages in 1’ and 0’s
     

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148. View Slide

149. ASCII
     1963
     Encoding,

     not encryption

     (like Morse code)
     E.g.,
     A: 1000001
     B: 1000010
     

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150. In Binary, we encrypt at the
     level of 1’s and 0’s
     

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151. This is called “bitwise”
     

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152. Bitwise anagram
     For example, consider this short sentence.
     01000110011011110111001000100000011001010111100001100001011011010111000001101100011001010010110000100000011000110
     11011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001101
     101000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101
     “Bitwise” rail fence cipher with 2 rails
     00010111010101000100011001000110010001100100011001000101011101110101011001000100010101000100011001100101010001010
     11001110101010001000101010001110100010001110101010010101011110000001011110010011011110010101011001000001001101110
     101101100110101011110000001110100010011101000011011000101111001110000011011011101011101011101010011011
     

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153. Bitwise substitution: XOR
     The XOR operator outputs a 1
     whenever the inputs do not
     match, which occurs when
     one of the two inputs is
     exclusively true
     0 XOR 0 = 0
     0 XOR 1 = 1
     1 XOR 0 = 1
     1 XOR 1 = 0
     

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154. Bitwise substitution: XOR
     For example, consider this short sentence.
     01000110011011110111001000100000011001010111100001100001011011010111000001101100011001010010110000100000011000110
     11011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001101
     101000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101
     Key: “Julius Caesar”
     01001010011101010110110001101001011101010111001100100000010000110110000101100101011100110110000101110010
     Output
     10001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101
     10111101101110011100110110100101100100011001010111001000100000011101000110100001101001011100110010000001110011001
     00010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111
     

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155. Bitwise substitution: XOR
     For example, consider this short sentence.
     010001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101
     101111011011100111001101101001011001000110010101110010001000000111010001101000011010010111001100100000011100110110
     1000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101
     Key: “random” 1|0’s length of plaintext
     000000111010001101000011010010111001100100000011100110110100001101111011100100111010000100000011100110110010101101
     110011101000110010101101110011000110110010101000110011011110111001000100000011001010111100001100001011011010111000
     0011011000110010100101100001000000110001101101111011011100111001101101001011001000110010101110010001
     Output
     100011001101111011100100010000001100101011110000110000101101101011100000110110001100101001011000010000001100011011
     011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001100100
     010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111
     

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156. View Slide

157. View Slide

158. Bitwise substitution: XOR
     For example, consider this short sentence.
     010001100110111101110010001000000110010101111000011000010110110101110000011011000110010100101100001000000110001101
     101111011011100111001101101001011001000110010101110010001000000111010001101000011010010111001100100000011100110110
     1000011011110111001001110100001000000111001101100101011011100111010001100101011011100110001101100101
     Key: “random” 1|0’s length of plaintext
     000000111010001101000011010010111001100100000011100110110100001101111011100100111010000100000011100110110010101101
     110011101000110010101101110011000110110010101000110011011110111001000100000011001010111100001100001011011010111000
     0011011000110010100101100001000000110001101101111011011100111001101101001011001000110010101110010001
     Output
     100011001101111011100100010000001100101011110000110000101101101011100000110110001100101001011000010000001100011011
     011110110111001110011011010010110010001100101011100100010000001110100011010000110100101110011001000000111001100100
     010000110100001111000011101010101010000000001000101001011010001010100000000000111010000001000010111
     

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159. Horst Feistel
     1971: Published
     “Lucifer” cipher for
     computer encryption
     First(?) Block Cipher
     

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160. View Slide

161. XOR
     S-box
     Permutation
     

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162. SP Network
     

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163. Lucifer Cipher: “block” cipher
     Break message into 128-bit blocks
     128-bit key
     16 rounds:
     Break block in half
     the f-function is calculated using
     that round's subkey and the left half
     of the block.
     The result is then XORed to the
     right half of the block, which is the
     only part of the block altered for that
     round.
     After every round except the last
     one, the right and left halves of the
     block are swapped.
     

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164. 256 bit message (in ASCII)
     01010100011010000110010100100000010101010101001101000001001000000100111001010011
     01000001001000000111001101110100011011110111001001100101011100110010000001111001
     01101111011101010111001000100000011101000111011101100101011001010111010001110011
     0010000100100001
     

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165. Break into 128-bit blocks
     01010100011010000110010100100000010101010101001101000001001000000100111001010011010000010010000001110011011101000110111101110010
     01100101011100110010000001111001011011110111010101110010001000000111010001110111011001010110010101110100011100110010000100100001
     The USA NSA stor
     es your tweets!!
     

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166. Generate 128-bit key
     awesomepassword!
     01100001011101110110010101110011011011110110110101100101011100000110000101110011011100110111011101101111011100100110010000100001
     

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167. Break block in half
     01010100011010000110010100100000010101010101001101000001
     The USA NSA stor
     0100111001010011010000010010000001110011011101000110111101110010
     

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168. Generate 72-bit sub-key
     awesomepassword!
     01100001011101110110010101110011011011110110110101100101011100000110000101110011011100110111011101101111011100100110010000100001
     a a
     01100001 01100001
     wesomep
     01110111011001010111001101101111011011010110010101110000
     

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169. Rotate key left 7 bytes
     password!awesome
     01110000011000010111001101110011011101110110111101110010011001000010000101100001011101110110010101110011011011110110110101100101
     7 bytes
     

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170. …
     

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171. View Slide

172. Data Encryption Standard
     (DES)
     1977
     Lucifer with 56-bit keys
     So the NSA could
     brute force keys if
     they “needed” to
     

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173. Ancient
     Steganography,

     Scytale
     Brute Force
     Key Search
     Caesar Shift
     Non-shifted

     Substitution
     Frequency

     Analysis
     Homophonic
     Substitution
     Renaissance
     Poly-alphabetic
     Substitution
     Le Chiffre
     Indéchiffrable
     Assembly-line
     Frequency Analysis
     Industrial
     Babbage
     Frequency
     Analysis
     One-Time
     Pad
     Enigma
     Cryptanalytic “Bombs”:
     Polish,
     British,
     US
     Lucifer,
     DES
     1971-1977
     Computer
     

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174. How hard is it to find a

     binary 56-bit key?
     

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175. 1001101010011010100110101001
     1010100110101001101010011010
     Unique Possible Permutations
     256
     72,057,594,037,927,936
     72 quadrillion (million billion)
     In 1976, estimated to cost $20M to build a computer to crack
     such a key
     Affordable to the NSA
     

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176. DES
     1971-1977
     Computer-
     powered
     Brute Force
     Key Search
     

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177. By Max Roser - https://ourworldindata.org/uploads/2019/05/Transistor-Count-over-time-to-2018.png, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=79751151
     

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178. 1100110101001101010011010100
     1101010011010100110101001101
     0
     Unique Possible Permutations
     256
     72,057,594,037,927,936
     72 quadrillion (million billion)
     257
     144,115,188,075,855,870
     144 quadrillion (million billion)
     

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179. DES
     1971-1977
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     

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180. 3DES EDE:

     DES: Encrypt, Decrypt, Encrypt
     https://www.researchgate.net/figure/Flowchart-of-3DES-encryption-and-decryption-algorithm-40_fig4_322277374
     

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181. What about messages that
     are longer than the key?
     

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182. Block cipher

     mode of operation
     

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183. Electronic Codebook (ECB)
     https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation
     

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184. https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation
     

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185. Attribution, https://commons.wikimedia.org/w/index.php?curid=828161
     

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186. Cipher Block Chaining (CBC)
     https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation
     

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187. Attribution, https://commons.wikimedia.org/w/index.php?curid=828161
     

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188. DES
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     3DES + CBC
     

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189. The forever problem of cryptography:
     Key distribution
     

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190. Banks literally flew people
     around with code-books of keys
     

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191. We need a way to
     communicate secret keys
     over non-secret channels.
     

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192. Whitfield Diffie
     Stanford AI Lab
     1974
     

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193. Martin
     Hellman
     IBM Watson Research
     Center 1968-1969
     

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194. New Directions in Cryptography
     Published 1976
     

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195. Alice, Bob, and Eve
     Alice and Bob need to communicate securely
     They need to share a secret
     They only have public channels between them
     “Eve is always eavesdropping”
     How can they share a secret without sharing it with
     Eve?
     

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196. Diffie-Hellman
     Key Establishment
     

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197. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-1
     

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198. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-1
     

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199. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-1
     

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200. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-1
     +
     ____ ____
     +
     

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201. The key can be anything that
     can encode to 1’s and 0’s
     So, anything … like a number.
     

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202. View Slide

203. And in MATH! , we have
     some 1-way functions!
     

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204. Modular Arithmetic
     aka “Clock” arithmetic
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/discrete-logarithm-problem
     

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205. To find 46 mod 12 …
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/discrete-logarithm-problem
     

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206. Wrap a cord 46 “hours” long
     around a 12-hour clock …
     … and it ends on 10
     

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207. Easy to perform …
     46 mod 12 is “congruent” to 10
     generator Modulus
     

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208. ? mod 12 ≡ 10
     … hard to reverse
     

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209. ? mod 12 ≡ 10
     22 mod 12 ≡ 10
     34 mod 12 ≡ 10
     46 mod 12 ≡ 10
     58 mod 12 ≡ 10
     70 mod 12 ≡ 10
     .. mod 12 ≡ 10
     … impossible to reverse!
     

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210. … impossible for recipient too!
     

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211. Alice picks an exponent
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     Prime Modulus
     
     “n”
     generator
     
     “g”
     

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212. Alice keeps her exponent secret
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     Prime Modulus
     
     “n”
     generator
     
     “g”
     

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213. “Discrete Logarithm” problem
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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214. “Discrete Logarithm” problem
     Have to resort to “brute force”
     guessing the exponent
     

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215. For small numbers, it’s easy, but
     not for a large prime modulus.
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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216. How can we turn that single
     exponent secret into 2 secrets?
     

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217. “Commutative” Arithmetic:

     Order of operands doesn’t matter
     3 + 5 5 + 3
     =
     = 8
     3 * 5 =
     = 15 5 * 3
     

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218. “Commutative” Arithmetic:

     Order of operands doesn’t matter
     323 332
     =
     = 729
     3 + 5 5 + 3
     =
     = 8
     3 * 5 =
     = 15 5 * 3
     

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219. Alice and Bob publicly agree on
     a generator and prime modulus
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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220. Alice picks a private number,
     and sends the result to Bob
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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221. Bob picks a private number,
     and sends the result to Alice
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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222. Now the cool part …
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2
     

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223. Alice raises Bob’s result to
     her private exponent
     and gets 10
     

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224. Bob raises Alice’s mixture to
     his private exponent
     and also gets 10!
     

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225. Because their results were calculated
     from the shared public generator and
     prime modulus
     

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226. So, they did the same calculation
     with exponents in different order,
     which doesn’t affect the result
     

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227. Public Key Cryptography!
     

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228. Diffie-Hellman

     Key Establishment
     3DES
     +
     

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229. DES
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     1970+
     3DES + CBC
     DH + 3DES + CBC
     1976
     

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230. View Slide

231. View Slide

232. Use Diffie-Hellman Exchange to make a key …
     … for Triple-DES …
     … with Cipher Block Chaining mode.
     … Encrypt-Decrypt-Encrypt …
     

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233. What’s RSA?
     

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234. Diffie-Hellman makes a new
     key between every 2 people!
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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235. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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236. Clifford Cox
     1971
     Trap Door

     One-way Function
     By Royal Society uploader - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=43268163
     

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237. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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238. The “e” means
     encrypt!
     “d” is for decrypt!
     https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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239. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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240. https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/intro-to-rsa-encryption
     

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241. View Slide

242. View Slide

243. View Slide

244. View Slide

245. View Slide

246. View Slide

247. Bob's number
     

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248. View Slide

249. View Slide

250. Ron Rivest, Adi Shamir,
     Leonard Adelman
     

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251. DES
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     1970+
     3DES + CBC
     DH/RSA + 3DES + CBC
     1976
     

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252. Public Key Certificates
     https://www.youtube.com/watch?v=704dudhA7UI
     Alice's
     Alice's
     Alice's
     

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253. Look!
     The public exponent and modulus!
     

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254. Another RSA public exponent and
     modulus
     

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255. View Slide

256. Quantum
     Computing
     For fun, profit, and
     breaking the whole
     world
     

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257. View Slide

258. View Slide

259. Public Key Certificates
     https://www.youtube.com/watch?v=704dudhA7UI
     Alice's
     Alice's
     Alice's
     Quantum-
     cracked
     

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260. View Slide

261. DES
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     3DES + CBC
     DH/RSA + 3DES + CBC
     Quantum
     Computing
     

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262. 2048-bit RSA key needs

     4096-qubit computer to crack
     

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263. View Slide

264. DES
     Computer-powered
     Brute Force Key Search
     Moore’s Law
     3DES + CBC
     DH/RSA + 3DES + CBC
     Quantum
     Computing
     Post-Quantum
     Cryptography
     

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265. View Slide

266. View Slide

267. View Slide

268. View Slide

269. Don’t invent your own crypto
     

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270. Mind your keys
     

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271. https://techcrunch.com/2019/10/21/nordvpn-confirms-it-was-hacked/
     

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272. Questions?
     Scytale
     Caesar Cipher
     Unshifted cipher
     Frequency Analysis
     Poly-alphabetic cipher
     Vigenere Square
     Enigma
     Lucifer/DES
     Modes of Encryption
     Diffie-Hellman
     RSA
     Quantum
     speakerdeck.com/groovecoder
     

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