Wordleを遊んで情報科学を勉強する

PR TIMES 社内勉強会 @2022/02/18

- 頻度分析・単一置換暗号の話
- 情報エントロピーの話

Transcript

1. ɹ135*.&4ࣾ಺ษڧձ
   8PSEMFΛ༡ΜͰ
   ৘ใՊֶΛษڧ͢Δ
   

   View Slide

2. ΞδΣϯμ
   ࣗݾ঺հ
   8PSEMFͱ͸
   ස౓෼ੳ
   Τϯτϩϐʔ
   ·ͱΊ
   

   View Slide

3. ࣗݾ঺հ
   ໊લɿߐؒ༸ฏ
   ৬ۀɿόοΫΤϯυΤϯδχΞ
   (JU)VCNFJIFJ
   5XJUUFSBQQF@T
   

   View Slide

4. 8PSEMFͱ͸
   

   View Slide

5. 8PSEMFͰ༡Μͩ͜ͱ͕͋Δਓ🙋
   

   View Slide

6. 8PSEMFͱ͸
   ̑จࣈͷ୯ޠΛ౰ͯΔήʔϜ
   จࣈͱҐஔ͕౰͍ͨͬͯͨΒ🟩
   จࣈ͕౰͍ͨͬͯͨΒ🟨
   จࣈ͕౴͑ʹؚ·Εͳ͍৔߹͸⬜
   ௅ઓ͸̒ճ·Ͱ
   

   View Slide

7. ྫ͑͹ɾɾɾ
   ਖ਼ղ͕803-%ͷ৔߹
   41&",ͱೖྗ͢Δͱ⬜⬜⬜⬜⬜͕ฦ͞ΕΔ
   108&3ͱೖྗ͢Δͱ⬜🟩🟨⬜🟨͕ฦ͞ΕΔ
   80345ͱೖྗ͢Δͱ🟩🟩🟩⬜⬜͕ฦ͞ΕΔ
   803-%ͱೖྗ͢Δͱ🟩🟩🟩🟩🟩͕ฦ͞ΕͯɺήʔϜʹউར
   

   View Slide

8. ࠓ೔͸͜ͷήʔϜͰ༡ͼͳ͕Β
   ৘ใՊֶ $4
   ͷษڧΛ͠·͢
   

   View Slide

9. ΞδΣϯμ
   ࣗݾ঺հ
   8PSEMFͱ͸
   ස౓෼ੳ
   Τϯτϩϐʔ
   ·ͱΊ
   ࠓ೔ֶͿࣄ
   

   View Slide

10. ͬͦ͘͞༡ΜͰߦ͖·͠ΐ͏
    

    View Slide

11. ॳखɺԿʹ͠·͔͢ʁ
    

    View Slide

12. 🟩🟩🟩🟩🟩ˡউͪ
    ⬜🟩🟩🟩🟩ˡ̐จࣈ౰͍ͨͬͯΔɺઌ಄̍จࣈ͕ҧ͏
    ⬜🟨⬜🟨⬜ˡ̎จࣈ౰͍ͨͬͯΔ
    ⬜⬜⬜⬜⬜ˡશવΘ͔Βͳ͍ʁ
    

    View Slide

13. 🟩ͱ🟨͕དྷΔͱخ͍͠
    

    View Slide

14. ͳΔ΂͘ਖ਼ղͷ̑จࣈʹ
    ࢖ΘΕ͍ͯΔจࣈΛೖྗ͍ͨ͠
    

    View Slide

15. ස౓෼ੳ
    

    View Slide

16. ୯Ұஔ׵҉߸ͷ࿩Λ͠·͢
    ͍͖ͳΓͰ͕͢ʜ
    

    View Slide

17. ୯Ұஔ׵҉߸
    ͭͷจࣈʹରͯ͠ɺৗʹಉ͡จࣈʹ
    ม׵͞ΕΔΑ͏ͳ҉߸
    γʔβʔ҉߸ɺ305ͳͲ͕༗໊
    γʔβʔ҉߸
    

    View Slide

18. ྫʢ305ʣ
    ΞϧϑΝϕοτΛจࣈγϑτͤͨ͞୯Ұஔ׵҉߸
    ฏจ ҉߸จ
    

    View Slide

19. ྫʢ305ʣ
    ΞϧϑΝϕοτΛจࣈγϑτͤͨ͞୯Ұஔ׵҉߸
    ҉߸จ
    🤔
    

    View Slide

20. ͜Εɺ࣮͸؆୯ʹղ͚·͢
    

    View Slide

21. ม׵લ͸zFz͕ଟ͘ɺม׵ޙ͸zSz͕ଟ͍
    ฏจ ҉߸จ
    

    View Slide

22. ม׵લ͸zWz͕গͳ͘ɺม׵ޙ͸zJz͕গͳ͍
    ฏจ ҉߸จ
    

    View Slide

23. จࣈͷग़ݱස౓͸ภΓ͕͋Γͦ͏
    

    View Slide

24. จষதͷจࣈͷग़ݱස౓
    ฏจ ҉߸จ
    

    View Slide

25. ୯Ұஔ׵҉߸͸͜͏΍ͬͯղ͘
    ฏจ Ұൠతͳจষͷจࣈͷग़ݱස౓ͱൺֱ
    ҉߸จ ҉߸จͷจࣈͷग़ݱස౓Λ෼ੳ
    

    View Slide

26. 8PSEMF΋ಉ͡ΞϓϩʔνͰ
    ղ͚ͳ͍Ζ͏͔ʁ
    

    View Slide

27. ස౓෼ੳGPS8PSEMF
    ొ࿥͞Ε͍ͯΔ̑จࣈͷӳ୯ޠ͸ ݸ͋Δ
    ͔͠͠ɺ࣮ࡍʹXPSEMFͰ౴͑ͱͯ͠࢖ΘΕΔ୯ޠ͸ ݸ
    ϫʔυϦετ͸(JU)VC͔ΒऔಘՄೳ
    ˠΑ͠ɺ෼ੳ͠Α͏
    ˞͜Ε͸ެࣜͷ΋ͷͰ͸ͳ͍Ͱ͢
    

    View Slide

28. ୯ޠʹจࣈ͕̍จࣈҎ্ग़ݱ͢Δස౓
    ΍͸ΓF͕ڧ͍ʢ໿ͷ
    ୯ޠʹؚ·ΕΔʣ
    ࣍఺ͰB΍Sʢ໿ʣ
    J M O P T UͳͲ͸Α͘ग़
    ݱ͢Δʢ໿ʣ
    K R Y [͸΄ͱΜͲग़ݱ͠
    ͳ͍ʢ໿ʣ
    

    View Slide

29. ͳΔ΂͘ਖ਼ղͷ̑จࣈʹ
    ࢖ΘΕ͍ͯΔจࣈΛೖྗ͍ͨ͠
    ໋୊
    

    View Slide

30. ग़ݱස౓ͷߴ͍F B SΛඞͣ࢖͏
    Ճ͑ͯJ M O P T UΛ࢖ͬͯ୯ޠ
    Λ࡞Δ
    ΍Δ͜ͱ
    

    View Slide

31. ୯ޠͷީิ
    w FBSO
    w FBSMT
    w FBSOT
    w FBSOU
    w FBSTU
    w MFBST
    w OFBST
    w TUFBS
    w UFBST
    

    View Slide

32. ୯ޠͷީิ
    w FBSO
    w FBSMT
    w FBSOT
    w FBSOU
    w FBSTU
    w MFBST
    w OFBST
    w TUFBS
    w UFBST
    ˢࠓճ͸͜ΕΛ࠾༻
    

    View Slide

33. ॳख5&"34ͰຒΊͯߦ͘
    

    View Slide

34. ྑ͍ॳख͕ଧͯͨ🙌
    

    View Slide

35. ࣍ͷखɺԿʹ͠·͔͢ʁ
    

    View Slide

36. ·ͣ͸۪௚ʹߟ͑ͯΈΔ
    

    View Slide

37. ࠓ෼͔͍ͬͯΔࣄ
    w "͸จࣈͱҐஔ͕߹͍ͬͯΔ
    w & 4͸Ͳ͔͜Ͱ࢖ΘΕ͍ͯΔ
    w 5 3͸࢖ΘΕͳ͍
    ɹɹˠ͜ͷ৘ใ͔Β৚݅Λ࡞Δ
    

    View Slide

38. ਖ਼ղͰ͋Δ৚݅
    w ̏จࣈ໨͸"
    w ̎จࣈ໨Ҏ֎ʹ&ؚ͕·ΕΔ
    w ̑จࣈ໨Ҏ֎ʹ4ؚ͕·ΕΔ
    w 5 3͸จࣈʹؚ·Εͳ͍
    

    View Slide

39. ୯ޠͷީิʢ̍̕௨Γʣ
    w BCBTF
    w DFBTF
    w DIBTF
    w MFBTF
    w MFBTI
    w QIBTF
    w TDBMF
    w TIBEF
    w TIBLF
    w TIBMF
    w TIBNF
    w TIBQF
    w TIBWF
    w TMBWF
    w TOBLF
    w TQBDF
    w TQBEF
    w TVBWF
    w VTBHF
    

    View Slide

40. ස౓෼ੳΑΓJ M O Pؚ͕·ΕΔจࣈ
    w BCBTF
    w DFBTF
    w DIBTF
    w MFBTF
    w MFBTI
    w QIBTF
    w TDBMF
    w TIBEF
    w TIBLF
    w TIBMF
    w TIBNF
    w TIBQF
    w TIBWF
    w TMBWF
    w TOBLF
    w TQBDF
    w TQBEF
    w TVBWF
    w VTBHF
    

    View Slide

41. ස౓෼ੳΑΓJ M O Pؚ͕·ΕΔจࣈ
    w BCBTF
    w DFBTF
    w DIBTF
    w MFBTF
    w MFBTI
    w QIBTF
    w TDBMF
    w TIBEF
    w TIBLF
    w TIBMF
    w TIBNF
    w TIBQF
    w TIBWF
    w TMBWF
    w TOBLF
    w TQBDF
    w TQBEF
    w TVBWF
    w VTBHF
    ˣࠓճ͸͜ΕΛ࠾༻
    

    View Slide

42. ̎ख໨4$"-&ͰຒΊͯߦ͘
    

    View Slide

43. 🟩͕૿͑ͨ🙌
    

    View Slide

44. ߋʹ୯ޠͷީิΛߜΔʢ̕௨Γʣ
    w TIBEF
    w TIBLF
    w TIBNF
    w TIBQF
    w TIBWF
    w TOBLF
    w TQBDF
    w TQBEF
    w TVBWF
    

    View Slide

45. ߋʹ୯ޠͷީิΛߜΔʢ̕௨Γʣ
    w TIBEF
    w TIBLF
    w TIBNF
    w TIBQF
    w TIBWF
    w TOBLF
    w TQBDF
    w TQBEF
    w TVBWF
    ˣࠓճ͸͜ΕΛ࠾༻
    

    View Slide

46. ̏ख໨4)"%&ͰຒΊͯߦ͘
    

    View Slide

47. 🟩͕૿͑ͨ🙌
    

    View Slide

48. ߋʹ୯ޠͷީิΛߜΔʢ̐௨Γʣ
    w TIBLF
    w TIBNF
    w TIBQF
    w TIBWF
    ˡ࣍͸͜ΕΛ࠾༻
    

    View Slide

49. ̐ख໨4)".&ͰຒΊͯߦ͘
    

    View Slide

50. ͸ͣΕͨ😥
    

    View Slide

51. ߋʹ୯ޠͷީิΛߜΔʢ̏௨Γʣ
    w TIBLF
    w TIBQF
    w TIBWF ˡ࣍͸͜ΕΛ࠾༻
    

    View Slide

52. ̑ख໨4)"7&ͰຒΊͯߦ͘
    

    View Slide

53. ͸ͣΕͨ😰
    

    View Slide

54. ߋʹ୯ޠͷީิΛߜΔʢ̎௨Γʣ
    w TIBLF
    w TIBQF ˡ࠷ޙ͸͜ΕΛ࠾༻
    

    View Slide

55. ϥετ4)"1&ͰຒΊͯߦ͘
    

    View Slide

56. ͸ͣΕͨ😱
    

    View Slide

57. ͳͥͳͷ͔
    

    View Slide

58. ৼΓฦͬͯΈΔ
    ̍ख໨͸ ௨Γ
    ̎ख໨͸௨Γ
    ̏ख໨͸௨Γ
    ̐ख໨͸௨Γ
    ̑ख໨͸௨Γ
    ̒ख໨͸௨Γ
    

    View Slide

59. ৼΓฦͬͯΈΔ
    ̍ख໨͸ ௨Γ
    ̎ख໨͸௨Γ
    ̏ख໨͸௨Γ
    ̐ख໨͸௨Γ
    ̑ख໨͸௨Γ
    ̒ख໨͸௨Γ
    ·Ͱ࡟ݮɺྑ͍ख
    

    View Slide

60. ৼΓฦͬͯΈΔ
    ̍ख໨͸ ௨Γ
    ̎ख໨͸௨Γ
    ̏ख໨͸௨Γ
    ̐ख໨͸௨Γ
    ̑ख໨͸௨Γ
    ̒ख໨͸௨Γ
    ·Ͱ࡟ݮɺඍົ
    

    View Slide

61. ৼΓฦͬͯΈΔ
    ̍ख໨͸ ௨Γ
    ̎ख໨͸௨Γ
    ̏ख໨͸௨Γ
    ̐ख໨͸௨Γ
    ̑ख໨͸௨Γ
    ̒ख໨͸௨Γ
    ·Ͱ࡟ݮɺඍົ
    

    View Slide

62. ৼΓฦͬͯΈΔ
    ̍ख໨͸ ௨Γ
    ̎ख໨͸௨Γ
    ̏ख໨͸௨Γ
    ̐ख໨͸௨Γ
    ̑ख໨͸௨Γ
    ̒ख໨͸௨Γ
    ͻͲ͍
    ͻͲ͍
    

    View Slide

63. ͳͥͳͷ͔
    

    View Slide

64. ॳखͰ෼͔ͬͨࣄ
    w "͸จࣈͱҐஔ͕߹͍ͬͯΔ
    w & 4͸Ͳ͔͜Ͱ࢖ΘΕ͍ͯΔ
    w 5 3͸࢖ΘΕͳ͍
    

    View Slide

65. ॳखͰ͸ଟ͘ͷ৘ใ͕ಘΒΕͨ
    

    View Slide

66. ௨Γ͔Β௨Γ·Ͱ
    ࡟ݮͨ͠
    

    View Slide

67. ̐ख໨Ͱ෼͔ͬͨࣄ
    w .͸࢖ΘΕͳ͍
    

    View Slide

68. ̐ख໨͸গ͠ͷࣄ͔͠
    ෼͔Βͳ͔ͬͨ
    

    View Slide

69. ௨Γ͔Β௨Γʹͳ͚ͬͨͩ
    

    View Slide

70. ͭ·ΓɺಘΒΕΔ৘ใ͕
    ଟ͍΄͏͕ྑ͍ख
    

    View Slide

71. ಘΒΕΔ৘ใͷྔΛ͸͔Δࣄ͸
    ग़དྷͳ͍ͩΖ͏͔ʁ
    

    View Slide

72. Τϯτϩϐʔ
    

    View Slide

73. ৘ใྔ
    ͦͷࣄ৅͕ͲΕ͚ͩ৘ใΛग़͔ͨ͠Λ͸͔Δई౓
    ࣄ৅͕ى͜Δ֬཰ ͱ͢Δͱ
    ৘ใྔ
    p
    I(p) = − log p
    

    View Slide

74. ؆୯ʹݴ͏ͱɺ௝͍͠ࣄ͸
    ಘΒΕΔ৘ใ͕ଟ͍
    

    View Slide

75. ৘ใྔͷྫ
    छྨͷΞϧϑΝϕοτ͔Β̍ͭΛ౰ͯΔ
    *
    −log2
    1
    26
    

    View Slide

76. ৘ใྔͷྫ
    छྨͷΞϧϑΝϕοτ͔Β̍ͭΛ౰ͯΔ
    *
    ɹˠ෼͔Γ͖͍ͬͯΔࣄ৅
    ɹɹˠಘΒΕΔ৘ใྔ͸̌
    −log2
    1
    1
    

    View Slide

77. ৘ใྔΛ࢖͑͹8PSEMF
    ΋ղ͚ͦ͏ͩʂ
    

    View Slide

78. Ͳ͏΍ͬͯ8PSEMFʹԠ༻͢Δ͔ʁ
    

    View Slide

79. ΤϯτϩϐʔΛ࠷େԽ͢Δ
    

    View Slide

80. Τϯτϩϐʔʢฏۉ৘ใྔʣ
    ͷ͢΂ͯͷࣄ৅ʹରͯ͠৘ใྔͷฏۉΛͱͬͨ΋ͷ
    ฏۉ৘ใྔ
    ɹɹˠ͍ͭ͜Λ࠷େԽ͢Ε͹Αͦ͞͏
    X
    H(X) = − ∑
    i
    pi
    log pi
    

    View Slide

81. ࣮ࡍʹ8PSEMFͰΤϯτϩϐʔ
    Λ࢖ͬͯΈΔ
    

    View Slide

82. ̐ख໨ͷީิ
    w TIBLF
    w TIBNF
    w TIBQF
    w TIBWF
    

    View Slide

83. 4)".&ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟩🟩⬜🟩
    w TIBNFɹˠɹ🟩🟩🟩🟩🟩
    w TIBQFɹˠɹ🟩🟩🟩⬜🟩
    w TIBWFɹˠɹ🟩🟩🟩⬜🟩
    

    View Slide

84. 4)".&ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟩🟩⬜🟩
    w TIBNFɹˠɹ🟩🟩🟩🟩🟩
    w TIBQFɹˠɹ🟩🟩🟩⬜🟩
    w TIBWFɹˠɹ🟩🟩🟩⬜🟩
    🟩🟩🟩⬜🟩
    
    🟩🟩🟩🟩🟩
    
    p
    3
    4
    p
    1
    4
    

    View Slide

85. 4)".&ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟩🟩⬜🟩
    w TIBNFɹˠɹ🟩🟩🟩🟩🟩
    w TIBQFɹˠɹ🟩🟩🟩⬜🟩
    w TIBWFɹˠɹ🟩🟩🟩⬜🟩
    🟩🟩🟩⬜🟩
    
    🟩🟩🟩🟩🟩
    
    p
    3
    4
    p
    1
    4
    4)".&
    
    H −
    3
    4
    log2
    3
    4
    −
    1
    4
    log2
    1
    4
    ≒ 0.81
    

    View Slide

86. Τϯτϩϐʔ͕େ͖͍୯ޠ
    Ͱ͸Ͳ͏ͳΔͷ͔
    

    View Slide

87. 4,*.1ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟨⬜⬜⬜
    w TIBNFɹˠɹ🟩⬜⬜⬜⬜
    w TIBQFɹˠɹ🟩⬜⬜⬜🟨
    w TIBWFɹˠɹ🟩⬜⬜⬜⬜
    ˞༧Ίܭࢉͯ͠ɺ͜ͷ୯ޠΛબΜͰ͍·͢
    

    View Slide

88. 4,*.1ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟨⬜⬜⬜
    w TIBNFɹˠɹ🟩⬜⬜⬜⬜
    w TIBQFɹˠɹ🟩⬜⬜⬜🟨
    w TIBWFɹˠɹ🟩⬜⬜⬜⬜
    🟩⬜⬜⬜⬜
    
    🟩🟨⬜⬜⬜
    
    🟩⬜⬜⬜🟨
    
    p
    2
    4
    p
    1
    4
    p
    1
    4
    

    View Slide

89. 4,*.1ΛબΜͩ৔߹
    w TIBLFɹˠɹ🟩🟨⬜⬜⬜
    w TIBNFɹˠɹ🟩⬜⬜⬜⬜
    w TIBQFɹˠɹ🟩⬜⬜⬜🟨
    w TIBWFɹˠɹ🟩⬜⬜⬜⬜
    🟩⬜⬜⬜⬜
    
    🟩🟨⬜⬜⬜
    
    🟩⬜⬜⬜🟨
    
    p
    2
    4
    p
    1
    4
    p
    1
    4
    4,*.1
    
    H −
    2
    4
    log2
    2
    4
    −
    1
    4
    log2
    1
    4
    −
    1
    4
    log2
    1
    4
    ≒ 1.5
    

    View Slide

90. 4)".&ΑΓ΋4,*.1ͷํ͕
    ಘΒΕΔ৘ใ͕ଟ͍
    

    View Slide

91. 4,*.1ͰຒΊͯߦ͘
    

    View Slide

92. ͸ͣΕͨ😥
    

    View Slide

93. Ͱ΋৘ใྔ͸େ͖͍😄
    

    View Slide

94. ̑ख໨ͷ୯ޠͷީิ͸ʜ
    w TIBLF
    ɹˠɹ̍௨ΓʹߜΒΕͨʂ
    

    View Slide

95. উͬͨʂʂ
    

    View Slide

96. Τϯτϩϐʔ͛͢ʔ
    

    View Slide

97. ͦ͏͍͑͹
    

    View Slide

98. 🟩ͱ🟨͸ݮͬͯྑ͍ͷ͔ʁ
    🤔
    

    View Slide

99. 🟩ͱ🟨͕དྷΔͱخ͍͠
    

    View Slide

100. 🟩ͱ🟨͕དྷΔͱخ͍͠
     ͜Ε͸ؒҧ͑
     

     View Slide

101. ਖ਼͘͠͸
     Τϯτϩϐʔ͕࠷େԽ͞ΕΔ
     ͱخ͍͠
     

     View Slide

102. ͪͳΈʹ
     Τϯτϩϐʔͷ࠷େԽ͸ॳखͰ΋దԠग़དྷΔ
     ɹˠɹιϧόʔ࡞ΔͳΒස౓෼ੳΑΓΤϯτϩϐʔ
     4"-&5͕࠷ڧͱ͍͏ͷ͕௨આ
     

     View Slide

103. ·ͱΊ
     

     View Slide

104. ࠓ೔ֶΜͩ͜ͱ
     ୯Ұஔ׵҉߸͸ස౓෼ੳͰղ͚Δ
     ࣗવݴޠͷจࣈʹ͸ग़ݱස౓ʹภΓ͕͋Δ
     ৘ใྔͱ͸ͦͷࣄ৅͕ͲΕ͚ͩ৘ใΛग़͔ͨ͠Λ͸͔Δई౓
     ৘ใྔ
     Τϯτϩϐʔͱ͸͢΂ͯͷࣄ৅ͷ৘ใྔͷฏۉ
     ฏۉ৘ใྔ
     I(p) = − log p
     H(X) = − ∑
     i
     pi
     log pi
     

     View Slide

105. ࢀߟ
     w IUUQTYDMPDIFIBUFCMPKQFOUSZ
     w IUUQTTPOPSPVTDIPDPMBUFDPNOPUFTJOEFYQIQ
     UJUMF5IF@CFTU@TUSBUFHJFT@GPS@8PSEMF
     w IUUQTHJUIVCDPNBMFYXPSEMF
     w IUUQTRJJUBDPNNBTBLB@QSPHSBNNJOHJUFNT
     BGFBBFECG
     w IUUQTGSFTINBOEFWXPSEMFMFBEFSCPBSE
     

     View Slide