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非對稱加密-以橢圓曲線密碼學ECC為例

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簡單介紹 ECC

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非對稱加密-以橢圓曲線密碼學ECC為例

  1. 1. 以橢圓曲線密碼學ECC為例例 淺談非對稱加密
  2. 2. Blog : lamb-mei.com 羊小咩 E-mail : lamb@lamb-mei.com FB : https://www.facebook.com/lamb.mei GitHub:https://github.com/lamb-mei/ Lamb Mei
  3. 3. / 503 為什麼要說這個題⺫ 圖片來來源 http://www.dailycold.tw/wp-content/uploads/2017/06/%E6%9C%AA%E5%91%BD%E5%90%8D-1.jpg
  4. 4. / 504 想了了解⼀一下 ECC 應⽤用
  5. 5. / 505 圖片來來源 https://dvblobcdnjp.azureedge.net//Content/Upload/Popular/Images/2018-10/572acefe-45b1-4c70-8aca-5f310d51f50f_m.jpg
  6. 6. / 506 密碼學 (Cryptography) 圖片來來源 https://www.flaticon.com/authors/surang
  7. 7. / 507 密碼學 Cryptography 對稱式加密 (Symmetric Encryption) 非對稱式加密 (Asymmetric Encryption)
  8. 8. / 508 圖片來來源 演算法圖鑑 對稱式加密 (Symmetric Encryption) DES、3DES、AES
  9. 9. / 509 非對稱式密碼學 asymmetric cryptography
  10. 10. / 5010 ⼜又稱 公開⾦金金鑰密碼學 Public-key cryptography
  11. 11. / 5011 圖片來來源 演算法圖鑑 非對稱式加密 (Asymmetric Encryption)
  12. 12. / 5012 圖片來來源 演算法圖鑑 非對稱式加密 (Asymmetric Encryption)
  13. 13. / 5013 圖片來來源 演算法圖鑑 非對稱式加密 (Asymmetric Encryption)
  14. 14. / 5014 圖片來來源 演算法圖鑑 非對稱式加密 (Asymmetric Encryption)
  15. 15. / 5015 非對稱式加密 (Asymmetric Encryption) RSA ECC 著名的演算法
  16. 16. / 5016 都是利利⽤用數學難題, 正向計算容易易但反推非常困難 非對稱式加密 (Asymmetric Encryption)
  17. 17. / 5017 橢圓曲線密碼學 Elliptic Curve Cryptography
  18. 18. / 5018 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 https://www.moedict.tw/%E5%8E%9F%E7%90%86.png
  19. 19. / 5019 橢圓曲線密碼學 Elliptic Curve Cryptography y = x + ax + b 32
  20. 20. / 5020 橢圓曲線密碼學 Elliptic Curve Cryptography 加法定義
  21. 21. / 5021 橢圓曲線密碼學 Elliptic Curve Cryptography 乘法定義
  22. 22. / 5022 橢圓曲線密碼學 Elliptic Curve Cryptography O∞ 定義
  23. 23. / 5023 橢圓曲線密碼學 Elliptic Curve Cryptography 橢圓曲線是連續的,並不適合⽤用於加密; 所以,我們必須把橢圓曲線變成離散的點 把橢圓曲線定義在有限域上
  24. 24. / 5024 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 https://www.zhihu.com/question/26662683
  25. 25. / 5025 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 https://www.zhihu.com/question/26662683
  26. 26. / 5026 橢圓曲線密碼學 Elliptic Curve Cryptography {p,a,b,G,n,h} ⼀一條橢圓曲線 p : ⼀一個質數 決定域 a , b : 曲線參參數 G : 基點 n : G的階 h : 商除整數
  27. 27. / 5027 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 https://www.moedict.tw/%E5%8E%9F%E7%90%86.png 聽完似乎很難的原理理 來來講個 ⼩小故事
  28. 28. / 5028 如何畫出⼀一隻⾺馬?
  29. 29. / 5029 如何畫出⼀一隻⾺馬?
  30. 30. / 5030 如何畫出⼀一隻⾺馬?
  31. 31. / 5031 如何畫出⼀一隻⾺馬?
  32. 32. / 5032 如何畫出⼀一隻⾺馬?
  33. 33. / 5033 如何畫出⼀一隻⾺馬? 就是這麼簡單
  34. 34. / 5034 橢圓曲線密碼學 Elliptic Curve Cryptography ECC 應⽤用 ECDSA (Elliptic Curve Digital Signature Algorithm) 數位簽名演算法 ECIES (Elliptic Curve Integrated Encryption Scheme) 集成加密⽅方式 ECDH (Elliptic Curve Diffie–Hellman key Exchange) ⾦金金鑰交換演算法
  35. 35. / 5035 橢圓曲線密碼學 Elliptic Curve Cryptography ECDH (Elliptic Curve Diffie–Hellman key Exchange)
  36. 36. / 5036 橢圓曲線密碼學 Elliptic Curve Cryptography ECDH (Elliptic Curve Diffie–Hellman key Exchange)
  37. 37. / 5037 n = 19 h = 1 橢圓曲線密碼學 Elliptic Curve Cryptography ECDH (Elliptic Curve Diffie–Hellman key Exchange)
  38. 38. / 5038 橢圓曲線密碼學 Elliptic Curve Cryptography ECDH (Elliptic Curve Diffie–Hellman key Exchange) 圖片來來源 :https://www.youtube.com/watch?v=F3zzNa42-tQ
  39. 39. / 5039 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 :https://www.youtube.com/watch?v=F3zzNa42-tQ 會選⽤用⼤大的數字和質數,使其幾乎無法計算
  40. 40. / 5040 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 :https://www.youtube.com/watch?v=F3zzNa42-tQ 優點 • 安全性能更更⾼高 160位ECC 和 1024位RSA、DSA有相同的安全强度 • 處理理速度更更快 在計算速度上,ECC比RSA、DSA快得多 • 頻寬要求更更低 • 儲存空間更更⼩小 ECC的密鑰⼤大⼩小參參數,與RSA、DSA相比要⼩小得多
  41. 41. / 5041 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 :https://www.youtube.com/watch?v=F3zzNa42-tQ • 設計困難,實現不容易易 缺點
  42. 42. / 5042 橢圓曲線密碼學 Elliptic Curve Cryptography 圖片來來源 :https://www.youtube.com/watch?v=F3zzNa42-tQ • 區塊鏈數位簽名 應⽤用 • 序號產⽣生驗證 • 基於⾝身份加密 • TLS/SSL 數位憑證 • …
  43. 43. 這次即便便是⼤大家的聰明才智 還是要DEMO⼀一下 圖片來來源 :http://www.dailycold.tw/wp-content/uploads/ 2017/06/%E6%9C%AA%E5%91%BD%E5%90%8D-1.jpg
  44. 44. / 5044 圖片來來源 :https://github.com/agens-no/EllipticCurveKeyPair Elliptic Curve Key Pair https://github.com/agens-no/EllipticCurveKeyPair 推薦很不錯的 ECC套件
  45. 45. / 5045 Elliptic Curve Key Pair But !
  46. 46. / 5046 Elliptic Curve Key Pair
  47. 47. / 5047 Elliptic Curve Key Pair 改為 public init(config: Config) { self.config = config } /Sources/EllipticCurveKeyPair.swift public init() {}將
  48. 48. / 5048 圖片來來源 :https://blog.udemy.com/wp-content/uploads/2014/05/shutterstock_175331306.jpg
  49. 49. / 5049 對稱式加密 (Symmetric Encryption) 非對稱式加密 (Asymmetric Encryption) 橢圓曲線密碼學(Elliptic Curve Cryptography) ECDSA (Elliptic Curve Digital Signature Algorithm) ECIES (Elliptic Curve Integrated Encryption Scheme) ECDH (Elliptic Curve Diffie–Hellman key Exchange) SUMMARY
  50. 50. / 5050 ⽺羊⼩小咩 2019 / 06 / 13 @ Cocoaheads Taipei 其餘的 我們iPlayground⾒見見 密碼學博⼤大精深

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