密码学原理技术-第六章-introduction to pulibc-key cryptography

文章目录

  • 总结
  • [Symmetric Cryptography revisited](#Symmetric Cryptography revisited)
    • [Symmetric Cryptography: Analogy](#Symmetric Cryptography: Analogy)
    • [Symmetric Cryptography: Shortcomings](#Symmetric Cryptography: Shortcomings)
  • [principles of asymmetric cryptography](#principles of asymmetric cryptography)
    • [Idea behind Asymmetric Cryptography](#Idea behind Asymmetric Cryptography)
    • [asymmetric(public key) cryptography](#asymmetric(public key) cryptography)
    • [aSymmetric Cryptography: Analogy](#aSymmetric Cryptography: Analogy)
  • [practical aspects of public-key cryptograpy](#practical aspects of public-key cryptograpy)
    • [basic protocol for public-key Encryption](#basic protocol for public-key Encryption)
    • [security Mechanisms of Public-Key Cryptography](#security Mechanisms of Public-Key Cryptography)
    • [basic key transport protocol](#basic key transport protocol)
  • [important public-key algorithm](#important public-key algorithm)
    • [how to build public-key algorithms](#how to build public-key algorithms)
    • [key lengths and security levels](#key lengths and security levels)
  • [essential number theory for public-key algorithm](#essential number theory for public-key algorithm)
    • [Euclidean algorithm](#Euclidean algorithm)
    • [extended Euclidean algorithm](#extended Euclidean algorithm)
      • [Euler's Phi Function(欧拉函数)](#Euler's Phi Function(欧拉函数))
      • [Fermat's Little Theorem](#Fermat's Little Theorem)
      • [欧拉定理(Euler's Theorem)](#欧拉定理(Euler's Theorem))

总结

Symmetric Cryptography revisited

Symmetric Cryptography: Analogy

Symmetric Cryptography: Shortcomings


principles of asymmetric cryptography

Idea behind Asymmetric Cryptography

asymmetric(public key) cryptography

aSymmetric Cryptography: Analogy

practical aspects of public-key cryptograpy

basic protocol for public-key Encryption

security Mechanisms of Public-Key Cryptography





basic key transport protocol

使用 AES 作为对称加密的混合加密协议

important public-key algorithm

how to build public-key algorithms

key lengths and security levels

essential number theory for public-key algorithm

Euclidean algorithm


原理证明

extended Euclidean algorithm

先列出标准欧几里得算法表格,然后一步一步回代(上一步余数的等式带入当前式子)

证明



12mod67和67mod12的最后得到的式子是一样的,所以不如直接用67mod12,因为12mod67会转换成67mod12,此时67是r0,12是r1

Euler's Phi Function(欧拉函数)


欧拉函数的高效计算方法


Fermat's Little Theorem

欧拉定理(Euler's Theorem)


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