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）