密码学原理技术-第十一章-Hash Functions

文章目录

• 总结
• [Why we need hash functions](#Why we need hash functions)
• • [Digital Signature with a Hash Function](#Digital Signature with a Hash Function)
  • [Basic Protocol for Digital Signatures with a Hash Function](#Basic Protocol for Digital Signatures with a Hash Function)
  • [Principal input--output behavior of hash functions](#Principal input–output behavior of hash functions)
• [Security properties](#Security properties)
• • [The three security requirements of hash functions](#The three security requirements of hash functions)
  • [Why the hash-based digital signature scheme is secure?](#Why the hash-based digital signature scheme is secure?)
  • [Collision Resistance and the Birthday Attack](#Collision Resistance and the Birthday Attack)
• Algorithms
• • [Constructing Hash Functions from Block Ciphers](#Constructing Hash Functions from Block Ciphers)
  • [Dedicatd Hash Functions -- MD4 family of hash functions](#Dedicatd Hash Functions -- MD4 family of hash functions)
• [Example: The Secure Hash Algorithm SHA-256](#Example: The Secure Hash Algorithm SHA-256)
• • SHA-2
  • • [SHA-256 Preprocessing](#SHA-256 Preprocessing)
    • [The SHA-256 Compression Function](#The SHA-256 Compression Function)
    • [Iteration j in the SHA-256 compression function](#Iteration j in the SHA-256 compression function)
• 资料

总结

Why we need hash functions

Digital Signature with a Hash Function

Basic Protocol for Digital Signatures with a Hash Function

Principal input--output behavior of hash functions

Security properties

The three security requirements of hash functions

Why the hash-based digital signature scheme is secure?

Collision Resistance and the Birthday Attack

2的80次方是当前计算机可达到的

Algorithms

Constructing Hash Functions from Block Ciphers

每个xi是分组加密的输入长度，最终哈希结果是xn经过e函数的结果

这个反过来了，但最终哈希结果是xn经过e函数的结果

Dedicatd Hash Functions -- MD4 family of hash functions

Example: The Secure Hash Algorithm SHA-256

SHA-2

总体框架

每块大小为 512 位

SHA-256 Preprocessing

The SHA-256 Compression Function

Iteration j in the SHA-256 compression function

资料

1. 关于许多哈希函数及其规范的概览：

   • http://ehash.iaik.tugraz.at/wiki/The_Hash_Function_Zoo

2. 生日悖论（Birthday Paradox）：

   • Wikipedia 提供了一个很好的解释：
   • http://en.wikipedia.org/wiki/Birthday_problem

3. SHA 标准：

   • SHA1+2 ：
     • http://csrc.nist.gov/publications/fips/fips180-2/fips180-2withchangenotice.pdf
   • SHA3 概述 ：
     • http://ehash.iaik.tugraz.at/wiki/The_SHA-3_Zoo

4. CrypTool：

   • CrypTool 是一个学习程序，同时也可以进行哈希操作：
   • http://www.cryptool.org/

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