目录
摘要Ⅲ
关键词Ⅲ
AbstractⅢ
引言
引言1
1密码学基本概念与发展1
1.1密码学基本概念1
1.2密码学的发展 2
1.2.1恺撒密码2
1.2.2维吉尼亚密码2
1.2.3普莱费尔密码3
1.2.4希尔密码3
1.2.5近代密码学4
1.2.6现代密码学4
2密码学中矩阵的作用4
2.1能够进行LU分解的矩阵4
2.2能够标准化的矩阵7
2.3线性方程组类型的矩阵7
3 用MATLAB实现希尔密码的加密与解密 8
3.1 MATLAB对希尔密码进行加密与解密8
4 总结 11
4．1 总结11
致谢11
参考文献12
浅谈矩阵在密码学中的应用
摘 要
本篇文章主要介绍了密码学的基础概念，密码学的发展趋势以及密码学在各个时期的不同特征。同时也介绍了高数中常用的数学工具矩阵以及密码学如何使用矩阵来对相关信息进行加密和破译。通过研究不同类型的矩阵怎么运作来将我们想要传达的信息加密成无意义或不可理解的信息，或者将无意义、不可理解的信息翻译成我们可理解的信息来比较不同矩阵在密码学中加解密的效率。矩阵的加密方式是密钥矩阵通过矩阵的运算法则来将想要表达的消息进行加密使之无意义或不可理解。而加密之后的信息的破译则需要通过矩阵的分解来将密文翻译成明文。由于矩阵的运算不满足乘法的交换律所以矩阵具有非交换属性，而具有非交换属性的矩阵加密的密码有很好的抵挡量子计算的攻击的潜能。这是现在广泛使用的公钥密码所不具备的优势。希尔密码就是使用矩阵加密的一种密码，所以希尔密码某种程度上可以很好的抵挡破译，保护信息的安全。同时本文也会从编程角度介绍希尔密码中怎样对信息加密以及快速求出矩阵密钥的逆,对密文进行解密从而完成希尔密码的快速加密和解密。
BRIEF TALKING ON THE APPLICATION OF MATRIX IN CRYPTOGRAPHY
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ABSTRACT
This paper mainly introduces the basic concepts of cryptography, the development trend of cryptography and the different characteristics of cryptography in different periods. At the same time, it also introduces the common mathematical tool matrix in high number and how to use the matrix to encrypt and decode the relevant information. By studying how different types of matrices work to encrypt the information we want to convey into meaningless or incomprehensible information, or translate the meaningless and incomprehensible information into understandable information to compare the encryption and decryption efficiency of different matrices in cryptography. The encryption method of matrix is that the key matrix encrypts the message to be expressed by the algorithm of matrix to make it meaningless or incomprehensible. The decipherment of encrypted information needs to translate ciphertext into plaintext through matrix decomposition. Because the operation of the matrix does not satisfy the commutative law of multiplication, the matrix has the non commutative property, and the encryption of the matrix with the non commutative property has a good potential to resist the attack of quantum computation. This is not the advantage of the public key password which is widely used now. Hill cipher is a kind of cipher using matrix encryption, so Hill cipher can resist decoding and protect information security to some extent. At the same time, from the programming point of view, this paper will also introduce how to encrypt the information and quickly find the inverse of the matrix key, and then decrypt the ciphertext to complete the fast encryption and decryption of the hill password.

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