伽罗瓦域GF(2~8)上高矩阵为密钥的Hill加密衍生  

Hill encryption derivative algorithm in Galois field GF(2~8) with high-matrix as key matrix

作　　者：刘海峰[1,2] 卢开毅 梁星亮 Liu Haifeng;Lu Kaiyi;Liang Xingliang(College of Electrical & Information Engineering, Shaanxi University of Science & Technology,Xi’an 710021,China;College of Arts & Sciences,Shaanxi University of Science & Technology,Xi’an 710021,China)

机构地区：[1]陕西科技大学电气与信息工程学院,西安710021 [2]陕西科技大学文理学院,西安710021

出　　处：《计算机应用研究》2019年第9期2773-2777,2782,共6页Application Research of Computers

基　　金：陕西省自然科学基础研究计划—青年项目(2017JQ1026);陕西省教育厅专项科学研究计划项目(17JK0102)

摘　　要：针对传统的Hill加密算法仅是利用伽罗瓦域GF(p)上可逆的数字方阵作为密钥矩阵与明文向量作模p乘法进行加密运算,提出了一种新的在伽罗瓦域GF(2)[x]/p(x)上以多项式高矩阵作为密钥矩阵的Hill加密衍生算法。在Hill加密衍生算法中,明文向量为明文字符对应的多项式构成的多项式向量,随机选取密钥矩阵的一列作为加密时的平移增量,在GF(2)[x]/p(x)上进行密钥矩阵与明文向量的模8次不可约多项式p(x)的乘法和加法,然后获得元素为多项式的密文向量,从而实现明文信息加密。当攻击者在不知道p(x)、密钥矩阵以及随机抽取的平移向量的情况下由密文破解得到明文的难度更大,从而提高了伽罗瓦域GF(2)[x]/p(x)上Hill加密衍生算法的抗攻击能力。In traditional Hill encryption algorithm,the modulo p multiplication of the invertible matrix and plaintext vector in Galois field GF( p) is used to calculate ciphertext vector,this paper proposed a new Hill encryption derivative algorithm in Galois field GF( 2)[x]/p( x),which took polynomial high-matrix as key matrix. In this new Hill encryption derivative algorithm,it composed plaintext vector of polynomial derived from corresponding plaintext,it selected a column of key matrix as translation increment randomly modulo eighth degree irreducible polynomial p( x) multiplication of the polynomial high-matrix and plaintext vector in Galois field GF( 2)[x]/p( x) was done,then carried out modulo eighth degree irreducible polynomial p( x) addition of the product and translation increment in Galois field GF( 2)[x]/p( x),thus it obtained the polynomial ciphertext vector,and achieved the purpose of encrypting the plaintext messages. Because it is more difficult to get plaintext from ciphertext under the condition that p( x),key matrix and random selected translation vector are unknown,the new Hill encryption derivative algorithm in Galois field GF( 2)[x]/p( x) improve the capability for anti-attack.

关 键 词：伽罗瓦域GF(2)[x]/p(x) Hill加密 多项式高矩阵 不可约多项式 

分 类 号：TN918.4[电子电信—通信与信息系统]