GF(2⁸)上高矩阵为密钥矩阵的Hill加密衍生算法
Hill Encryption Derivative Algorithm in Finite Field GF(2⁸) with High-Matrix as Key Matrix

针对传统的Hill加密算法仅是利用有限域GF（p）上可逆的数字方阵作为密钥矩阵与明文向量做模P乘法进行加密运算，提出了一种新的在有限域GF（2⁸）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（2⁸）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.由于在不知道有限域的8次不可约多项式、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，从而提高了有限域GF（2⁸）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 finite field GF(P) are used to calculate ciphertext vector. This paper proposes a new Hill encryption derivative algorithm in finite field GF(2⁸), which takes polynomial high-matrix as the key matrix. In this new Hill encryption derivative algorithm, plaintext vector is composed of the polynomial derived from the corresponding plaintext, a column of key matrix is selected as translation increment randomly modulo eighth degree irreducible polynomial p(x) multiplication of the polynomial high-matrix and plaintext vector in finite field GF(2⁸) is done. Then modulo eighth degree irreducible polynomial p(x) addition of the product and translation increment in finite field GF(2⁸) is carried out, thus the polynomial ciphertext vector is obtained, and the purpose of encrypting the plaintext messages is achieved. Because it is more difficult to get plaintext from ciphertext under the condition that eighth degree irreducible polynomial, key matrix and random selected translation vector are unknown, the new Hill encryption derivative algorithm in finite field GF(2⁸) improves the capability for anti-attack