引用本文: 刘海峰, 卢开毅, 梁星亮.GF(28)上高矩阵为密钥矩阵的Hill加密衍生算法[J].西南大学学报（自然科学版）,2018,40(11):41~47
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DOI：10.13718/j.cnki.xdzk.2018.11.007

Hill Encryption Derivative Algorithm in Finite Field GF(28) with High-Matrix as Key Matrix
LIU Hai-feng, LU Kai-yi, LIANG Xing-liang1,2
1. College of Electrical and Information Engineering, Shannxi University of Science and Technology, Xi'an 710021, China;2. College of Arts and Sciences, Shannxi University of Science and Technology, Xi'an 710021, China
Abstract:
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.
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