| 由整数有限域矩阵方程及其解的逆矩阵实现的新密码体系 |
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| 引用本文： | 朱群娣,严深海,黄贤通.由整数有限域矩阵方程及其解的逆矩阵实现的新密码体系[J].应用数学与计算数学学报,2014(4):461-467. |
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| 作者姓名： | 朱群娣 严深海 黄贤通 |
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| 作者单位： | 赣南师范学院数学与计算机科学学院,江西赣州341000 |
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| 基金项目： | 江西省自然科学基金资助项目（2009GZS0004） |
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| 摘 要： | 基于整数有限域中一类矩阵方程的唯一解问题,结合能实现秘密共享的Diffie-Hellman协议,设计了一种以下三角阵的逆矩阵为明文、以对称矩阵为密文、密文信息冗余的密码体系.数值算例验证了新密码体系的可行性和正确性.
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| 关 键 词： | 有限域 整数矩阵方程 Diffie-Hellman协议 逆矩阵 新密码体系 |
New cryptosystem by solution of integer matrix equations and its inverse matrix over finite fields |
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| ZHU Qun-di,YAN Shen-hai,HUANG Xian-tong.New cryptosystem by solution of integer matrix equations and its inverse matrix over finite fields[J].Communication on Applied Mathematics and Computation,2014(4):461-467. |
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| Authors: | ZHU Qun-di YAN Shen-hai HUANG Xian-tong |
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| Institution: | (College of Mathematics and Computer Science, Gannan Normal University Ganzhou 341000, Jiangxi Province, China) |
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| Abstract: | A new cryptosystem is designed based on the unique solution of matrix equations over the finite integer field and the Diffie-Hellman protocol which can realize the secret sharing.It takes the inverse matrix of a lower triangular matrix as the plaintext and the symmetric matrix as the ciphertext,with redundant ciphertext information.The numerical experiment shows that the new cryptosystem is feasible and correct. |
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| Keywords: | finite field integer matrix equation Diffie-Hellman protocol inverse matrix new cryptosystem |
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