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  

New cryptosystem by solution of integer matrix equations and its inverse matrix over finite fields

作　　者：朱群娣[1] 严深海[1] 黄贤通[1] 

机构地区：[1]赣南师范学院数学与计算机科学学院,江西赣州341000

出　　处：《应用数学与计算数学学报》2014年第4期461-467,共7页Communication on Applied Mathematics and Computation

基　　金：江西省自然科学基金资助项目(2009GZS0004)

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.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.

关 键 词：有限域 整数矩阵方程 DIFFIE-HELLMAN协议 逆矩阵 新密码体系 

分 类 号：O151.21[理学—数学] TN918.1[理学—基础数学]