In this paper, a new HILL cryptosystem with tripartite witness capacity is designed by solving the quadratic inverse eigenvalue problem in Galois field. The numerical experiments demonstrate that the system is feasible. In the cryptosystem, key matrix is dynamically constructed with enhanced communication security. Both communicating parties construct the matrix, which strengthens non-repudiation. Organizers participate in and witness the construction of key matrix to improve the unforgeability. The cryptosystem algorithm is concise and convenient for hardware to be reused.% 求解有限域中的逆二次特征问题，设计了一类新的HILL密码体系（NEW-HILL），数值实验说明了该密码体系的可行性。该密码体系动态构造密钥矩阵，增强了安全性，通信双方参与构造密钥矩阵，增强了不可抵赖性，组织者参与且见证构造密钥矩阵，增强了不可伪造性，该密码体系算法简练，便于固化为硬件，重复使用。
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