26、ZHFE密码系统的安全性分析与密钥修改

ZHFE密码系统的安全性分析与密钥修改

1. ZHFE的Q - 秩分析

在ZHFE密码系统中，当 (q_i + q_j > D) 且 (i, j \neq 1) 时，(\alpha_{ij} = 0)。此时，(L_{00}f_0 + L_{01}f_1) 具有如下形式：
[
\begin{bmatrix}
\alpha_{00} & \frac{\alpha_{01}}{2} & \frac{\alpha_{02}}{2} & \cdots & \frac{\alpha_{0D}}{2} & 0 & \cdots & 0 \
\frac{\alpha_{01}}{2} & \alpha_{11} & \frac{\alpha_{12}}{2} & \cdots & \frac{\alpha_{1D}}{2} & \frac{\alpha_{1(D + 1)}}{2} & \cdots & \frac{\alpha_{1(n - 1)}}{2} \
\alpha_{02} & \frac{\alpha_{12}}{2} & \alpha_{22} & \cdots & \frac{\alpha_{2D}}{2} & 0 & \cdots & 0 \
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \
\frac{\alpha_{0,D}