$$ \begin{bmatrix} f_{RS}(1)=a & b & c\\ d & e & f \end{bmatrix} \cdot \begin{bmatrix} 1 & \tau\\ \tau^2 & \tau^3 \\ \tau^4 & \tau^5 \\ \end{bmatrix}

\begin{bmatrix} f_{comm_1}(\tau) = a + b\tau^2 + c\tau^4 \\ f_2(\tau) =d\tau + e\tau^3 + f\tau^5 \end{bmatrix}^T $$

$$ h_i(x)=\frac{f_1(x)-y_{1,i}}{x-i}+\frac{f_2(x)-y_{2,i}}{x-i}+\dots+\frac{f_k(x)-y_{k,i}}{x-i} $$

Convert the above to:

$$ h_i(x)(x-i)=f_1(x)-y_{1,i}x^{power(1,i)}+f_2(x)-y_{2,i}x^{power(2,i)}+\dots+f_k(x)-y_{k,i}x^{power(k,i)} $$

$$ h_i(\tau)(\tau-1)=\sum_{j=1}^{k}f_j(\tau)-\sum_{j=1}^{k}y_{j,i}\tau^{(i-1)n + (j-1)} $$

$$

g^{h(x)(x-i)} = g^{\sum_{j=1}^{k}f_j(\tau)-\sum_{j=1}^{k}y_{j,i}\tau^{(i-1)n + (j-1)}} $$

$$

g^{h(\tau)}g^{\tau-i} = \frac{C_T}{g^{\sum_{j=1}^{k}y_{j,i}\tau^{(i-1)n + (j-1)}}} $$