1. Setup
   1. item 1:

$$\left( \{g^{s^k}\}_{k\in[d]}, \{g_l^{l_i(s)}, g_r^{r_i(s)}, g_o^{o_i(s)}\}_{i\in\{0,...,n\}}, \\\ \{g_l^{α_{l}l_i(s)}, g_r^{α_{r}r_i(s)}, g_o^{α_{o}o_i(s)}, g_l^{βl_i(s)}g_r^{βr_i(s)}g_o^{βo_i(s)}\}_{i\in\{m+1,...,n\}}, \\\ g_l^{t(s)}, g_r^{t(s)}, g_o^{t(s)}, g_l^{α_{l}t(s)}, g_r^{α_{r}t(s)}, g_o^{α_{o}t(s)}, g_l^{βt(s)}, g_r^{βt(s)}, g_o^{βt(s)} \right)$$

2. item 2