Multi-secret sharing (Packed secret sharing) - Some questions
I believe there is a typo in the paper: instead of $k$ elements $a_1, \dots, a_k$ there should actually be $n$ fixed public elements, i.e. $a_1, \dots, a_n \in \mathbb F$. To secret-share, first determine $p(x)$ based on the dealer's secrets. Then, give $p(a_i)$ to player $i$ for each $1 \leq i \leq n$.