Abstract: We study the power of multi-linear secret-sharing schemes. On the one hand, we prove that ideal multi-linear secret-sharing schemes, in which the secret is composed of p field elements, are more powerful than schemes in which the secret is composed of less than p field elements (for every prime p). On the other hand, we prove super-polynomial lower bounds on the share size in multi-linear secret-sharing schemes. Previously, such lower bounds were known only for linear schemes. This is joint work with Amos Beimel, Carles Padro, and Ilya Tyomkin