# Threshold lower than $\dfrac{n}{2}$ in distributed key generation

While I was studying protocols for distributed key generation with malicious adversaries, Gennaro et al.$$^{[1]}$$ pointed out that the protocols that provide both secrecy and robustness should have a threshold lower than $$\dfrac{n}{2}$$. However, I do not see how the robustness of the scheme can compromise the secrecy of the protocol in the case of a threshold higher than $$\dfrac{n}{2}$$.

Does someone have an explanation for this?

[1] R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin, “Secure distributed key generation for discrete-log based cryptosystems,” in International Conference on the Theory and Applications of Cryptographic Techniques, pp. 295– 310, Springer, 1999.