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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.

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