The security of the improvement on the generalization of threshold signature and authenticated encryption

Wang et al., in 2000, proposed a generalized group-oriented threshold signature scheme and a generalized authenticated encryption scheme with shared verification. Tseng et al., in 2001, showed that both schemes are insecure; because any attacker is able to reveal the group secret keys from two previously valid threshold signatures. They further presented two improvements on Wang et al.'s schemes to against the attacks. Unfortunately, this paper will show that the improved schemes are still breakable.