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In the (t, n) threshold signature schemes with the assistance of a trusted party, the trusted party easily becomes the targets of attack. And an authority which can be trusted by all players doesn't exist. So the schemes without a trusted party were proposed to solve those security problems. But all of the conventional schemes without a trusted party cannot withstand conspiracy attacks. A novel (t, n) threshold signature scheme with a weakened trusted party is proposed, in which the group secret key is composed of two parts. Any t or more group players cannot cooperate to reveal the group secret key and the weakened trusted party only knows a part of player's secret key.
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