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Assume we have a (t,n) threshold signature scheme in which the secret key is shared between the n group users. If at least t users sign a certain message . Can we build the scheme in such away that a user outside the group can combine the signature shares of the message to get a complete signature ??? As I am still confused, some papers define the combiner of shares should be a member in the group, others don't.

If it doable , what are the privacy or security issues with the scheme I propose ??

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