Let's sign collectively! Distributed signatures API

So is it possible to use blockchain to avoid off-chain interaction between group members? Sth like the following:

  1. A group member proposes a transaction by putting her request to a specified box’s registers accessible by group members (they can use a shared box spendable by all group members to produce such a box with desired registers in order to avoid identity disclosure).
  2. Group members see the request and if they agree, they produce commitment and put it on blockchain like before.
  3. When reaching the threshold, one can simulate other commitments and do the same thing as before.
  4. One of the group members can generate the valid transaction.
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