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need an understanding of this

Hello people
I need to understand how this shamir secrete sharing scheme works,i get the idea that you would send a mesage to people who dont trust each other and if certain amount of people get the message then the message is displayed.
My problem is now how you make sure that the first people to receive the message do no know the secrete before all the required amount of people get the message. :?:

cjsin
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