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I want to simulate following physical activity in cryptography.

Person X has written integers 1, 2, ..., 10 in seperate paper slips. He needs to distribute these slips to 10 people without knowing which slip is given to whom. So, he purchase 10 similar envelops and puts one slip in each envelop. Once all slips are enveloped, he takes all envelops and threw them all in air to shuffle. Now he does not know which envelop contains which number. Now, he distributes these envelops to the 10 people.

I thought we can use commitments to simulate envelop process, but even if we use commitments, they will still be distinguishable and hence, person X can still map the nos to their respective commited envelops. Where I am missing here and if not commitment, which scheme can I use here?

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