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Ref: Mental Poker Revisited by Barnett and Smart.

I am looking at mental poker problem.

Generally, the shuffling process is done by a single player who starts the game and not by all players.

But, in the paper, while discussing the operation of shuffling the deck (Section 4.2), the author mentions the shuffle-encrypt by the starting single player as the "Privately Mask" operation which means the cards are shuffled only for others and not for the first player. The author mentions that for cards to be shuffled for all the players, cards have to be "Publicaly Masked" which involves everybody else to remask (reencrypt) all the cards. But, this is not what happens in actual play - in actual play, only the first person shuffles the deck.

Can a single player publicaly shuffle the deck? Can it be done by letting the first player attaching some zero-knowledge proof of that? But, then what proof would it be?

This is important in my scenario since players join gradually and only a single player starts the game and others keep joining gradually later on. Before the second player joins the game, the cards should be in shuffled order which means the first player should not know which card is at which index.

Is there a scheme for this? How can it be done?

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