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Thanks to a certain pandemic going around I was wondering whether there is any cryptographic way to remotely deal cards without the dealer being able to know them and without requiring to trust a server for that. My first impulses involved and but that is probably not even related... Some first thoughts:

Given a stack $S$ of $N$ cards, $n$ shall be dealt to each hand $H_i, i\in\{1,2,...,p\}$ of $p$ players with the following requirements:

  1. $N\ge n\cdot p$ (obviously)
  2. Once a card has been drawn it cannot be drawn by someone else as well, i.e. $$\forall i\neq j: H_i\cap H_j = \{\}$$
  3. No one must be able to determine which cards anyone else has nor which ones remain in the stack. Just passing around the encrypted state of a shuffle bag is thus not good enough. Maybe everyone should contribute some encrypted randomness which in a second round is used to determine the dealt cards?
  4. At some point one must be able to proof a specific card is§ currently in the hand.

Is there any method which can achieve this?


§ I guess a blockchain could be used to keep track of the cards changing places later on

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I think you are looking for "mental poker".

Here is a video of Ron Rivest specifically discussing how to deal cards via mail/internet.

The paper here might also be a good read (from the creators of RSA).

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  • $\begingroup$ Sounds perfect, thanks! $\endgroup$ Dec 12 '20 at 16:50

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