How to extend the "poker by phone" protocol to three?

Question

Programming

There are 52 cards, 2 players A and B, it is necessary to distribute so that none of them knows each other's cards .
Algorithm:
1. A and B secretly choose two switching cryptosystems from each other.
2. A encrypts all 52 cards with his key, shuffles them, and sends ciphertexts to B.
3. B randomly selects 5 ciphertexts for A from them and sends them to him.
4. And with the help of his cryptosystem, he decrypts his cards.
5. B randomly chooses 5 for himself from the remaining ciphers, encrypts them with his key and sends them to A.
6. A decrypts them with his key and sends them to B.
7. B finally decrypts his cards with his key.
How to extend this algorithm to three players?

Answer 1

This task is sometimes referred to as "mental poker". I found this article, maybe it will help you. The protocol itself is described on page 5 (p. 88), starting with the words Proof of Theorem 1.

Answer 2

Well, just someone is a server (he is a croupier in fact). First, he does everything according to the AB algorithm, then CD (everything is the same, but the keys are different).