After ZK-shuffle, how can we let people who got the same number card know each other without letting anyone else know?

Justin Zhang

6/7/24, 2:50 AM

In mental poker, we can use ZK-shuffle to deal cards to the players such that the cards are kept private to each player (https://hackmd.io/@nmohnblatt/SJKJfVqzq). Suppose we deal exactly one card to each player, I wonder if there is any way for the players who got the cards with the same number to know this fact without revealing it to anyone else? (Like the three players who got 3-spade, 3-heart, 3-diamond now all know each other. This essentially divide the players into "blackout rooms" by the number on their card, but only the people in each blackout room know who is in the room.) The player can talk to each other through private channels.

Would it be easier if there are only two type of card -- 0 and 1 -- and we only need the 1s to know each other? This spun out of an effort to see if it is possible to implement the Mafia game (https://en.wikipedia.org/wiki/Mafia_(party_game)) in a decentralized fashion on the blockchain. The first phase of such a game would deal the role cards of mafia/villager to the players but would need to let the mafias know each other.

Thans! <3

0 + 1

multiparty-computation

zero-knowledge-proofs

mental-poker

shuffle

Justin Zhang

6/7/24, 10:10 PM

I realized that this can be solved using pairwise MPC using garbled circuit, like described here https://crypto.stackexchange.com/questions/52443/is-there-a-cryptographic-way-a-la-mental-poker-two-people-can-determine-if-the Wonder how can I make this secure in practice against malicious adversaries? I haven't found a version of garbled circuit that is safe against malicious adversaries. Maybe we can add ZKP to it but that seems non-trivial. Thanks!!!

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: After ZK-shuffle, how can we let people who got the same number card know each other without letting anyone else know?

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