🎲Cards shuffling

RACE Poker's decentralized shuffling

Algorithm described here can be applied for any number of players. For simplicity, we consider a situation when 2 players are in the game: Alice & Bob.

• Shuffled data in RACE is a virtual deck of cards represented in the form of cipher text

• RACE Poker utilizes commutative encryption scheme, which means when data is encrypted more than once, the order of encryption does not matter.

Shuffling procedure

• When game starts transactor generates a deck of 52 cards

• Transactor generates initial encryption key and encrypts every card of the deck with it

Synchronous stream cipher is used for encryption that satisfies:

$encrypt(k2,encrypt(k1,x))≡encrypt(k1,encrypt(k2,x))$$encryptpartial(k)∘decryptpartial(k)≡identity$

C stands for the collection of 52 cards:

$C=(c1,c2, ..., c52)$ The whole collection is encrypted with a single key

$Cencrypted=encrypt(k,C)=(encrypt(k,c1),…,encrypt(k,c52))$

• Transactor when provides the encrypted deck to the first player, say, Alice.

• Alice generates encryption key A and used it to encrypt each card of the deck.

• Alice shuffles all the cards and passes double encrypted and shuffled deck to Bob.

• With her and transactor's encryption in place, Bob can’t know what card is what.

• Bob generates encryption key B and encrypts each card of encrypted and shuffled deck.

In this step Alice & Bob encrypt & shuffle collection of 52 cards each with own single key

• Bob passes triple encrypted and double shuffled deck back to Alice.

• Alice decrypts each card using her secret key A.

• This leaves Bob’s and Transactor's encryption in place, so she can’t know what card is what

• Alice generates 52 unique keys to encrypt every single card individually.

• Alice passes the deck back to Bob.

• Bob decrypts each card using his key B.

• This leaves Alice’s individual encryption in place, so he can’t know what card is what.

• Now Bob generates 52 unique keys to encrypt every single card individually.

• Then Bob passes the deck back to transactor.

In these steps Alice & Bob encrypt each card with an independent key:

$K=(k1,k2,…,k52)$$Cencrypted=encrypt(K,C)=(encrypt(k1,c1),…,encrypt(k52,c52))$

$K=(k1,k2,…,k52)$K=(k1,k2,…,k52)$Cencrypted=encrypt(K,C)=(encrypt(k1,c1),…,encrypt(k52,c52))$

The final encryption with 52 keys

The whole shuffle procedure made by all clients:

The whole encryption procedure made by all clients:

• Transactor now removes its initial encryption.

• Transactor publishes the deck for everyone playing

• The deck is shuffled & every card of it is encrypted with Alice & Bobs individual keys

That means both Alice & Bob don't know what card is in what position now.

To reveal cards Alice & Bob need to share cards' individual keys with each other.

Until Alice shares a certain key, Bob and server doesn't know what card it is.

Alice & Bob can now play the game and share the keys according to the game logic.

Players, server need to run the same encryption/decryption process for game to go.

Alice & Bob have to reach consensus on the game progress, and transactor to verify it.

Final result

• Combining the two procedures, we have:

• For each shuffled card at index m:

• To know the face of card Cm, players need a list of secrets for card at index m from all players.

Encrypted communication	Key sharing & decryption