Re: Card Playing Protocol?

[Arsen Ray Arachelian <rarachel@prism.poly.edu>]

On Sun, 17 Jul 1994, Roy M. Silvernail wrote:

> -----BEGIN PGP SIGNED MESSAGE-----
> 
> >       D1(E2(E1(Card,eK1),eK2),dK1) = E2(Card,eK2)
> 
> I think I see a problem with XOR here.  Seems to me that D and E are the
> same operation (DE == ED == D^2 == E^2 == 0).  So is this true?
> 
> E1(E2(Card,eK2),OldCardBeforeEncryption) == eK2
> 
> Looks like Alice can cheat pretty easily.  (if I'm wrong here, please
> let me know)

Nope.  Alice's key is not Bob's key, so they can't cancel each other out.
ie:  Say Alice's key is 3 and Bob's key is 7 and the plaintext to encrypt
is 0.

Alice encrypts with her key, you get 3.
Bob encrypts with his key, you get 7.
Both encrypt and you get 4.
Bob decrypts the dualy encrypted message, and he gets 7 again.
Alice decrypts the dualy encrypted message and she gets 3.

But Bob doesn't know what the card is if its encrypted by Alice.
alice doesn't know what card it is if it's encrypted by Bob.
Only when the message is decrypted by one part can the other see it.  But
since you're sending the whole deck, there's no way one of the could cheat.

Now neither Bob nor Alice use XOR as a cypher.  They use a cypher such as
DES or IDEA in a rng mode whose output they XOR to the deck of cards to
encrypt or decrypt.

> Assuming your random number generator is good, this would be faster:
> 
> //shuffle the deck:
> for (i = (4*13+2) - 1; i >= 0; i--)
>  {
>   c1=rand() % (i)   <-- change % (i) into % 54 and I'll agree with you *;
>   swapcards(&cards[c1],&cards[i]);
>  }
> 
> This will randomize the whole deck in one pass.  Remember, though, that

The reason I say this is that you're not really shuffling the cards very
well.  If a card is at the front of the deck, the odds are that it will
remain between the front of the deck and its relative position.  While
larger cards at the back of the deck are likely to swap themselves with
the ones in front just as likely as the ones in the back, this is a bit
one sided.  This is off the top of the my head and what's obvious in crypto
may not be actual, so Kent may want to test this out to see just how random
the shuffle is.

> seasoned card players will notice that this deck doesn't act like a real
> deck.  This is because the traditional method of shuffling doesn't
> randomize the whole pack.  It performs a series of permutations with a
> small random content.  Although slower and far less random, it might be
> a plus to implement a realistic hand shuffle.  Here's a (really) rough
> 10-minute untested hack.  Feel free to optimize it!  :)
> 
> //hand-shuffle the deck
> #define DECK_END 53
> #define DECK_SIZE 54
> int     deck_split, tmp_index, left, right, x, y;
> cardtype    cards[DECK_SIZE], tmp[DECK_SIZE];
> 
> 
> 
> while(passess--) {
>     decksplit = (rand() % 10) + 22);  // split the deck within 10 card
>                                       // of the center.
>     left = 0;
>     right = decksplit;
>     tmp_index = 0;
>     while(left < decksplit && right <= DECK_END) {
>         y = rand() % 4;
>         for(x = 0;x < y;x++) {
>             if(left >= decksplit) {
>                 break;
>             }
>             tmp[tmp_index++] = cards[left++];
>         }
>         y = rand() % 4;
>         for(x = 0;x < y;x++) {
>             if(right <= DECK_END) {
>                 break;
>             }
>             tmp[tmp_index++] = cards[right++];
>         }
>     }
>     for(x = 0;x <= DECK_END;x++) {  // copy the deck back
>         cards[x] = tmp[x];
>     }
> }
> 
> This always drops the left hand cards first, which you might want to
> randomize too.  But if you watch people shuffling cards, you'll notice
> that a given player usually drops one side first.

Yes, but the goal of shuffling is to randomize cards.  If you simulate it,
you're giving seasoned players a bigger advantage with the "odds" :-)  Then
again, the desireability of this is left to the implementor, so Kent you
decide which you want to do.

Seasoned players will prefer the second method, however, this may be less
random, and may infact weaken the security given by the protocol and
encrypting the deck because they may "guess" where the cards are likely to be.

Other issues: should the deck be reshuffled after each hand is played, or
should it continue to be used for the next few hands?  In "real" poker you
reshuffle occasionaly (anyone know the actual "rule" for this?)

Someone may build a good algorith to play poker.  You have no way of knowing
that you're playing against a machine or a human.  However, in the least you
can be sure that the machine can't cheat.  Though you could train it to be
very smart and keep track of every card that's been played and have it
calculate the odds for each next hand.  Casual players won't match this
"skill" but pros will.