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Underlying Mathematics for Creating Random Events, Securing Them, and Verifying Them at Game End

Collaborative Random Event Generation

The collaborative random event generation process allows the creation of a random event that cannot be predicted or controlled by any of the parties within the process. This description of the process includes a Game Server, Regulator, and a set of players called Player(1) through Player(N). The process uses irreversible transforms, described later.

First, the Game Server creates a random number:

Random(Game Server)

Next, the Game Server computes an irreversible transform of the random number and provides it to players:

Irreversible Transform(Random(Game Server))

The regulator (an optional independent third party auditor) and each player also computes a random number:

Random(Regulator), Random(Player(1)), Random(Player(2)), Random(Player(3)), ... Random(Player(N))

The regulator (optional) and players then provide irreversible transforms of their respective random numbers to Game Server and to each other:

Irreversible Transform (Random(Regulator)),

Irreversible Transform (Random(Player(1))),

Irreversible Transform(Random(Player(2))),

Irreversible Transform(Random(Player(3))), …

Irreversible Transform (Random(Player(N))).

Once all parties receive these irreversible transforms, the players then provide their random numbers to the Game Server and each other:

Random(Regulator), Random(Player(1)), Random(Player(2)), Random(Player(3)), ... Random(Player(N))

The Game Server then combines the player random numbers with its own random number to create the collaborative random key or game key:

Game key = Collaborative Random key =

Function (Random(Game Server), Random(Regulator), Random(Player(1)), Random(Player(2)), Random(Player(3)), ... Random(Player(N)))

This function could be as simple as an “exclusive or”.

The Collaborative Random key, or Game key is used to generate the random events for the game.

Secret or Simultaneous Actions

The protection of secrets starts with the data (such as the location of the queen in Three Card Monte) being protected:

Secret

The irreversible transform of the secret is created and provided to the other party with whom the secret is supposed to be shared at a later point:

Irreversible Transform(Secret)

When the time comes for the secret to be revealed, an “alleged” secret is provided by the person who made the secret decision to the party that wishes to verify the secret:

Alleged Secret

The verifier then computes the irreversible transform of the alleged secret and compares it with the previously received irreversible transform of the secret:

Compare

Irreversible Transform(Alleged Secret)

with

Irreversible Transform(Secret) that was previously received

If they agree, then the actual secret has been revealed and the honesty of the alleged secret confirmed. Because of the properties of irreversible transforms, no other secret could have created the received secret and the receiver cannot reconstruct the actual secret until it is revealed.

For simultaneous actions, the same process is used, but both parties create and send the irreversible transform of the proposed simultaneous action. After each party has received the irreversible transform of the other’s secret, they verify the action, as described for secret decisions.

Game Verification

The verification activities described for collaborative random event generation and secret or simultaneous actions are used together to verify a game.

In the SecurePlay Solutions Patent, this collaborative random key is rebuilt during the verification phase. To verify that the Game Server did not manipulate the game events, the previously stored:

Irreversible Transform(Random(Game Server))

Can be compared with the received alleged random number during game verification:

Alleged Random(Game Server)

If the Game Server keys match, then the game can be verified by reconstructing the Game key and verifying that the observed game events match with the reconstructed game events (i.e. a person received a 7 of Spades and not a King of Clubs to lose at Blackjack). If the Game Server keys do not match or the reconstructed game does not match the observed game, then there is a basis for challenging the game. For honest Game Servers, this also creates evidence that cheating did not occur and therefore can protect against disgruntled players.

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Copyright 1998 - 2008. SECUREPLAY™, IT GLOBALSECURE™, PLAYNOEVIL™ and IT ARMOR™ are registered trademarks. SECUREPLAY™ technology protects against network cheating, and is available via license from IT Globalsecure at www.secureplay.com  using patented technology from QUIXOTIC SOLUTIONS, an IT GLOBALSECURE™ affiliated company. Software protected by software license, including Simple Open Source and Commercial licenses, and one or more the following U.S. and International patent numbers: U.S. Patent 6,030,288, U.S. Patent 6,165,072, European Patent Office EP1016049A1,and World Intellectual Property Organization WO9912135C1 and additional filings worldwide. IT GlobalSecure, Quixotic Solutions, and Urban Revivals LLC are affiliated companies. Proud supporter of Classical Violin in Washington DC 
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