Provably Fair

Introduction

When a new game starts, a bullet is placed in a random chamber of the revolver. Each time a user pulls the revolvers trigger, RNG Gaming Bots check whether the bullet is in the current chamber being fired.

The bullet position in the revolver chamber is generated at the start of the game. The position of the bullet in the revolver chamber must be publicly available at the start of the game. Otherwise, if the bullet position were published at the end of the game, it would be impossible to prove that the bullet position in the revolver chamber isn't being manipulated.

However, if the bullet position in the revolver chamber were to be published at the start of each game, each player would know exactly where the bullet is, and the game would be broken.

Therefore, the bullet position in the revolver chamber must be encrypted and published at the start of each game, while the keys to decrypt the bullet position must be published at the end of the game.

But how can RNG Gaming prove that the number is not predetermined at the start of the game?

And how can RNG Gaming prove the number has been randomly generated?

And how can RNG Gaming prove that the bullet position has not been manipulated as the game progresses?

Randomness and Fairness

RNG Gaming uses a Verifiable Random Function (VRF) to generate random numbers for each game. These random numbers can be encrypted and published at the start of the game. At the end of the game, the decryption key, as well as mathematical proofs that the number was in fact randomly generated and untampered during the game are published and saved onto the Solana blockchain.

When the game ends, the bot sends the following as part of an end_game transaction.

alpha

• Description: alpha is created by concatenating the UNIX time with an array of each player's bets.

• Why It Is Important: alpha ensures that the proof and resulting beta are specific to the particular game instance.

salt

• Description: salt is a randomly generated string using pythons secrets token hex library.

• Why It Is Important: salt adds an additional layer of randomness, ensuring that even if the seed and proof are reused, the resulting beta will be different. This prevents predictability and ensures each game's outcome is unique.

seed_hash

• Description: seed_hash is the hashed value of randomly generated seed and salt, using PBKDF2 HMAC with a specified number of iterations. The seed itself is not revealed to maintain security, and is not needed for cryptographic validation. The seed is generated using pythons secrets token hex library.

• Why It Is Important: seed_hash allows for deterministic regeneration of the beta value during verification without exposing the raw seed. It provides a secure way to tie the randomness to a specific game instance while maintaining the seed's privacy.

proof

• Description: proof is a digital signature generated for a random number beta using a random private key and the input message alpha.

• Why It Is Important: proof ties the random number to the private key and the specific game parameters alpha. It provides cryptographic proof that the number was generated legitimately and has not been tampered with.

beta

• Description: beta is the randomly generated number in hexadecimal format. This number is converted into an integer and modulo'ed with the size of the revolver chambers.

• Why It Is Important: beta is derived from a seed hash, salt, and proof, ensuring it is deterministic yet unpredictable. It serves as the basis for determining the bullet's chamber index, providing randomness and fairness in the game.

public_key

• Description: public_key is the public key of the randomly generated private key. Each game has its own public and private key pair.

• Why It Is Important: public_key is used to verify the digital signature proof. It ensures that the proof was generated by the corresponding random private key, maintaining the integrity and authenticity of the game's setup.

The VRF implementation ensures that the random number beta is not predetermined by using a cryptographically secure, randomly generated seed and salt, combined with a unique input message alpha and generating a proof using a random private key. The resulting bullet index is random due to the unpredictable nature of the seed and salt, and its integrity is verified through public key validation of the proof and consistent recalculation of beta, preventing any manipulation. This process guarantees fairness and transparency in the game's outcome.

VRF Implementation

For more details regarding exact implementation and more in-depth documentation, please visit the following Github repository.

GitHub - 0xlucyy/vrf: A provably fair Verifiable Random Function (VRF) that provides cryptographic outputs to confirm games were fairGitHub