Provably Fair: Cryptographic Verification Protocol

The Provably Fair protocol is a cryptographic scheme that provides verifiable determinism of outcome generation without the possibility of manipulating results after the parameters are fixed. The protocol architecture is based on a commitment scheme: the server fixes its parameters before the start of the round, providing the operator with a hash commitment h = H(server_seed ∥ nonce), where H is a cryptographic hash function and ∥ is the concatenation operation. After the round is completed, the server discloses the server_seed, allowing independent verification of the outcome correctness. This approach mathematically guarantees the impossibility of aposteriori modification of the result.

The core of the protocol is the HMAC-SHA256 algorithm, which ensures the generation of a deterministic pseudorandom value based on a combination of server and client seeds. Formally: result = HMAC-SHA256(server_seed, client_seed ∥ nonce ∥ round_id), where HMAC is defined as H((K ⊕ opad) ∥ H((K ⊕ ipad) ∥ m)), K is the key (server_seed), and m is the message (client_seed ∥ nonce ∥ round_id). The client seed is generated on the operator side and can be modified at any time before the start of the round, which makes it impossible for either party to predict the result. The nonce is incremented automatically, ensuring the uniqueness of each round.

The outcome verification algorithm is implemented as an independent deterministic function that takes open parameters (server_seed, client_seed, nonce) as input and returns the round result. The verification procedure: (1) calculating hash = HMAC-SHA256(server_seed, client_seed:nonce:round); (2) extracting the first 4 bytes of the hash: hex_segment = hash[0:8]; (3) converting to an integer: int_value = parseInt(hex_segment, 16); (4) normalizing to the range [0, 1): float_value = int_value / (2³² − 1); (5) mapping onto the outcome space via the inverse distribution function. Each step is deterministic, allowing any third-party observer to independently reproduce the result.

The cryptographic strength of the protocol is determined by the properties of the SHA-256 hash function used. Collision resistance guarantees the computational impossibility of finding two different inputs with the same hash: the complexity of the attack is O(2¹²⁸) operations (birthday paradox). Preimage resistance with a complexity of O(2²⁵⁶) excludes the recovery of the server_seed from its hash. An additional layer of protection is the periodic rotation of the server seed with the publication of the previous one for full audit verification of the entire chain of rounds.