Draw Protocol Specification (v1.0.0)

Mathematical Formulation

For each winner rank $k$, a cryptographic pseudorandom 256-bit integer $X_k$ is derived using HMAC-SHA256:

digest = HMAC_SHA256(serverSeed, `${clientSeed}:${drawIndex}:${rejectionAttempt}:${manifestHash}:${beaconValue}`)

Where:

• serverSeed: 64-character unhashed hexadecimal string revealed after entries lock.
• clientSeed: Operator or community client seed string.
• drawIndex: 0-indexed integer of the winner rank being drawn (0 for 1st place, 1 for 2nd, etc.).
• rejectionAttempt: Integer starting at 0, incremented if a rejection sampling roll falls outside the uniform modulo window.
• manifestHash: SHA-256 hash of all entrants formatted as `platform:userId:weight` sorted alphabetically.
• beaconValue: External entropy (e.g. latest Bitcoin block hash or stream timestamp).

Rejection Sampling Without Modulo Bias

Simple modulo arithmetic ($X \pmod N$) introduces a statistical bias toward lower numbers when $2^256$ is not evenly divisible by the total pool weight $W$. Buzzeee eliminates modulo bias by discarding numbers in the remaining tail:

const DIGEST_SPACE = 1n << 256n;
const target = DIGEST_SPACE - (DIGEST_SPACE % poolWeight);

// If the derived integer falls in the unbiased window, accept the winner:
if (x < target) {
  const winningTicket = x % poolWeight;
  return selectEntrantByTicket(winningTicket);
}
// Otherwise, reject and increment rejectionAttempt++ to roll again.