Editing Multiplayer RNG

[[Category:Research]]
For a while now my friend Koz has been throwing around the idea of a peer-to-peer multiplayer card game. These games rely heavily on random numbers for things like drawing from card decks. Here's my idea for a protocol to accomplish that.

== Overview ==
The protocol assumes the following:

* Players can generate numbers they trust to be random
* Players distrust numbers generated by other players
* These random numbers are secret unless told to other player

These assumptions seem reasonable to me at least and match my expectations of multiplayer games.

The protocol I propose here works like this:

# Each player generates a random number
# They prove to other players they have generated their number
# All players reveal their numbers
# The numbers are mixed to generate a final random number seed

Step 2 is necessary to prevent players from picking numbers could unmix other player's numbers.

The mixing agent here needs to ensure that no player's randomness (or entropy) is removed, only added.

== Concrete specification ==
Using modern cryptography primitives the protocol works like this.

Each player does this:

# Agree on which players will be participating in the generation
# Generate a random 256-bit number
# Hash the number using BLAKE3
# Announce the hash to other players
# Wait for other players to announce hashes
# Associate the hash with the announcing player
# If a player doesn't send a hash, bail out of generation
# Announce the random number
# Wait for other players to announce random numbers
# All players wait for all random numbers to arrive
# If a player doesn't send a number, bail out of generation
# Associate the number with the announcing player
# Hash each player's number using BLAKE3
# Validate that the hash matches the hash sent earlier
# If a hash doesn't match, bail out of generation
# XOR together all player's numbers to create a final number seed

This requires two round trips and results in a number with an entropy of at least 256 bits.

This is a large number intended for seeding some per-turn number generator, such as picking multiple cards from a deck or calculating damage.

== Prior work ==
Credit for the original idea comes from [https://stackoverflow.com/questions/224058/distributed-random-number-generation Distributed Random Number Generation] on StackOverflow. However that protocol has a few oddities to me at least:

Instead of generating a large random number that's easy to pass from some source of entropy (like random bytes), it generates a smaller number. This requires using a random number generator to get a small number, salting the number to avoid guessing the hash (by generating a larger random number like we do), and then use addition as the mixing agent.

That seems trickier to implement.