you base the random dice roll on the proof of work of the block chain. proofs of work generate randomness because (proof by contradiction) if they didn’t it would be easy to find the next block and make a bunch of money.
EDIT: more concretely, in a blockchain, “miners” compute a “hash” of the chain up to the latest block, with an extra random “nonce”. they then check if this hash has a certain distinguishing feature (eg 5 leading zeros). if it doesn’t have this feature, the recompute the hash with a new nonce. the rest of the bits in the hash thus become random. thus, if you commit to using a future hash to determine your lottery, it can be guaranteed to be random (or prove you have enough money to manipulate the block chain which is very difficult)
you base the random dice roll on the proof of work of the block chain. proofs of work generate randomness because (proof by contradiction) if they didn’t it would be easy to find the next block and make a bunch of money.
EDIT: more concretely, in a blockchain, “miners” compute a “hash” of the chain up to the latest block, with an extra random “nonce”. they then check if this hash has a certain distinguishing feature (eg 5 leading zeros). if it doesn’t have this feature, the recompute the hash with a new nonce. the rest of the bits in the hash thus become random. thus, if you commit to using a future hash to determine your lottery, it can be guaranteed to be random (or prove you have enough money to manipulate the block chain which is very difficult)
does this need to be done 8 billion times or just for the number of olympic participants? I guess this is a resource question.
just for the number of participants. and there’s a construction (a pseudorandom generator) thatll let you do it with one block