Several agencies are selected to participate. Each significant player in this game should be in a position to trust at least one of these agencies. Each day each agency produces a random 128 bit number by whatever means it finds appropriate. They each publish the secure hash of their number. After all such hashes have been published and disseminated they each publish their respective numbers. It is incumbent on each agency to verify the receipt of every hash and keep its number secret until all hashes are available. After each number has been published the public nonce is the exclusive-or of the numbers from each agency.
Any stake holder is in a position to verify the integrity of these public nonces if they trust at least one of the agencies and monitor the published hashes and subsequent agency nonces. To corrupt the system requires coordinated corruption in every agency.