Generation of a publicly verifiable bias-resistant distributed randomness is one of the actual problems in blockchain and its various applications. The complexity of this problem increases significantly for consensus algorithm operating on a decentralized network topology on the assumption that there are neither a trusted third party nor a trusted dealer. Such situation is caused by the fact that the logical structure of algorithms intended to solve the subtasks typical for this problem be- comes much more complicated. Besides, there arise some subtasks caused by the complete distribution of the analyzed blockchain network. One of such nontrivial subtasks is the implementation of random re-ordering of the parties, based on generated randomness. This random reordering de- fines the roles of the parties in the next epoch, and is intended to support equal access of the parties to the functioning of the blockchain network. We present a simplified version of the generation of a publicly verifiable reliable distributed randomness for the consensus protocol operating on a decentralized network topology on the assumption that there are nei- ther a trusted third party nor a trusted dealer. On this base we solve the problem of the random re-ordering for parties which will participate in the implementation of the next epoch.