The current disclosure is directed towards efficiently generating random sequences on a large-scale peer-to-peer network. In one example, the disclosure provides for selecting a first node based on a block generation order, where the first node is selected to generate a current block, adding a first signature share of the first node to the current block, adding at least a second signature share from a previously selected node to the current block, generating a random sequence based on the first signature share and the second signature share, adding the random sequence to the current block, and publishing the current block to a blockchain maintained by a node pool. In this way, a random sequence may be generated on-chain, with linear messaging complexity, without relying on a single trusted party/apparatus, which may thereby decrease a probability of any single party controlling the random sequence produced.