Systems and techniques are provided for random oracles in open networks. A node computing device of an open network may choose a random secret. The random secret may be a numeric or alphanumeric value. The node computing device may distribute shares of the random secret to node computing devices that are members of essential subsets for the node computing device. The node computing device may receive a share of a random secret from a second node computing device. The node computing device may be a member of an essential subset of the second node computing device. The node computing device may sign a deterministic seed message using the share of the random secret received from the second node computing device to generate a signature share. The node computing device may reveal the signature share and may receive a random value in response.