Abstract: Nodes determine a first measure of difficulty for a first branch of a split blockchain and a second measure of difficulty for a second branch of the split blockchain. The first measure of difficulty is based on a measure of block generation frequency of each node that mined for the split blockchain during a window that comprises blocks of the first branch. The second measure of difficulty is based on a measure of block generation frequency of each node that mined for the split blockchain during a window that comprises blocks of the second branch. One of the first branch and the second branch is identified as a legitimate branch based on a comparison of the first measure of difficulty and the second measure of difficulty.

Abstract: The current disclosure is directed towards providing methods and mechanisms enabling computationally efficient cross-chain messaging and message validation between subchains of a large-scale decentralized network. In one example, the current disclosure provides for determining if a message generated by a first subchain, received at a second subchain, represents a valid, consensually generated message of the first subchain, by comparing the received message with a public-key-share list of the first subchain stored in the second subchain. In one example, the current disclosure provides for a method comprising receiving a first message from a first subchain at a smart contract of a second subchain, wherein the smart contract of the second subchain comprises a public-key-share list of the first subchain, determining if the first message is valid based on the public-key-share list, and executing a transaction based on the first message responsive to the first message being determined valid.

Abstract: Nodes determine a first measure of difficulty for a first branch of a split blockchain and a second measure of difficulty for a second branch of the split blockchain. The first measure of difficulty is based on a measure of block generation frequency of each node that mined for the split blockchain during a window that comprises blocks of the first branch. The second measure of difficulty is based on a measure of block generation frequency of each node that mined for the split blockchain during a window that comprises blocks of the second branch. One of the first branch and the second branch is identified as a legitimate branch based on a comparison of the first measure of difficulty and the second measure of difficulty.

Abstract: A packet including a message intended for a smart contract associated with the second subchain and a node identifier is constructed at each of a plurality of nodes associated with the first subchain. The message constructed by the plurality of nodes are identical and may be a transaction request requesting the smart contract to execute on a blockchain. Each of the packets is sent to one or more nodes associated with the second subchain. The packets and messages received by one or more of a plurality of nodes associated with the second subchain are monitored and processed at the second subchain to determine if a consensus on request has been reached from the first subchain. If a consensus on request has been reached from the first subchain, the smart contract associated with the second subchain executes on the blockchain in accordance with the transaction request.