Abstract: A computer-implemented method of creating different versions of a tree structure overlaid on a blockchain, wherein the method is performed by a tree creator and comprises: creating one or more target child nodes of a target parent node, each target child node comprising a respective data payload; and forming a respective edge between each target child node and the target parent node by associating each of the target child nodes with a respective link identifier, wherein the respective link identifier is based on at least one off-chain parameter.

Abstract: A computer-implemented method of sharing blockchain transactions, wherein the method is performed by a first party and comprises: receiving, from a second party over a QUIC connection, a payment destination, wherein the payment destination comprises a public key and/or a public-key-based address; and sending a transaction to the second party over the QUIC connection, wherein the transaction comprises an output locked to the payment destination.

Abstract: A computer-implemented method of deriving keys of a hierarchical key structure, wherein the method is performed by a first party and comprises: generating a target index of a target child key, wherein the target index is generated based on a first result of inputting at least a target message to a first hash function; and deriving the target child key of a level in a hierarchy of a key structure based on a) a parent key of a preceding level in the hierarchy, and b) a second result of inputting at least i) the parent key, and ii) the target index, to a second hash function.

Abstract: A method comprising, by a client device: identifying one or more target transactions, recorded on a blockchain, that contain operating system software stored in a payload of the one or more target transactions, the operating system software comprising at least part of an operating system, at least including some executable code of the operating system; accessing the operating system software from the payload of the one or more target transactions as stored on the blockchain; and running, on the client device, the operating system software as accessed from the one or more target transactions, the running comprising executing the executable code of the operating system.

Abstract: A method of using a tree structure overlaid on a blockchain, wherein each node of the tree is a different transaction. The method comprises: inspecting the blockchain to identify at least part of the tree structure, including identifying a target child node which includes a record of a file in the respective payload of that node, and identifying a path comprising one or more edges back through the tree structure from the target child node to the root node. The method then comprises: A) for each edge along the identified path from target child node back to root node, checking that the respective child node is signed by a key associated with the respective parent node, and B) checking that a current instance of the file matches the record included in the target child node. The current instance of the file is verified at least on condition of these checks.

Abstract: A computer-implemented method of identifying a double-spend attempt of a blockchain transaction output, wherein the method is performed by a transmitting entity and comprises: generating a first probabilistic filter, wherein the first probabilistic filter encodes a respective identifier of each of a first plurality of spent blockchain transaction outputs available to the transmitting entity; and making the first probabilistic filter available to a receiving entity.