Abstract: A specialized network (“merchant”) node to facilitate fast distribution of blockchain transactions over a network of interconnected nodes, as subset of which are merchant nodes interconnected by an overlay network. The merchant node includes a memory storing an assigned portion of a distributed mempool structured as a distributed hash table, the distributed mempool containing pending transactions awaiting confirmation. The merchant node operates by receiving a transaction, including a transaction identifier; hashing the new transaction identifier to obtain a key; determining, using the key, whether the transaction is stored in the distributed mempool or not and, if not, then storing the transaction in the distributed mempool as a pending transaction; and sending the transaction to a set of nodes other than merchant nodes using peer-to-peer connections. The invention may be used in conjunction with the Bitcoin blockchain or an alternative.

Abstract: A method of propagating data packets in a network of nodes is disclosed.

Abstract: A computer-implemented method of partitioning a blockchain network into shards is disclosed. The method comprises the steps of identifying a transaction id of a blockchain transaction and allocating the transaction to a shard based on the transaction id.

Abstract: There may be provided a computer-implemented method. It may be implemented using a blockchain network such as, for example, the Bitcoin network.

Abstract: A method of obtaining digitally signed data is disclosed. The method comprises sending first data (e2) from at least one of a plurality of first participants to at least one second participant, wherein the first data is based on second data (e) accessible to at least one said first participant, and the second data is inaccessible to the or each said second participant. A digital signature (s1) of the first data is received from at least one said second participant, and the digital signature of the first data is processed, by a plurality of the first participants, to provide shares of a digital signature(s) of the second data, wherein the digital signature of said second data is accessible by means of a threshold number of said shares and is inaccessible to less than said threshold number of shares.

Abstract: A computer-implemented security may be implemented on a blockchain comprising applying a one-way function to a first secret value to create a first veiled secret value; communicating the first veiled secret value to a user; receiving a second veiled secret value from the user, wherein the second veiled secret value is created by applying a one-way function to the second secret value; and constructing a first blockchain transaction comprising the first veiled secret value and the second veiled secret value, the first blockchain transaction arranged to be unlockable to transfer control of a first resource upon provision of both the first secret value and the second secret value to a respective blockchain transaction.

Abstract: The invention provides a computer-implemented control method and corresponding system. The method may control or influence a device, system or other resource such as a technical process. The invention can provide a mechanism for emulating or otherwise executing the functionality of a logic gate via a computer-based distributed ledger (blockchain). This may be the Bitcoin blockchain or an alternative network/protocol. The invention provides logic embedded within a redeem script such that it determines which particular private keys have been used to sign an unlocking script, and then interprets the provision of those keys in accordance with a predetermined function.

Abstract: A method to participate in a blockchain-implemented token distribution process is disclosed. The token distribution process divides an initial quantity of tokens at an input address associated with an input node into a plurality of sub-quantities and uses a mixer node to distribute the sub-quantities to multiple output addresses associated with respective output nodes using a blockchain. The token distribution process utilizes a hierarchical token distribution scheme to recruit the mixer node. The hierarchical token distribution scheme involves a first commitment channel (Ui ? Uij) for a first transaction between the upstream node and a recruited mixer node (Uij), and for each of the plurality of downstream nodes, a second commitment channel (Uij ? Uijk) for a second transaction between the mixer node and a selected downstream node, wherein an unlocking script for the first transaction is derived from an unlocking script for any one of the second transactions.

Abstract: A method of controlling and coordinating of processing steps in a distributed system is disclosed. The method may be implemented by a node in a cyclically-ordered set of nodes participating in a blockchain network. The method includes receiving, from an immediately subsequent node, values corresponding to combinations of possible outcomes of processing steps associated with nodes from that node through to a node immediately preceding a supervisor node. The values are based on public keys associated with the nodes corresponding to possible outputs and the supervisor's public key. State values are generated based on the values and public keys corresponding to the possible outcomes further to a processing step of the node and are shared with the supervisor and an immediately previous node. A blockchain transaction is prepared to transmit control of a resource from the node to the immediately subsequent node upon supply of one of a set of unlocking values corresponding to the received values.

Abstract: Techniques described herein can be utilized to implement a protocol for performing an unbiased selection of a particular worker node among a plurality of worker nodes to execute a computational task. Nodes of a distributed network may register to join a group membership by generating quantities derived at least in part from a hierarchical data structure, such as an accumulation tree, whose parameters are defined by a manager node. The manager node may utilise the quantities provided by the plurality of worker nodes to perform an unbiased selection of a worker node from among the plurality of worker nodes to perform a computational task. The invention is particularly suited, but not limited to, for use in a blockchain network such as Bitcoin. In at least some cases, the manager node cannot determine, based on quantities supplied by the worker nodes, whether a particular worker node was selected to perform the computational task.

Abstract: A computer-implemented method is described for enabling recovery of one or more digital assets held on a blockchain by a user under a public key Pk after a corresponding private key Sk for accessing the one or more digital assets is lost. The computer implemented method comprises setting access for the one or more digital assets held on the blockchain under the public key Pk and accessible using the corresponding private key Sk of the user such that the one or more digital assets are also accessible using a private key x shared by a congress on the blockchain network, the congress comprising a group of users on the blockchain network, each member of the congress having a private key share xi, the private key share xi to be used in a threshold signature scheme in which at least a threshold of private key shares must be used to generate a valid signature through the combination of partial signatures of the congress to access the one or more digital assets on behalf of the user.

Abstract: The invention relates to distributed ledge technologies such as consensus-based blockchains. Computer-implemented methods for securely providing undetermined data from a determined or undetermined source are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. A first transaction to validate is received at a node in a blockchain network, with the first transaction including a first script that includes at least a first value, at least a portion of which includes data that is unconstrained by a second script, and a second value. A second transaction is obtained. The second transaction having been validated and including the second script that, as a result of being executed, causes the node to obtain the first value and the second value as a result of execution of the first script, and validate, based at least in part on first value and the second value, that the data is associated with a data source.

Abstract: A method of controlling and coordinating of processing steps in a distributed system can be implemented by an initiator node of a cyclically-ordered set of nodes participating in a blockchain network (e.g., Bitcoin blockchain). The method includes generating a private key and cryptographic shares thereof for the nodes of the set and distributing them. A locking value is determined based on the shares and a transaction is arranged to transmit control of a resource responsive to supply of a corresponding unlocking value. A circuit of transactions amongst the nodes each arranged to transmit control of a resource responsive to supply of an unlocking value corresponding to a locking value determined based on the share distributed to a first node of one of two adjacent nodes and a value received from another node immediately previous to it is prepared. The initiator node may belong to a cyclically-ordered set of initiator nodes.

Abstract: The invention relates to distributed ledger technologies such as consensus-based blockchains. Computer-implemented methods for locking and unlocking transaction inputs and outputs are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. A group of entities form a group in with membership may be proven using an accumulation tree. A variety of methods are described for generating the accumulation tree, including methods that use a central authority and methods that use a decentralized protocol in place of the central authority. In various implementations, parties are able to unlock transaction outputs that are based on group membership without revealing their identity generally.

Abstract: The invention provides methods and systems which enable additional functionality to be inserted into blockchain scripts with ease and in an effective and manner. According to one embodiment, the invention provides a blockchain-implemented method comprising the steps of arranging a plurality or selection of scripting language primitives to provide, upon execution, the functionality of a high-level scripting language primitive, wherein the scripting language is associated with a blockchain protocol; inserting the plurality of scripting language primitives at least once into a script; and inserting the script into blockchain transaction (Tx). The high-level scripting language primitive may perform, for example, an arithmetic operation such as multiplication or division. The scripting language primitives may be called op-codes, words or commands, and are native to the scripting language. The scripting language may be Script, and the blockchain protocol may be a version of the Bitcoin protocol.

Abstract: The invention relates to efficient zero knowledge verification of composite statements that involve both arithmetic circuit satisfiability and dependent statements about the validity of public keys (key-statement proofs) simultaneously. The method enables a prover to prove this particular statement in zero-knowledge. More specifically, the invention relates to a computer-implemented method for enabling zero-knowledge proof or verification of a statement (S) in which a prover proves to a verifier that a statement is true while keeping a witness (W) to the statement a secret. The invention also relates to the reciprocal method employed by a verifier who verifies the proof.

Abstract: There may be provided a computer-implemented method. It may be implemented at least in part using a blockchain network such as, for example, the Bitcoin network.

Abstract: A method of transferring control of a digital asset (2) is disclosed. The method comprises distributing shares dAi of a first private key dA of an elliptic curve cryptography (ECC) system among a plurality of first participants (4). The first private key is accessible by means of a first threshold number (6) of shares dAi of the first private key, and is inaccessible in the absence of the first threshold number of shares, and access to the digital asset (2) is provided by digital signature of a first encrypted message with the first private key. Shares of a deterministic key Dk of the cryptography system are distributed among the either the first participants or a plurality of second participants, wherein the deterministic key is accessible by means of a second threshold number of shares of the deterministic key, and is inaccessible in the absence of the second threshold number of shares.

Abstract: An implementation of the present application provides a computer-implemented method to increase the security of a blockchain-implemented transaction, the transaction including participation from a plurality of participating nodes, each participating node participating as a message originator, selector, and propagator. The method, implemented at a participating node, includes: receiving ciphertext from a prior node and determining whether the participating node is a selector node for said ciphertext received from the prior node. When the participating node is the selector node for said ciphertext, the method includes selecting a subset of said ciphertext, decrypting the selected subset of said ciphertext to provide opted ciphertext and transmitting said opted ciphertext to the next node. When the participating node is other than the selector node for said ciphertext, the method includes decrypting said ciphertext received from the prior node and transmitting the decrypted ciphertext to the next node.

Abstract: A system for performing transaction mixing between a plurality of users on a blockchain is provided. The blockchain may be, for example, the Bitcoin blockchain. The system is configured to carry out the steps of: (i) preparing a first commitment transaction arranged to transmit control of a resource from a source address of a first user to a receiving address of a second user; (ii) preparing a second commitment transaction arranged to transmit control of a resource from a source address of the second user to a receiving address of a further user; (iii) preparing a further commitment transaction arranged to transmit control of a resource from a source address of the further user to either: (a) a receiving address of the first user; or (b) a receiving address of a yet further user and repeating step (iii) until option (a) is performed to complete a transaction chain; and (iv) executing the transaction chain. At least one of the users is randomly chosen from the plurality.