Abstract: A computer-implemented method of enabling users to access broadcasted messages using blockchain transactions comprising: determining a set of users eligible to access a message; maintaining a key graph comprising a plurality of nodes representing keys, generating an encrypted message; determining a set of encrypted data items; obtaining a message transaction comprising: a respective input associated and signed by each respective user, a respective input associated with and signed by the broadcasting party, a respective output associated with and locked to a respective public key of the respective user and/or a public key of the broadcasting party, and a respective output comprising the set of encrypted data items; causing the message transaction to be submitted to a blockchain network; and broadcasting the encrypted message to at least the set of users.

Abstract: A computer implemented method of facilitating a consumption tax on a purchase of one or more goods and/or services by a buyer from a seller, wherein at least the buyer is a buyer-seller who makes an onward sale based on said goods and/or services. The method comprises, by the seller of the purchase, obtaining a first blockchain transaction that can be redeemed by a second blockchain transaction meeting either of two alternative conditions: a first condition requiring at least that the second blockchain transaction is signed with a cryptographic signature of the buyer, and a second condition requiring at least that the second blockchain transaction is signed with at least a cryptographic signature of a tax authority; and in response to receiving a payment of the consumption tax from the buyer, sending the first blockchain transaction to be recorded on a blockchain.

Abstract: A blockchain-implemented transaction from an originator node is to be broadcast. The originator node is communicatively coupled to proxy nodes. The method, implemented by a proxy node, includes: receiving a transaction including an input taking x+r units of computing resources, an output providing x units to the output address and another output providing d+r units to a 1-of-n multi-signature address unlockable by any one of a set of private keys associated the proxy nodes. The proxy node selects a quantity of computing resources, t units, to be allocated to the proxy node for broadcasting the transaction and having it included in the blockchain and generates a further transaction taking d+r units sourced from the multi-signature address and an output providing t units to the proxy node. The proxy node broadcasts both transactions timed to permit their inclusion in the same block of the blockchain.

Abstract: A computer-implemented method to participate in a token transfer process for transferring a first quantity of token from a sender node to a recipient node using a blockchain is disclosed. The token transfer process includes a plurality of participating nodes and execution of a set of indirect token transactions between multiple pairs of the participating nodes.

Abstract: A method for enabling a second party to determine a shared cryptographic key, comprising: generating a puzzle blockchain transaction comprising one or more outputs, each output comprising a puzzle locking script, wherein each puzzle locking script comprises a target public key and is configured to, when executed together with a unlocking script comprising a candidate value, convert the candidate value into a candidate public key and require the candidate public key to match the target public key; and sending the puzzle blockchain transaction to one or more nodes of a blockchain network and/or the second party, wherein the first party is configured to generate the shared cryptographic key based on the first private key, the second public key, and each target public key, and wherein the second party is configured to generate the shared cryptographic key based on the second private key, the first public key, and each candidate value.

Abstract: Contributions to a work by contributors having respective levels in a defined hierarchy are recorded in one or more blockchain transactions. One or more lower-level contributors provide, to a higher-level contributor, one or more lower-level contributions respectively, and the higher-level contributor provides a higher-level contribution responsive to the one or more lower-level contributions. A higher-level contributor transaction comprises one or more inputs, which in turn comprise: one or more pointers to one or more spendable outputs of one or more lower-level contributor transactions and one or more transaction signatures. The transactions contain contributions commitments which, together with the one or more pointers, represent the relationship between the higher-level contributor and the lower-level contributors within the defined hierarchy. The one or more transaction signatures prove that relationship.

Abstract: A computer-implemented method for transmitting and/or submitting digital content such as feedback for an entity to a blockchain is disclosed. This may be, for example, the Bitcoin blockchain. The method, which is implemented at a first node, includes: submitting, to the blockchain, a first transaction for committing a first quantity of tokens to transfer to a second node associated with the entity, the first transaction having a first output; generating a first content for submission to the blockchain; and submitting, to the blockchain, a second transaction that returns a second quantity of the committed first quantity of tokens to an address associated with the first node, the second transaction having the first output of the first transaction as an input, wherein the first content is used to unlock the first output of the first transaction.

Abstract: Methods and systems for enabling conditional access to a resource, where the condition is the performance of a task. This task can be executed by one party on behalf of another. The entity controlling access creates a task that includes broadcasting a transaction on the blockchain, with multiple outputs, including a locking-output. Additional transactions ensure access to the resource only upon task completion. Access is achieved by initially broadcasting the resource, conditionally available, then broadcasting the transaction that fulfills the condition. Multi-signatures and a refund mechanism are used to lock access, with multi-signatures spread across transactions. Initial deposit broadcast makes the resource available but locked by a first multi-signature and tied to a refund mechanism. The task and transaction have a locking-output secured by a second multi-signature linked to the refund mechanism.

Abstract: A computer-implemented method of generating a transaction for a blockchain, the transaction being for transferring an amount of a digital asset from a first party to a second party. The method comprises generating a first transaction comprising an output locking the amount of the digital asset, the output comprising an output script comprising a plurality of criterion components each requiring a respective input data item, and a plurality of counter script components. Each criterion component is associated with one of the counter script components. The output script is configured so as to, when executed alongside an input script of a second transaction, i) increment a counter each time a respective criterion component is satisfied by a respective input data item of the input script, and ii) to require the counter to increment to at least a predetermined number in order to be unlocked by the input script.

Abstract: A computer-implemented method of making a decision on a blockchain is provided. The method comprises providing a blockchain voting commitment transaction (2) redeemable by means of a first signature (?(Am), ?(Bm)) associated with a selection (A, B) and a second signature (?(A), ?(B)) associated with the selection, providing each of a plurality of participants (Ui) with at least one share (kA,i, kB,i) of at least one respective secret value (kA, kB) wherein a threshold number of shares is required in order to execute said second signature, and submitting the blockchain voting commitment transaction (2) to the blockchain.

Abstract: A method of propagating data packets in a network of nodes is disclosed. The method, implemented at one of the nodes, includes: generating at least one data packet of a first type; collecting a set of data packets of the first type during a first time period, the set including the at least one generated data packet and one data packet of the first type received from one or more first nodes in the network; and for each data packet in the set: randomly select two or more neighbouring nodes connected to said one of the nodes; transmit, to each of the two or more selected neighbouring nodes: the data packet, wherein the two or more selected neighbouring nodes are configured to relay the data packet to one or more second nodes in the network using a mode of data propagation arbitrarily selected for that neighbouring node.

Abstract: A computer-implemented method for submitting feedback for an entity to a blockchain is disclosed. The method, which is implemented at one of a plurality of participating nodes, includes: obtaining a first key, the first key being one of a fixed set of keys distributed to participating nodes that are eligible to submit feedback for the entity; generating first feedback (rj) of the entity for submission to the blockchain; encrypting the first feedback (rj) using at least the first key; and submitting the encrypted first feedback to a mixing service, the mixing service being configured to generate a mixed transaction based on the encrypted first feedback and at least one other encrypted feedback submission from one or more eligible participating nodes.

Abstract: A method for decision-making on a blockchain includes receiving first public keys from participants, where the first public keys are related to first private keys. The first public keys are combined to generate second public keys, where the second public keys are decisions based on selections among the participants. Third public keys, which correspond to the second public keys, are communicated to the participants. A voting blockchain transaction is generated, where an input script is executed by using a digital signature that corresponds to each participant's first private key, which corresponds to a participant's selection. Output of the voting transaction is a script that represents a decision based on the participants' selections. A payment blockchain transaction is generated, where execution of an output of the payment transaction requires a digital signature that corresponds to a third public key, which corresponds to the decision of the voting transaction.

Abstract: A computer-implemented method to participate in a token transfer process for transferring a first quantity of token from a sender node to a recipient node using a blockchain is disclosed. The method comprising: joining a token transfer process as a participating node in the indirect anonymous transfer protocol; obtaining a list of indirect token transactions for which the first node is either an input node or an output node for in the indirect anonymous transfer protocol; generating, in collaboration with other participating nodes of the indirect anonymous transfer protocol, a commitment channel between the first node and each of the other participating nodes for which an indirect token transaction identified in the list obtained by the first node, and collaborating with all the other participating nodes and executing the indirect token transactions in which the first node is involved, using the generated commitment channels.

Abstract: A computer-implemented method of generating a transaction for a blockchain, the transaction being for transferring an amount of a digital asset from a first party to a second party. The method comprises generating a first transaction comprising an output locking the amount of the digital asset, the output comprising an output script comprising a plurality of criterion components each requiring a respective input data item, and a plurality of counter script components. Each criterion component is associated with one of the counter script components. The output script is configured so as to, when executed alongside an input script of a second transaction, i) increment a counter each time a respective criterion component is satisfied by a respective input data item of the input script, and ii) to require the counter to increment to at least a predetermined number in order to be unlocked by the input script.

Abstract: A computer-implemented method to generate a unidirectional commitment channel to send one or more tokens from a sender node to a recipient node using a blockchain is disclosed. The method is implemented by a processing resource that performs steps comprising: generating a first commitment transaction representing a commitment component in which a specified set of tokens is sent or committed for transfer from the first node to the second node; generating a return transaction which returns all tokens from the second node to the first node; signing the return transaction and, based on the signing of the return transaction, signing the commitment transaction; creating one or more further return transactions to reflect the transfer of tokens being made off the blockchain.

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 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 to a node 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 shared with the supervisor and a previous node. A blockchain transaction is prepared to transmit control of a resource from the node to the subsequent node upon supply of unlocking values corresponding to the received values.

Abstract: A computer-implemented method to participate in a token transfer process for transferring a first quantity of token from a sender node to a recipient node using a blockchain is disclosed. The token transfer process includes a plurality of participating nodes and execution of a set of indirect token transactions between multiple pairs of the participating nodes.

Abstract: A computer-implemented method for transmitting and/or submitting digital content such as feedback for an entity to a blockchain is disclosed. This may be, for example, the Bitcoin blockchain. The method, which is implemented at a first node, includes: submitting, to the blockchain, a first transaction for committing a first quantity of tokens to transfer to a second node associated with the entity, the first transaction having a first output; generating a first content for submission to the blockchain; and submitting, to the blockchain, a second transaction that returns a second quantity of the committed first quantity of tokens to an address associated with the first node, the second transaction having the first output of the first transaction as an input, wherein the first content is used to unlock the first output of the first transaction.

Abstract: A method of providing credentials to enable a second party to verify an identity of a first party. The first party is associated with a first public key which is registered with a third party. One or more first credentials are provided to the second party. A request transaction is obtained, which comprises a) an input comprising a signature generated based on a respective private key of the third party, and b) an output locked to a second public key of the first party. The second public key is based on the first public key. A confirmation transaction is generated. The confirmation transaction comprises an input that references the output of the request transaction, and a signature generated based on a private key corresponding to the second public key of the first party. The confirmation transaction is transmitted to nodes of a blockchain network for inclusion in a blockchain.