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. At least in one embodiment of the present invention, 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: 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 method of making a decision on a blockchain is disclosed. First public keys are received from each of a plurality of participants (A, B, C), wherein each first public key represents a possible selection by a participant and is related to a corresponding first private key by a cryptographic operation having a homomorphic property. The first public keys are combined to generate second public keys, wherein each second public key represents a possible decision based on a combination of possible selections. Third public keys, corresponding to the second public keys, are communicated to the participants. A voting blockchain transaction is generated (Tc voting), wherein an input of the voting transaction is a script executable by means of a digital signature corresponding to a first private key of each of a plurality of the participants, wherein each first private key represents a selection made by the participant.

Abstract: A method of propagating data packets in a network of nodes is disclosed. The method includes: collecting a set of first data packets during a first time period, the set including at least one data packet received from one or more first nodes in the network; generating a first mapping that assigns the first data packets of the set for relay to one or more neighbouring nodes connected to the node; computing a decorrelation metric value for the first mapping; determining whether the decorrelation metric value for the first mapping satisfies a first condition; in response to determining that the decorrelation metric value for the first mapping does not satisfy the condition of transmitting the first data packets of the set to neighbouring nodes according to the second mapping.

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 and devices for verifying a digital resource by a plurality of node devices in a blockchain network. The plurality of nodes have respective private key shares, where a collective private key of a collective private-public key pair is based on a set of the respective private key shares, and where each node has a nodal private-public key pair. The digital resource may be encrypted using a digital resource crypto public key, the digital resource crypto public key including combination of a nodal public key and a collective public key. The digital resource may be submitted to a repository system by broadcasting a commitment transaction and a subsequent reveal or rescind transaction of a commitment channel, the commitment channel formed between a respective node and a principal node. Decrypting the encrypted digital resource is based on retrieving private key share contributions from the plurality of nodes participating in verifying the digital resource.

Abstract: A method for propagating data packets in a network of nodes is disclosed. The method comprises: collecting a set of first data packets during a first time period, the set including at least one first data packet received from one or more first nodes in the network; determining an available bandwidth in the network node's links to a plurality of neighbouring nodes connected to the network node; determining a mapping that assigns each of the first data packets for relay to one or more neighbouring nodes, the mapping indicating an expected time of relay of each of the first data packets, and transmitting the first data packets of the set to the plurality of neighbouring nodes according to the determined mapping.

Abstract: Techniques are presented to enable recovery of one or more digital assets held on a blockchain after a private key 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, each member of the congress having a private key share xi to be used in a threshold signature scheme used to generate a valid signature. As a result of the private key Sk being lost, the congress accesses the one or more digital assets on behalf of the user in response to the user proving their identity to the congress by providing a recovery password.

Abstract: A method of propagating data packets in a network of nodes is disclosed. The method, implemented at one of the nodes, includes: collecting a set of first data packets during a first time period, the set including at least one data packet received from one or more first nodes in the network; obtaining a plurality of encoded data packets, each one of the plurality of encoded data packets being generated by combining two or more first data packets of the set using network coding; determining a mapping of the plurality of encoded data packets and the first data packets of the set to one or more neighbouring nodes connected to the node; and transmitting the plurality of encoded data packets and the first data packets of the set to the one or more neighbouring nodes according to the determined mapping.

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

Abstract: First secrets are generated by a first party. The first secrets are encrypted by the first party utilizing elliptic curve cryptography to obtain data points representing encrypted versions of the first secrets. A message, which includes the data points, is sent by the first party to a second party. A first transaction created by the second party is verified by the first party ensuring that cryptographic locks generated by the second party are based on allowed linear combinations of encrypted versions of the first secrets and encrypted versions of second secrets generated by the second party. One secret from the first secrets is randomly selected by the first party. Another message, which includes the one secret, is sent by the first party to the second party such that the second party can generate a cryptographic key that unlocks a cryptographic lock of the cryptographic locks generated by the second party.

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 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: A computer-implemented includes sending a public key associated with a particular node in a cyclically-ordered set of nodes participating in a blockchain network to an initiator node; receiving, by the particular node from a node immediately previous to the particular node in the cyclically-ordered set, a first value based on public keys associated with each node from the particular node through to the initiator node; determining a locking value based on the first value and the public key associated with the particular node; and preparing using the locking value, a transaction arranged to transmit control of a resource from a source address associated with the particular node to a receiving address of a node immediately subsequent to the particular node. The control of the resource is to be transmitted responsive to satisfaction of an execution condition including supply of an unlocking value corresponding to the locking value.

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 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: 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 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.