Abstract: Systems and methods described relate to executing, by a third computing entity different from a first computing entity and a second computing entity, a smart contract generated by the first computing entity and the second computing entity. A verification key is determined based on a power of a secret, the power of the secret being based on first and second sets of elliptic curve points. The smart contract comprising a first input from the first computing entity and a second input from the second computing entity are received. The smart contract is executed by computation of a function on an input to produce an output. A proof of correct execution of the smart contract is produced. A blockchain transaction is generated using an output of the smart contract. The generated blockchain transaction using the verification key and the proof of correct execution is validated by a fourth computing entity.

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

Abstract: Determining when and/or how to execute a program or script published to a blockchain network may rely on data that is external to the blockchain. A prover (e.g., a node of the blockchain network) may perform one or more computations on behalf of a client, such as the execution of the program. To execute the program properly, the prover may rely on external data, which the prover may obtain from a data provider that has a trust relationship with the client (e.g., the client accepts as valid data provided by a trusted data provider). Systems and methods described herein may be utilized by a prover to provide cryptographically verifiable assurances of the authenticity of input data purportedly obtained from a data provider, the input data utilized in the execution of a program or script published to a blockchain network. An example of a blockchain network is a Bitcoinbased network.

Abstract: A computer-implemented method is disclosed that includes: receiving, at a mempool node of distributed mempool network (DMP) implementing a distributed hash table (DHT), a request to update routing information of the mempool node; initializing a set of random walks within a key space of the DHT; generating a first record in an first table based at least in part on a first identification information stored in a second of a long-distance table type; generating a second record in a third table of the long-distance table type by at least performing a first random walk of the set of random walks, the second record containing a second identification information and an address associated with the second identification information; generating a third record in a fourth table of a short-distance table type by at least obtaining records from a table maintained by a second mempool node of the DMP network.

Abstract: In a distributed system, a first computer system may require computationally verifiable assurances of the authenticity and integrity of computations (e.g., performed as part of the execution of a program) performed by a second computer system. Methods described herein may be utilized to enforce and/or ensure the correct execution of a program. The first computer system may delegate execution of a program to a second computer system and a protocol may be employed to constrain the second computer system to perform a correct execution of the program. The protocol may include mitigation and correction routines that mitigate and/or correct the incorrect execution of a program. In various systems and methods described herein, the protocol may utilize a blockchain network such as a Bitcoin-based blockchain network.

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: A blockchain that can be used to generate an immutable transaction history of data produced by the set of digital twins. In the case of an error or failure, parties of interest can then access and analyze an immutable record of data. The invention may be used in conjunction with the Bitcoin blockchain or another blockchain protocol.

Abstract: A computer-implemented method for a node of a blockchain network comprising receiving or generating data for distribution in the blockchain network, said node having a plurality of interfaces, said data corresponding to an object such as a transaction or a block. The transaction can be a Bitcoin transaction for recordal in a blockchain. The method determines a correlation matrix having correlation coefficients representing the correlation between data processed at each interface of said node. From the correlation matrix a correlation index for each interface is determined. A threshold or indicator is calculated and data or objects such as Bitcoin transactions are relayed from nodes via interfaces according to a set of correlation coefficients of interface receiving the data. An indicator or threshold can derived from the correlation matrix and data is relayed if the correlation between the receiving interface and the other interface is lower than the indicator.

Abstract: A computer implemented method and system is described which uses blockchain technology as a storage system for data acquired from a digital twin. The blockchain can be used to generate an immutable transaction history of data produced by the digital twin. In the case of an error, failure, incident, or accident, parties of interest can then access and analyse an immutable set of data. The blockchain network can also execute a digital smart contract based on the data received from a digital twin. The invention may be used in conjunction with the Bitcoin blockchain or another blockchain protocol.

Abstract: Systems and methods described herein relate to techniques in which multiple parties each generate and exchange quantities that are based on a shared secret (e.g., powers of the shared secret) without exposing the shared secret. According to a protocol, two or more parties may exchange sets of elliptic curve points generated over polynomials that can be used, by each of the two or more parties, to determine a power of a shared secret. The protocol may be utilised as part of determining parameters for a smart contract that is broadcast to a blockchain network (e.g., Bitcoin). Based on the protocol, an additional party (e.g., a third party different from the two or more parties) may perform a computational task such as execution of the smart contract.

Abstract: Systems and methods described herein relate to techniques in which multiple parties each generate and exchange quantities that are based on a shared secret (e.g., powers of the shared secret) without exposing the shared secret. According to a protocol, two or more parties may exchange sets of elliptic curve points generated over polynomials that can be used, by each of the two or more parties, to determine a power of a shared secret. The protocol may be utilised as part of determining parameters for a smart contract that is broadcast to a blockchain network (e.g., Bitcoin). Based on the protocol, an additional party (e.g., a third party different from the two or more parties) may perform a computational task such as execution of the smart contract.

Abstract: Methods and devices for propagating transactions in a network of nodes, each node having one or more connections to other nodes. The method includes receiving a plurality of incoming transactions over a time period; combining the plurality of incoming transactions using network coding to generate a composite message; sending the composite message to one or more nodes in the network; and determining an adjusted time period based on an equilibrium constant parameter and a count of transactions in the plurality of incoming transactions received over the time period.

Abstract: The invention relates to distributed ledger technologies such as consensus-based blockchains. A blockchain transaction may include digital resources that are encumbered by a locking script that encodes a set of conditions that must be fulfilled before the encumbered resources may be used (e.g., transferring ownership/control of encumbered resources). A worker (e.g., a computer system) performs one or more computations to generate a proof, which is encoded as part of an unlocking script. A verification algorithm may utilize the proof, a verification key, and additional data such as a cryptographic material associated with the worker (e.g., a digital signature) to verify that digital assets of the transaction should be transferred. As a result of the validation of this transaction, any third party is able to check the contract was executed corrected rather than re-executing the contract, thus saving computational power.

Abstract: The invention relates to distributed ledger technologies such as consensus-based blockchains. Computer-implemented methods for reducing arithmetic circuits derived from smart contracts are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. A set of conditions encoded in a first programming language is obtained. The set of conditions is converted into a programmatic set of conditions encoded in a second programming language. The programmatic set of conditions is precompiled into precompiled program code. The precompiled program code is transformed into an arithmetic circuit. The arithmetic circuit is reduced to form a reduced arithmetic circuit, and the reduced arithmetic circuit is stored.

Abstract: Methods and devices that manage the secure distribution of credentials from a group of autonomous specialized nodes to a requesting node. The secure distribution of credentials may uses secret share and a group private key that none of the nodes reconstructs or possesses. The credentials include an identifier for the requesting node and a secret point that the node assembles from portions of the secret point provided by each of a plurality of the specialized nodes, where the secret point is based on the group private key and a map-to-point hash of the requesting node's identifier.

Abstract: Methods and devices that manage the secure distribution of credentials from a group of autonomous specialized nodes to a requesting node. The secure distribution of credentials may uses secret share and a group private key that none of the nodes reconstructs or possesses. The credentials include an identifier for the requesting node and a secret point that the node assembles from portions of the secret point provided by each of a plurality of the specialized nodes, where the secret point is based on the group private key and a map-to-point hash of the requesting node's identifier.

Abstract: Methods and devices for propagating transactions in a network of nodes, each node having one or more connections to other nodes. The method includes determining that one of the nodes is a bottleneck for propagation of transactions; receiving, over a first time period, a plurality of new transactions from one or more first nodes in the network of nodes; combining the plurality of new transactions using network coding and a local encoding vector to generate a message; and sending the message and a global encoding vector to one or more second nodes in the network of nodes instead of sending the plurality of new transactions to the one or more second nodes. The network may be a blockchain network.

Abstract: Techniques and computer-implemented methods are presented to be implemented on a distributed mempool network (DMP) implementing a distributed hash table (DHT). The method includes: receiving, at a mempool node of a DMP, a request to update routing information of the mempool node; initializing a set of random walks within a key space of the DHT, the set of random walks used for generating a set of key-value records; selecting a particular iteration of a long-distance table of a set of long-distance tables; selecting, from the particular iteration of the long-distance table, a pointer within a range between identification information and a key; and transmitting a query to another mempool node associated with the pointer, wherein the other mempool node maintains a set of weight associated connections to a set of mempool nodes, wherein the weight is proportional to the level of trust in the connection.

Abstract: A method for propagating data packets in a network of nodes is disclosed. The method includes collecting a set of first data packets during a first period from peer nodes in the network of time; determining an available bandwidth in the links of network nodes to a plurality of neighbouring nodes connected to the network node; assigning mappings for first data packets for relay to one or more neighbouring nodes. Based on a bandwidth, determine a range of possible values for peer nodes to which the first data packet is assigned for mappings; then selecting a number in the determined range to set as a first number of peer nodes to set a first length of time delay in relaying the first data packet to one or more peer nodes; and transmitting the first data packets of the set to the plurality of neighbouring nodes according to the mapping.

Abstract: Methods and devices for propagating transactions in a network of nodes, each node having one or more connections to other nodes. The method includes receiving a plurality of incoming transactions over a time period; combining the plurality of incoming transactions using network coding to generate a composite message; sending the composite message to one or more nodes in the network; and determining an adjusted time period based on an equilibrium constant parameter and a count of transactions in the plurality of incoming transactions received over the time period.