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 encoding a digital contract between first and second parties of a blockchain network, the digital contract being for transferring an amount of a digital asset from the first to the second party based on a condition being fulfilled; the method comprising: obtaining a plurality of data elements, each representing a different contract condition, wherein at least one of the conditions is linked to the second party; generating a hash tree based on the data elements, wherein the hash tree comprises: i) first leaf hashes generated by hashing a respective data element, and second leaf hashes comprising at least one hash key generated by hashing a secret value known only to the trusted third party, ii) internal hashes, and iii) a root hash; and making the root hash available to the first party for inclusion in a transaction of the blockchain.

Abstract: Systems and methods for generating min-increment counting bloom filters to determine count and frequency of device identifiers and attributes in a networking environment are disclosed. The system can maintain a set of data records including device identifiers and attributes associated with device in a network. The system can generate a vector comprising coordinates corresponding to counter registers. The system can identify hash functions to update a counting bloom filter. The system can hash the data records to extract index values pointing to a set of counter registers. The system can increment the positions in the min-increment counting bloom filter corresponding to the minimum values of the counter registers. The system can obtain an aggregated public key comprising a public key. The system can encrypt the counter registers using the aggregated shared key to generate an encrypted vector. The system can transmit the encrypted vector to a networked worker computing device.

Abstract: A method of validating transactions for recordal in a blockchain comprises receiving one or more transactions at a node of a blockchain network. For each received transaction a protocol for validating the transaction is applied. The protocol is configured to allow a termination opcode to be included in an output script of the transaction. The termination opcode is configured to, upon being executed by the node, a) terminate execution of the output script, and b) not to invalidate the transaction based only on the inclusion of the termination opcode in the output script. The protocol is also configured to disallow any instance of the termination opcode from being included in an input script of the transaction, said disallowing comprising the node at least invalidating the transaction if any instance of the termination opcode is included in the input script.

Abstract: A method of executing transactions of a blockchain network. A first transaction comprises at least a first output comprising a first locking script of a stack-based scripting language, the first locking script comprising a portion of the first locking script to be executed before a first instance of an opcode is executed. A second transaction comprises a first unlocking script that references the first output in the first transaction. Upon executing the first instance of the opcode, execution of the first locking script is terminated whilst not invalidating the first transaction. A first data element is read from at least one stack, wherein the first data element is generated during execution of the first unlocking script and the portion of the first locking script. The first data element as read from the at least one stack is supplied to an off-chain function, wherein the function is configured to generate a result based on at least said first data element.

Abstract: Aspects of the disclosure are directed to estimating a frequency histogram for users across multiple platforms while maintaining accuracy, security, privacy, and/or computational efficiency thresholds. The frequency histogram can be estimated unbiasedly with a configurable variance. The computations for generating the frequency histogram can be differentially private, satisfy provable security, and be efficient.

Abstract: A computer-implemented method, the method performed by a controller configured to communicate with a blockchain and with a network comprising one or more devices, the method comprising: maintaining identification information comprising an index number assigned to each of the one or more devices; receiving one or more input-output pairs of a blockchain transaction, wherein each input-output pair is associated with an assigned index number and wherein each input-output pair comprises data from a device of the one or more devices; generating a blockchain transaction based on the one or more input-output pairs; sending the blockchain transaction to the blockchain.

Abstract: A computer-implemented method comprising, at a verifying nodes of a blockchain network: obtaining a first transaction which comprises runnable code; receiving a second transaction which includes information comprising at least a submitted instance of an r-part and an s-part of a first ECDSA signature, and further comprising a nonce; and running the code from the first transaction. The code is configured to verify that HPoW(ƒ(r,d)) meets a predetermined condition defined in the code, and to return a result of true on condition thereof, where r is the submitted instance of the r-part, d is the nonce, HPoW is a hash function, and f is a function combining q and d.

Abstract: Methods and devices for propagating blocks in a blockchain network. At a mining node, while hashing a first block header of a first candidate block, the mining node sends, to other mining nodes, a first message specifying transactions and their order in a first ordered set of transactions contained in the first candidate block. The mining also receives a second message specifying transactions and their order in a second ordered set of transactions contained in a second candidate block being mined by a second mining node. If the mining node succeeds in mining the candidate block it notifies other mining nodes by providing them with a coinbase transaction, hash value, and timestamp. If another mining node is successful, then the mining node receives information from the other mining node from which, in conjunction with the second message, it can assemble the second candidate block and validate it.

Abstract: Methods and devices for propagating blocks in a blockchain network. At a mining node, while hashing a first block header of a first candidate block, the mining node sends, to other mining nodes, a first message specifying transactions and their order in a first ordered set of transactions contained in the first candidate block. The mining also receives a second message specifying transactions and their order in a second ordered set of transactions contained in a second candidate block being mined by a second mining node. If the mining node succeeds in mining the candidate block it notifies other mining nodes by providing them with a coinbase transaction, hash value, and timestamp. If another mining node is successful, then the mining node receives information from the other mining node from which, in conjunction with the second message, it can assemble the second candidate block and validate it.

Abstract: A computer-implemented method comprising, at a verifying nodes of a blockchain network: obtaining a first transaction which comprises runnable code; receiving a second transaction which includes information comprising at least a submitted instance of an r-part and an s-part of a first ECDSA signature, and further comprising a nonce; and miming the code from the first transaction. The code is configured to verify that HPoW(ƒ(r, d)) meets a predetermined condition defined in the code, and to return a result of true on condition thereof, where r is the submitted instance of the r-part, d is the nonce, HPoW is a hash function, and f is a function combining q and d.

Abstract: Systems and methods for generating min-increment counting bloom filters to determine count and frequency of device identifiers and attributes in a networking environment are disclosed. The system can maintain a set of data records including device identifiers and attributes associated with device in a network. The system can generate a vector comprising coordinates corresponding to counter registers. The system can identify hash functions to update a counting bloom filter. The system can hash the data records to extract index values pointing to a set of counter registers. The system can increment the positions in the min-increment counting bloom filter corresponding to the minimum values of the counter registers. The system can obtain an aggregated public key comprising a public key. The system can encrypt the counter registers using the aggregated shared key to generate an encrypted vector. The system can transmit the encrypted vector to a networked worker computing device.

Abstract: A computer-implemented method of generating a share of a shared private key, wherein each participant of a group of participants has a respective share of a master private key, and wherein the method is performed by a first participant of the group and comprises: generating a first share of a first shared private key based on a first share of the master private key and a first hash value, wherein the first hash value is generated by hashing a nonce value one or more times.

Abstract: Systems and methods for generating min-increment counting bloom filters to determine count and frequency of device identifiers and attributes in a networking environment are disclosed. The system can maintain a set of data records including device identifiers and attributes associated with device in a network. The system can generate a vector comprising coordinates corresponding to counter registers. The system can identify hash functions to update a counting bloom filter. The system can hash the data records to extract index values pointing to a set of counter registers. The system can increment the positions in the min-increment counting bloom filter corresponding to the minimum values of the counter registers. The system can obtain an aggregated public key comprising a public key. The system can encrypt the counter registers using the aggregated shared key to generate an encrypted vector. The system can transmit the encrypted vector to a networked worker computing device.

Abstract: A method of validating transactions for recordal in a blockchain comprises receiving one or more transactions at a node of a blockchain network. For each received transaction a protocol for validating the transaction is applied. The protocol is configured to allow a termination opcode to be included in an output script of the transaction. The termination opcode is configured to, upon being executed by the node, a) terminate execution of the output script, and b) not to invalidate the transaction based only on the inclusion of the termination opcode in the output script. The protocol is also configured to disallow any instance of the termination opcode from being included in an input script of the transaction, said disallowing comprising the node at least invalidating the transaction if any instance of the termination opcode is included in the input script.

Abstract: A computer-implemented method of constructing a candidate block of a blockchain, wherein the method comprises: obtaining an ordered sequence of blockchain transactions; obtaining a transaction representation by hashing a data object, wherein the data object comprises the ordered sequence of blockchain transactions; and constructing the candidate block, wherein the candidate block comprises the transaction representation.

Abstract: A method of recording a target transaction in a blockchain, comprising: obtaining an updated version of the target transaction, being updated relative to a pre-existing first version; and instead of the first version, sending the updated version to be propagated through a network of nodes to be recorded in the blockchain. The target transaction comprises an input comprising an unlocking script and a pointer to an output of a first transaction, the output of the first transaction comprising a locking script specifying a plurality of alternative conditions for unlocking that output. The unlocking script of the first version of the target transaction is configured to unlock the first output of the first transaction based on a first of said alternative conditions, and the unlocking script of the updated version is configured to unlock it based on a second one of said alternative conditions.

Abstract: A method comprising: providing a first transaction specifying an output amount of a digital asset to greater than pointed to by its inputs, wherein an output of the first transaction comprises a locking script specifying a condition; over a side channel, receiving an input from each of multiple users, and adding each received input to the first transaction; and once a target is reached, whereby the total input amount pointed to by the inputs of the first transaction is equal to or exceeds the output amount, causing the first transaction and a second transaction to be published to a blockchain network to be recorded in a blockchain. The second transaction comprises an input pointing to the output of the first transaction and comprising an unlocking script meeting said condition. The condition requires the unlocking script to include a media key enabling the users to access the item of media content.

Abstract: A server of media content makes a first transaction available to users that includes a first output specifying an amount of a digital asset to transfer to a second party, and a total of zero or more inputs wherein a total input amount of the digital asset specified in any outputs of any source transactions pointed to by the zero or more inputs is less than a total output amount of the digital asset specified by the one or more outputs. Inputs are received from users of a side channel. Once a target is reached, the first transaction and a second transaction are recorded in a blockchain, wherein the second transaction comprises an input pointing to the first output of the first transaction and an unlocking script meeting a condition that requires the unlocking script to include a media key enabling the users to access the item of media content.

Abstract: At least one proof transaction is received at a node of a blockchain network and comprises at least one Elliptic Curve Digital Signature Algorithm (ECDSA) signature and at least one zero-knowledge proof (ZKP) component. The node verifies the ECDSA signature of the at least one proof transaction based on a public key associated with the ECDSA signature and a signed part of the at least one proof transaction, and determined whether the ZKP component is correct for the ECDSA signature and a defined hash value and a defined hash function, in that it proves an ephemeral key counterpart to an r-part of the ECDSA signature to be a preimage of the defined hash value with respect to the defined hash function.