Abstract: There may be provided a computer-implemented method. It may be implemented using a blockchain such as, for example, the Bitcoin blockchain. The computer-implemented method includes: i) joining a congress by transferring, by a node operating in a proof-of-work blockchain network, one or more digital assets to a congress pool having one or more other digital assets associated with other members of a congress; ii) detecting, by the node, a special transaction of digital assets on the proof-of-work blockchain network to an address associated with the congress pool, the special transaction satisfying determined criteria; and iii) minting, by the node, one or more digital assets on a proof-of-stake blockchain network in response to detecting the special transaction.

Abstract: A method of digitally signing a message is disclosed. The method comprises distributing first shares of a first secret value among a plurality of participants, wherein the first secret value is a private key accessible by means of a first threshold number of the first shares, and is inaccessible to less than the first threshold number of the first shares; distributing second shares of a second secret value among the participants, wherein the second secret value is an ephemeral key, wherein said ephemeral key is inaccessible to less than said first threshold number of said second shares; and distributing third shares of a third secret value among the participants, wherein each third share is adapted to be applied to a message to generate a respective fourth share of a fourth secret value, wherein the fourth secret value is the message signed with the private key and using the ephemeral key.

Abstract: Techniques are presented to instantiate an event chain with a first block, wherein the first block is timestamped with an instantiation time; monitor for an event associated with a monitoring request; signal to other nodes in a plurality of nodes based on the monitoring by providing a commitment to a plurality of nodes in the plurality of nodes, wherein based on occurrence of the event providing either a dummy signal or an indicator comprising an encryption private key share held by the node, wherein the commitment is provided to the other nodes in the plurality of nodes; monitor for commitments from the other nodes in the plurality of nodes, wherein each commitment comprises a dummy signal or an encryption key share; process the commitments received from the other nodes to obtain an encryption private key share; and identify the encryption private key based on the analysis of the commitments.

Abstract: The invention relates to a method of enabling zero-knowledge proof or verification of a statement (S) for enabling exchange of data between a prover and a verifier, wherein the prover has access to first data on a first blockchain, and the verifier has access to second data on a second blockchain. In the method, a prover sends to a verifier a set of data including a statement, which for a given function circuit output and an elliptic curve point, the function circuit input is equal to the corresponding elliptic curve point multiplier. The statement can be that the prover knows a private key for an address on a blockchain network.

Abstract: There may be provided a computer-implemented method. It may be implemented using a blockchain such as, for example, the Bitcoin blockchain. The computer-implemented method includes: i) joining a congress by transferring, by a node operating in a proof-of-work blockchain network, one or more digital assets to a congress pool having one or more other digital assets associated with other members of a congress; ii) detecting, by the node, a special transaction of digital assets on the proof-of-work blockchain network to an address associated with the congress pool, the special transaction satisfying determined criteria; and iii) minting, by the node, one or more digital assets on a proof-of-stake blockchain network in response to detecting the special transaction.

Abstract: A computer-implemented method includes: storing an encryption public key that is associated with a group of nodes, each node in the group associated with a private key share, the private key shares associated with a threshold private key reconstruction scheme for the group to allow an encryption private key associated with the encryption public key to be determined from at least a threshold of the private key shares; iteratively obtaining a plurality of indicators provided by a plurality of nodes of the group, each of the indicators representing one of an encryption private key share or a dummy signal; and identifying the encryption private key by iteratively: i) selecting a subset of the indicators; ii) calculating a possible shared secret; and iii) evaluating each possible shared secret against the encryption public key to determine whether the possible shared secret is the encryption private key. The invention is suited for implementation on a blockchain.

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: 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 using a blockchain such as, for example, the Bitcoin blockchain. The computer-implemented method includes: i) joining a congress by transferring, by a node operating in a proof-of-work blockchain network, one or more digital assets to a congress pool having one or more other digital assets associated with other members of a congress; ii) detecting, by the node, a special transaction of digital assets on the proof-of-work blockchain network to an address associated with the congress pool, the special transaction satisfying determined criteria; and iii) minting, by the node, one or more digital assets on a proof-of-stake blockchain network in response to detecting the special transaction.

Abstract: Provided herein is a computer-implemented method, a system, and a non-transitory computer-readable storage medium. The system may be implemented using a blockchain network. The computer-implemented method includes: i) attaching a digital asset of a first entity to an exchange platform; ii) computing a first shared key associated with the digital asset using a key of the first entity and a first key of the exchange platform; iii) generating and broadcasting a first blockchain transaction to a blockchain network; and iv) initiating, by the first entity, transfer of ownership of the digital asset from a first entity to a second entity; v) computing a second key and a second shared key; vi) replacing the first key associated with the exchange platform with the second key associated with the exchange platform; and vii) detaching, by the second entity, the deposit from the exchange platform using the second shared key.

Abstract: A method of digitally signing a message is disclosed. The method comprises distributing first shares of a first secret value among a plurality of participants, wherein the first secret value is a private key accessible by means of a first threshold number of the first shares, and is inaccessible to less than the first threshold number of the first shares; distributing second shares of a second secret value among the participants, wherein the second secret value is an ephemeral key, wherein said ephemeral key is inaccessible to less than said first threshold number of said second shares; and distributing third shares of a third secret value among the participants, wherein each third share is adapted to be applied to a message to generate a respective fourth share of a fourth secret value, wherein the fourth secret value is the message signed with the private key and using the ephemeral key.

Abstract: A digital time-lock contract specifies that an agent holds an encryption private key corresponding to an encryption public key on a blockchain network and then releases the encryption private key to the blockchain network within a specified time window. An agent provides a first cryptographic asset for holding and then releasing the encryption private key to the blockchain network, the first cryptographic asset being transferrable when the encryption private key is released to the blockchain network within the specified time window. A client provides a second cryptographic asset to the agent for holding and then releasing the encryption private key to the blockchain network, the second cryptographic asset being transferrable when the encryption private key is released to the blockchain network within the specified time window. The digital time-lock contract can be broadcast to the blockchain network for mining onto the blockchain.

Abstract: A method is presented for secure determination of a solution (S) to a computational task by a pooled resource or group having a plurality of participants (P), the group operating in a trust-less, or dealer-free, system or manner. Access to a resource or reward is offered in exchange for the solution. Individuals generate their own key pair and use their public key to establish with the group an initial shared public key that they can all use to find a solution to the task. The resource or reward can be secured by the verified shared public key. Because the private keys of each participant were used in the determination of the initial shared public key that lead to the solution then participants must then collaborate to unlock the resource or reward because the corresponding shared private key can only be generated by all participants or a pre-agreed threshold of participants.

Abstract: A method of transferring access to a digital asset is disclosed. The method comprises receiving a first blockchain transaction (4) from a first participant (6) by each of a plurality of second participants (8), (10). The first participant (6) has a first private key of a first private-public key pair of a cryptography system, and each participant (6), (8), (10) has a respective first share of a second private key of a second private-public key pair of the cryptography system, and the first blockchain transaction is signed with the first private key. Signature of the first blockchain transaction with the first private key is verified by each second participant (8), (10). A respective first share is applied to the first blockchain transaction to generate a respective second share of a second blockchain transaction signed with the second private key.

Abstract: There may be provided a computer-implemented method that includes: broadcasting, by a node in a blockchain network, a transaction to transfer one or more digital assets to a public group address associated with a congress public key, the public group being associated with one or more other digital assets associated with other members of a congress; generating a private key share 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 combination of partial signatures on behalf of the congress, wherein other holders of the private key shares are the other members of the congress who have joined the congress by transfer of respective digital assets to the public group address; and using the private key share to cooperatively generate a valid signature for a transaction from the public group address.

Abstract: There may be provided a computer-implemented method. It may be implemented using a blockchain such as, for example, the Bitcoin blockchain. The computer-implemented method includes: i) joining a congress by transferring, by a node operating in a proof-of-work blockchain network, one or more digital assets to a congress pool having one or more other digital assets associated with other members of a congress; ii) detecting, by the node, a special transaction of digital assets on the proof-of-work blockchain network to an address associated with the congress pool, the special transaction satisfying determined criteria; and iii) minting, by the node, one or more digital assets on a proof-of-stake blockchain network in response to detecting the special transaction.

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: There may be provided a computer-implemented method. It may be implemented using a blockchain such as, for example, the Bitcoin blockchain. The computer-implemented method includes: i) joining a congress by transferring, by a node operating in a proof-of-work blockchain network, one or more digital assets to a congress pool having one or more other digital assets associated with other members of a congress; ii) detecting, by the node, a special transaction of digital assets on the proof-of-work blockchain network to an address associated with the congress pool, the special transaction satisfying determined criteria; and iii) minting, by the node, one or more digital assets on a proof-of-stake blockchain network in response to detecting the special transaction.

Abstract: A digital time-lock contract specifies that an agent holds an encryption private key corresponding to an encryption public key on a blockchain network and then releases the encryption private key to the blockchain network within a specified time window. An agent provides a first cryptographic asset for holding and then releasing the encryption private key to the blockchain network, the first cryptographic asset being transferrable when the encryption private key is released to the blockchain network within the specified time window. A client provides a second cryptographic asset to the agent for holding and then releasing the encryption private key to the blockchain network, the second cryptographic asset being transferrable when the encryption private key is released to the blockchain network within the specified time window. The digital time-lock contract can be broadcast to the blockchain network for mining onto the blockchain.

Abstract: A computer-implemented method includes: storing an encryption public key that is associated with a group of nodes, each node in the group associated with a private key share, the private key shares associated with a threshold private key reconstruction scheme for the group to allow an encryption private key associated with the encryption public key to be determined from at least a threshold of the private key shares; iteratively obtaining a plurality of indicators provided by a plurality of nodes of the group, each of the indicators representing one of an encryption private key share or a dummy signal; and identifying the encryption private key by iteratively: i) selecting a subset of the indicators; ii) calculating a possible shared secret; and iii) evaluating each possible shared secret against the encryption public key to determine whether the possible shared secret is the encryption private key. The invention is suited for implementation on a blockchain.