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.

Abstract: The invention relates to secure determination of a solution (S) to a computational task by a dealer-free threshold signature group. Access to a resource or reward is offered in exchange for the solution. The method enables individuals in said group to work together in a trust-less, or dealer-free manner. To achieve this, 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, in parallel, to find a solution to the task. Their own private keys remain secret and, therefore, the collaboration is trust¬less, and operates efficiently, because a verified shared public key is created using the initial shared public key that was used when a solution is found and verified. The resource or reward can be secured by the verified shared public key.

Abstract: Embodiments of the invention provide enhanced security solutions which are enforced through the use of cryptographic techniques. It is suited for, but not limited to, use with blockchain technologies such as the Bitcoin blockchain. Methods and devices for generating an elliptic curve digital signature algorithm signature (r, w) are described.

Abstract: There may be provided a computer-implemented method. The computer-implemented method includes: i) broadcasting, by a node in a blockchain network (such as, for example, the Bitcoin 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; ii) 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, and 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 iii) 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 network such as, for example, the Bitcoin network.

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: Embodiments of the invention provide enhanced security solutions which are enforced through the use of cryptographic techniques. It is suited for, but not limited to, use with blockchain technologies such as the Bitcoin blockchain. Methods and devices for generating an elliptic curve digital signature algorithm signature (r, w) are described.

Abstract: This specification describes a system and method that enables bitcoin signed transactions to be accepted as a payment for goods and services instantly and off-line, without the need to wait for confirmation that the transaction is included in a valid block, or even for confirmation that a transaction has been received by the network. Building on the concept of a one-time signature implemented within bitcoin script, this method involves a payer providing the payee with a special compensation key at the point-of-sale which can be used to claim a time-locked deposit output when combined with a ‘revealed’ private key, if (and only if) a double-spend is perpetrated by the payee. The validity of this compensation key is guaranteed via a novel type of zero-knowledge -proof, which is highly efficient: the proof can be generated in ˜5 milliseconds and can be verified in ?30 milliseconds.

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. 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: The invention relates to secure determination of a solution (S) to a computational task by a dealer-free threshold signature group. Access to a resource or reward is offered in exchange for the solution. The method enables individuals in said group to work together in a trust-less, or dealer-free manner. To achieve this, 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, in parallel, to find a solution to the task. Their own private keys remain secret and, therefore, the collaboration is trust¬less, and operates efficiently, because a verified shared public key is created using the initial shared public key that was used when a solution is found and verified. The resource or reward can be secured by the verified shared public key.

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: 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. The method includes the prover sending to the 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.

Abstract: There may be provided a computer-implemented method. The computer-implemented method includes: i) broadcasting, by a node in a blockchain network (such as, for example, the Bitcoin 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; ii) 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, and 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 iii) using the private key share to cooperatively generate a valid signature for a transaction from the public group address.

Abstract: The invention relates to distributed ledger technologies such as consensus-based blockchains. Computer-implemented methods for smart contract outcome determination are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. A set of conditions is determined between counterparties, with the set of conditions having a plurality of possible outcomes that includes a first possible outcome associated with a first distribution of a digital asset and a second possible outcome associated with a second distribution, different from the first distribution, of the digital asset. A counterparty transaction is created that includes, as output, the set of conditions encoded into computer-executable instructions and the digital asset. An outcome is received from a third party, with the outcome corresponding to the first possible outcome or the second possible outcome.

Abstract: The invention relates to distributed ledger technologies such as consensus-based blockchains. Computer-implemented methods for smart contract outcome determination are described. The invention is implemented using a blockchain network, which may be, for example, a Bitcoin blockchain. Assent to determine an outcome of a set of conditions is communicated to a set of counterparties, with the set of conditions having a first possible outcome and a second possible outcome. A first private key share corresponding to the first possible outcome and a second private key share corresponding to the second possible outcome are generated using a secret sharing protocol. An amount of a digital asset is transferred to an address associated with a first blockchain 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.