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: 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 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: Techniques are presented for using a processing resource to control access to a resource. Steps comprise generating an elliptic curve digital signature algorithm signature comprising a first signature component, r, and a second signature component, w, the generation step comprising: forming, by a node, a signing group with other nodes; obtaining, by the node, based on a secure random number: a) a multiplicative inverse of the secure random number; and b) the first signature component, r, wherein the first signature component is determined based on the secure random number and an elliptic curve generator point; determining, by the node, a partial signature; receiving partial signatures from other nodes of the signing group; generating the second component; and using the signature to control access to the and/or transfer of a resource over a computer-implemented network.

Abstract: Techniques are presented for a computer-implemented method that may be implemented using a blockchain network. The computer-implemented method includes: monitoring a system to detect a challenge to a proposer string in response to a request, and as a result of detecting the challenge: placing a first digital asset and a second digital asset under exclusive control of a group of nodes via a public key associated with a group of nodes, wherein the first and second digital assets are configured to be released when a threshold number of members of the group of nodes generate a valid signature for the public key associated with the group of nodes; resolving the challenge using a blockchain network; and distributing, by the group of nodes, digital assets from the first digital asset and the second digital asset to one or more parties of the system based at least in part on the solution.

Abstract: Provided herein are techniques for performing a detachment phase of an off-chain cryptocurrency transaction between untrusted parties using an exchange platform, with an entity requesting that a destination node detach a cryptocurrency deposit from the exchange platform. It may be implemented using a blockchain network. A computer-implemented method includes: i) receiving a request, by a first entity, to detach a deposit from an exchange platform; ii) determining whether detachment of the deposit is allowed by verifying ownership of the first entity and ensuring that a timeout has not been reached; iii) generating a shared key using a transmitted exchanged key and an attachment private key of the first entity; iv) verifying the shared key with the exchange platform; and v) generating a blockchain transaction to detach the deposit and provide the deposit to the entity.

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: 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 computer-implemented method that may be implemented using a blockchain network including monitoring a computational task distribution system to detect a challenge to a proposer string provided by a proposer computer system in response to a request made by a requester computer system, and as a result of detecting the challenge, at least: resolving the challenge using a first blockchain network by at least selecting a solution from a set of solutions provided to the first blockchain network, the set of solutions at least including the proposer string; and distributing digital assets from the first digital asset and the second digital asset to one or more parties of the computational task distribution system based at least in part on the solution.

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: 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: This 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 method includes sending to the verifier a statement (S) represented by an arithmetic circuit configured to implement a function circuit and determine whether a function circuit output (h) and an elliptic curve point (P), the function circuit input (s) to a wire of the function circuit is equal to the corresponding elliptic curve point multiplier (s); individual wire commitments and a batched commitment for wires of the circuit; a function circuit output (h); proving key (PrK) to enable the verifier to determine that the circuit is satisfied and calculate the elliptic curve point (P) to validate the statement, determin that the prover holds the witness (w) to the statement.

Abstract: Provided herein are a process, an apparatus, and an article of manufacture for confiscating a digital asset due to malicious members or malicious attacks. A process in the form of a computer-implemented method includes: i) detecting malicious activity by a malicious party, wherein the malicious party is one of the other members of the a congress; and ii) confiscating at least a portion of digital assets previously transferred to the a public group address by the malicious party. Security mechanisms disclosed herein for confiscating a digital asset leverage the use of a congress that is secured, in part, through distributed generation of private key share. The security mechanisms further allow a self-governing, decentralized group to be formed, with the threshold signature scheme allowing the group to control digital assets encumbered by a public key associated with the group.

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: 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: 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. A method is disclosed for a prover proving to a verifier that a statement is true, while keeping a witness (w) to the statement a secret, and a verifier using a reciprocal method to verify the proof. The prover sends, to the verifier, data including a statement represented by an implemented function circuit, individual wire commitments and/or a batched commitment for the function circuit of the statement, a given function circuit output, and a proving key. Based on the sent data, the verifier is able to determine satisfiability of the function circuit, calculate an elliptic curve point, and validate the statement, thus determining that the prover holds the witness to the statement and ensuring the data complies with the statement.

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: The invention relates to a computer-implemented method for enabling zero-knowledge proof or verification of a statement in which a prover proves to a verifier that a statement is true while keeping a witness to the statement a secret. 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. The data includes individual wire commitments and/or a batched commitment for wires of the circuit, a function circuit output, and a prover key, which enables the verifier to determine that the circuit is satisfied and calculate the elliptic curve point and validate the statement, thus determining that the prover holds the witness to the statement.

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.