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 method in accordance with the invention includes: providing to a hub, from an enclave associated with a TEE at a node, an enclave public key; establishing a channel with the hub by broadcasting to a blockchain network a funding transaction which encumbers a digital asset with a first public key, a second public key and a third public key such that the encumbrance of the digital asset may be removed by: 1) both a first signature generated from a first private key corresponding to the first public key and a second signature generated from a second private key corresponding to the second public key; or 2) a third signature, valid for the third public key, the third public key associated with a group; receiving a commitment transaction encrypted with the enclave public key; detecting a failure; and issuing a failsafe activation request to the group using data from the enclave.

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 blockchain-implemented security method involving a requestor and a group of nodes, which includes generating a cryptographic key of the requestor based on a password chosen by the requestor and first quantities sent by the group of nodes (which are derived from private key shares of the group of nodes and a generator function of a digital signature scheme employing a bilinear mapping on an elliptic curve). A cryptographic signature for a requestor blockchain transaction can be generated where the signature corresponds to the requestor's cryptographic key. The signature can be based on the password and second quantities sent by the group of nodes (which are also derived from the group private key shares). The method can further include verifying the cryptographic signature of the blockchain transaction using the requestor's cryptographic key.

Abstract: There may be provided a computer-implemented method. The computer-implemented method includes: i) after a proof-of-stake token is transferred to an address of a determined type on a proof-of-stake blockchain, adding a record of the transfer of the proof-of-stake token to the proof-of-work blockchain; ii) identifying a node, from a group of nodes, to participate in adding a block to the proof-of-stake blockchain, the identifying based on the proof-of-work blockchain; and iii) including a block submitted by the identified node in the proof-of-stake blockchain.

Abstract: A computer-implemented method for generating an identity-based cryptographic key, the method comprising: obtaining a set of private key shares and a set of corresponding public key shares, wherein each private key share is generated based on the personal identifier, and wherein at least one of the set of private key shares is generated by a respective one of a set of key-generating parties; generating an identity-based private key based on each of the one or more private key shares; and generating a partial identity-based public key, wherein the partial identity-based public key is generated based on each of the set of corresponding public key shares; transmitting the partial identity-based public key to at least one of the set of key-generating parties for generating the identity-based public key; and/or generating the identity-based public key, wherein the identity-based public key comprises the personal identifier and the partial identity-based public 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: A computer-implemented method is described for enabling recovery of one or more digital assets held on a blockchain by a user under a public key Pk after a corresponding private key Sk for accessing the one or more digital assets is lost. The computer implemented method comprises setting access for the one or more digital assets held on the blockchain under the public key Pk and accessible using the corresponding private key Sk of the user such that the one or more digital assets are also accessible using a private key x shared by a congress on the blockchain network, the congress comprising a group of users on the blockchain network, each member of the congress having a private key share xi, the private key share xi 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 the combination of partial signatures of the congress to access the one or more digital assets on behalf of the user.

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: 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 blockchain-implemented security method involving a requestor and a group of nodes, which includes generating a cryptographic key of the requestor based on a password chosen by the requestor and first quantities sent by the group of nodes (which are derived from private key shares of the group of nodes and a generator function of a digital signature scheme employing a bilinear mapping on an elliptic curve). A cryptographic signature for a requestor blockchain transaction can be generated where the signature corresponds to the requestor's cryptographic key. The signature can be based on the password and second quantities sent by the group of nodes (which are also derived from the group private key shares). The method can further include verifying the cryptographic signature of the blockchain transaction using the requestor's cryptographic key.

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: Embodiments of the present disclosure provides protocols, methods and systems which provides advantages such as the resistance of centralisation of mining on a blockchain network, preferably a Proof-of-Work blockchain. A method in accordance with an embodiment may comprise generating a plurality of non-parallelisable challenges (or “puzzles”) and allocating one of said plurality of challenges to each miner on the network. The miner uses an inherently sequential (non-parallelisable) algorithm to find a solution to his allocated challenge. The challenges are generated by a committee of nodes, and a new set of challenges is generated for each block.

Abstract: A computer-implemented method is described for enabling recovery of one or more digital assets held on a blockchain by a user under a public key Pk after a corresponding private key Sk for accessing the one or more digital assets is lost. The computer implemented method comprises setting access for the one or more digital assets held on the blockchain under the public key Pk and accessible using the corresponding private key Sk of the user such that the one or more digital assets are also accessible using a private key x shared by a congress on the blockchain network, the congress comprising a group of users on the blockchain network, each member of the congress having a private key share xi, the private key share xi 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 the combination of partial signatures of the congress to access the one or more digital assets on behalf of the user.

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: There may be provided a computer-implemented method. It may be implemented at least in part using a blockchain network such as, for example, the Bitcoin network.

Abstract: There may be provided a computer-implemented method. It may be implemented at least in part using a blockchain network such as, for example, the Bitcoin network.

Abstract: There may be provided a computer-implemented method. The computer-implemented method includes: i) after a proof-of-stake token is transferred to an address of a determined type on a proof-of-stake blockchain, adding a record of the transfer of the proof-of-stake token to the proof-of-work blockchain; ii) identifying a node, from a group of nodes, to participate in adding a block to the proof-of-stake blockchain, the identifying based on the proof-of-work blockchain; and iii) including a block submitted by the identified node in the proof-of-stake blockchain.