Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
  • H04L9/3255—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using group based signatures, e.g. ring or threshold signatures
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
  • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
  • H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
  • H04L9/088—Usage controlling of secret information, e.g. techniques for restricting cryptographic keys to pre-authorized uses, different access levels, validity of crypto-period, different key- or password length, or different strong and weak cryptographic algorithms
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/50—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using hash chains, e.g. blockchains or hash trees

Definitions

• a sender can use their own private key to sign a message, e.g. to prove that the message is being sent by the sender, and/or to indicate that the sender agrees with the message.
• the signer i.e. the party generating the signature
• Creating a digital signature based on a message means supplying the message and private key to a function that generate the signature based on both the message and private key.
• the signature is added to (e.g. tagged onto) the message or otherwise associated with the message.
• anyone with the signer's corresponding public key can use the same message and the digital signature on the message to verify whether the signature was validly created, i.e.
• a common use of a shared secret is as a shared private key of a private-public key pair. That is, the private key may be distributed amongst a group of participants such that no single participant has access to the private key. Therefore no single participant can generate a valid signature of a message. Instead, some or all of the participants must together generate the private key in order for the signature to be generated.
• a computer-implemented method of generating a share of a digital signature wherein each participant of a group of participants has a respective share of a first shared private key, and wherein the method is performed by a first participant of the group and comprises: obtaining a first message; generating a first data item based on at least a hash of a first external data item; generating a first ephemeral private key share of an ephemeral private key, wherein the first ephemeral private key share is generated based on the first data item and a respective data item generated by each other participant; generating an ephemeral public key corresponding to the ephemeral private key; generating a first signature share based on the first message, the first ephemeral private key share, a first share of the first shared private key, and the ephemeral public key; and making the first signature share available to a coordinator for generating a first signature based on
• a computer-implemented method of verifying that a digital signature has been partly generated by a first participant wherein the method is performed by a verifying party and comprises: obtaining a first signature comprising first and second signature components; obtaining a candidate first external data item from the first participant, and one or more respective public key corresponding to a respective data items, one for each other participant; generating a candidate public key based on a hash of the candidate first external data item; generating a candidate ephemeral public key based on the candidate public key and the obtained one or more public keys; generating a candidate first signature component based on the candidate ephemeral public key; and verifying that the first signature has been partly generated by the first participant based on whether the candidate first signature component corresponds to the first signature component.
• the first participant generates a share of digital signature for signing a message.
• the message may be a transaction, e.g. the signature may be included in an input of a transaction for unlocking an output of a previous transaction.
• the message may be any form of message, e.g. a document, and does not necessarily need to be related to the blockchain.
• the signature share is generated at least in part based on an ephemeral private key share, e.g. a share of a one-time use private key.
• the ephemeral private key share is generated at least in part based on external information, i.e. the "external data item".
• Figure 3A is a schematic block diagram of a client application
• Figure 4 is a schematic block diagram of an example system for implementing embodiments of the present invention.
• each transaction 152 comprises at least one input and at least one output.
• Each output specifies an amount representing a quantity of a digital asset as property, an example of which is a user 103 to whom the output is cryptographically locked (requiring a signature or other solution of that user in order to be unlocked and thereby redeemed or spent).
• Each input points back to the output of a preceding transaction 152, thereby linking the transactions.
• Each block 151 also comprises a block pointer 155 pointing back to the previously created block 151 in the chain so as to define a sequential order to the blocks 151.
• Each of the blockchain nodes 104 is configured to forward transactions 152 to other blockchain nodes 104, and thereby cause transactions 152 to be propagated throughout the network 106.
• Each blockchain node 104 is configured to create blocks 151 and to store a respective copy of the same blockchain 150 in their respective memory.
• Each blockchain node 104 also maintains an ordered set (or "pool") 154 of transactions 152 waiting to be incorporated into blocks 151.
• the ordered pool 154 is often referred to as a "mempool”. This term herein is not intended to limit to any particular blockchain, protocol or model. It refers to the ordered set of transactions which a node 104 has accepted as valid and for which the node 104 is obliged not to accept any other transactions attempting to spend the same output.
• the input of the present transaction 152j also comprises the input authorisation, for example the signature of the user 103a to whom the output of the preceding transaction 152i is locked.
• the output of the present transaction 152j can be cryptographically locked to a new user or entity 103b.
• the present transaction 152j can thus transfer the amount defined in the input of the preceding transaction 152i to the new user or entity 103b as defined in the output of the present transaction 152j .
• a transaction 152 may have multiple outputs to split the input amount between multiple users or entities (one of whom could be the original user or entity 103a in order to give change).
• a transaction can also have multiple inputs to gather together the amounts from multiple outputs of one or more preceding transactions, and redistribute to one or more outputs of the current transaction.
• the blockchain node 104 forwards it to one or more other blockchain nodes 104 in the blockchain network 106. These other blockchain nodes 104 apply the same test according to the same blockchain node protocol, and so forward the new transaction 152j on to one or more further nodes 104, and so forth. In this way the new transaction is propagated throughout the network of blockchain nodes 104.
• the definition of whether a given output is assigned (e.g. spent) is whether it has yet been validly redeemed by the input of another, onward transaction 152j according to the blockchain node protocol.
• Another condition for a transaction to be valid is that the output of the preceding transaction 152i which it attempts to redeem has not already been redeemed by another transaction. Again if not valid, the transaction 152j will not be propagated (unless flagged as invalid and propagated for alerting) or recorded in the blockchain 150. This guards against double-spending whereby the transactor tries to assign the output of the same transaction more than once.
• An account-based model on the other hand guards against double-spending by maintaining an account balance. Because again there is a defined order of transactions, the account balance has a single defined state at any one time.
• blockchain nodes 104 In addition to validating transactions, blockchain nodes 104 also race to be the first to create blocks of transactions in a process commonly referred to as mining, which is supported by "proof-of-work". At a blockchain node 104, new transactions are added to an ordered pool
• the blockchain nodes then race to assemble a new valid block 151 of transactions 152 from the ordered set of transactions 154 by attempting to solve a cryptographic puzzle.
• this comprises searching for a "nonce" value such that when the nonce is concatenated with a representation of the ordered pool of pending transactions 154 and hashed, then the output of the hash meets a predetermined condition.
• the predetermined condition may be that the output of the hash has a certain predefined number of leading zeros. Note that this is just one particular type of proof-of- work puzzle, and other types are not excluded.
• a property of a hash function is that it has an unpredictable output with respect to its input. Therefore this search can only be performed by brute force, thus consuming a substantive amount of processing resource at each blockchain node 104 that is trying to solve the puzzle.
• the first blockchain node 104 to solve the puzzle announces this to the network 106, providing the solution as proof which can then be easily checked by the other blockchain nodes 104 in the network (once given the solution to a hash it is straightforward to check that it causes the output of the hash to meet the condition).
• the first blockchain node 104 propagates a block to a threshold consensus of other nodes that accept the block and thus enforce the protocol rules.
• the ordered set of transactions 154 then becomes recorded as a new block 151 in the blockchain 150 by each of the blockchain nodes 104.
• a protocol also exists for resolving any "fork” that may arise, which is where two blockchain nodesl04 solve their puzzle within a very short time of one another such that a conflicting view of the blockchain gets propagated between nodes 104. In short, whichever prong of the fork grows the longest becomes the definitive blockchain 150. Note this should not affect the users or agents of the network as the same transactions will appear in both forks.
• the blockchain protocol rules may require a maturity period, for example 100 blocks, before this special transaction may be redeemed.
• a regular (non-generation) transaction 152 will also specify an additional transaction fee in one of its outputs, to further reward the blockchain node 104 that created the block 151n in which that transaction was published. This fee is normally referred to as the "transaction fee", and is discussed blow.
• each of the blockchain nodes 104 takes the form of a server comprising one or more physical server units, or even whole a data centre.
• any given blockchain node 104 could take the form of a user terminal or a group of user terminals networked together.
• each blockchain node 104 stores software configured to run on the processing apparatus of the blockchain node 104 in order to perform its respective role or roles and handle transactions 152 in accordance with the blockchain node protocol. It will be understood that any action attributed herein to a blockchain node 104 may be performed by the software run on the processing apparatus of the respective computer equipment.
• the node software may be implemented in one or more applications at the application layer, or a lower layer such as the operating system layer or a protocol layer, or any combination of these.
• Two parties 103 and their respective equipment 102 are shown for illustrative purposes: a first party 103a and his/her respective computer equipment 102a, and a second party 103b and his/her respective computer equipment 102b. It will be understood that many more such parties 103 and their respective computer equipment 102 may be present and participating in the system 100, but for convenience they are not illustrated.
• Each party 103 may be an individual or an organization. Purely by way of illustration the first party 103a is referred to herein as Alice and the second party 103b is referred to as Bob, but it will be appreciated that this is not limiting and any reference herein to Alice or Bob may be replaced with "first party" and "second "party” respectively.
• the computer equipment 102 of each party 103 comprises respective processing apparatus comprising one or more processors, e.g. one or more CPUs, GPUs, other accelerator processors, application specific processors, and/or FPGAs.
• the computer equipment 102 of each party 103 further comprises memory, i.e. computer-readable storage in the form of a non-transitory computer-readable medium or media.
• This memory may comprise one or more memory units employing one or more memory media, e.g. a magnetic medium such as hard disk; an electronic medium such as an SSD, flash memory or EEPROM; and/or an optical medium such as an optical disc drive.
• the memory on the computer equipment 102 of each party 103 stores software comprising a respective instance of at least one client application 105 arranged to run on the processing apparatus.
• any action attributed herein to a given party 103 may be performed using the software run on the processing apparatus of the respective computer equipment 102.
• the computer equipment 102 of each party 103 comprises at least one user terminal, e.g. a desktop or laptop computer, a tablet, a smartphone, or a wearable device such as a smartwatch.
• the computer equipment 102 of a given party 103 may also comprise one or more other networked resources, such as cloud computing resources accessed via the user terminal.
• the client application 105 comprises at least a "wallet” function.
• This has two main functionalities. One of these is to enable the respective party 103 to create, authorise (for example sign) and send transactions 152 to one or more bitcoin nodes 104 to then be propagated throughout the network of blockchain nodes 104 and thereby included in the blockchain 150. The other is to report back to the respective party the amount of the digital asset that he or she currently owns.
• this second functionality comprises collating the amounts defined in the outputs of the various 152 transactions scattered throughout the blockchain 150 that belong to the party in question.
• the instance of the client application or software 105 on each computer equipment 102 is operatively coupled to at least one of the blockchain nodes 104 of the network 106. This enables the wallet function of the client 105 to send transactions 152 to the network 106.
• the client 105 is also able to contact blockchain nodes 104 in order to query the blockchain 150 for any transactions of which the respective party 103 is the recipient (or indeed inspect other parties' transactions in the blockchain 150, since in embodiments the blockchain 150 is a public facility which provides trust in transactions in part through its public visibility).
• the wallet function on each computer equipment 102 is configured to formulate and send transactions 152 according to a transaction protocol.
• each blockchain node 104 runs software configured to validate transactions 152 according to the blockchain node protocol, and to forward transactions 152 in order to propagate them throughout the blockchain network 106.
• the transaction protocol and the node protocol correspond to one another, and a given transaction protocol goes with a given node protocol, together implementing a given transaction model.
• the same transaction protocol is used for all transactions 152 in the blockchain 150.
• the same node protocol is used by all the nodes 104 in the network 106.
• An alternative type of transaction protocol operated by some blockchain networks may be referred to as an "account-based" protocol, as part of an account-based transaction model.
• each transaction does not define the amount to be transferred by referring back to the UTXO of a preceding transaction in a sequence of past transactions, but rather by reference to an absolute account balance.
• the current state of all accounts is stored, by the nodes of that network, separate to the blockchain and is updated constantly.
• transactions are ordered using a running transaction tally of the account (also called the "position"). This value is signed by the sender as part of their cryptographic signature and is hashed as part of the transaction reference calculation.
• an optional data field may also be signed the transaction. This data field may point back to a previous transaction, for example if the previous transaction ID is included in the data field.
• FIG. 2 illustrates an example transaction protocol.
• This is an example of a UTXO-based protocol.
• a transaction 152 (abbreviated "Tx") is the fundamental data structure of the blockchain 150 (each block 151 comprising one or more transactions 152). The following will be described by reference to an output-based or "UTXO" based protocol. However, this is not limiting to all possible embodiments. Note that while the example UTXO-based protocol is described with reference to bitcoin, it may equally be implemented on other example blockchain networks.
• each transaction (“Tx") 152 comprises a data structure comprising one or more inputs 202, and one or more outputs 203.
• Each output 203 may comprise an unspent transaction output (UTXO), which can be used as the source for the input 202 of another new transaction (if the UTXO has not already been redeemed).
• the UTXO includes a value specifying an amount of a digital asset. This represents a set number of tokens on the distributed ledger.
• the UTXO may also contain the transaction ID of the transaction from which it came, amongst other information.
• the transaction data structure may also comprise a header 201, which may comprise an indicator of the size of the input field(s) 202 and output field(s) 203.
• the header 201 may also include an ID of the transaction. In embodiments the transaction ID is the hash of the transaction data (excluding the transaction ID itself) and stored in the header 201 of the raw transaction 152 submitted to the nodes 104.
• TxT Alice's new transaction 152j
• Txo The preceding transaction 152i
• n and Tx1 are just arbitrary labels. They do not necessarily mean that Txois the first transaction in the blockchain 151, nor that Tx1 is the immediate next transaction in the pool 154. Tx1 could point back to any preceding (i.e. antecedent) transaction that still has an unspent output 203 locked to Alice.
• One of the one or more outputs 203 of the preceding transaction Txo comprises a particular UTXO, labelled here UTX0 0 .
• Each UTXO comprises a value specifying an amount of the digital asset represented by the UTXO, and a locking script which defines a condition which must be met by an unlocking script in the input 202 of a subsequent transaction in order for the subsequent transaction to be validated, and therefore for the UTXO to be successfully redeemed.
• the locking script locks the amount to a particular party (the beneficiary of the transaction in which it is included).
• the locking script defines an unlocking condition, typically comprising a condition that the unlocking script in the input of the subsequent transaction comprises the cryptographic signature of the party to whom the preceding transaction is locked.
• the locking script (aka scriptPubKey) is a piece of code written in the domain specific language recognized by the node protocol. A particular example of such a language is called "Script" (capital S) which is used by the blockchain network.
• the locking script specifies what information is required to spend a transaction output 203, for example the requirement of Alice's signature. Unlocking scripts appear in the outputs of transactions.
• the unlocking script (aka scriptSig) is a piece of code written the domain specific language that provides the information required to satisfy the locking script criteria. For example, it may contain Bob's signature. Unlocking scripts appear in the input 202 of transactions.
• UTX0 0 in the output 203 of Txo prises a locking script [Checksig PA] which requires a signature Sig PA of Alice in order for UTX0 0 to be redeemed (strictly, in order for a subsequent transaction attempting to redeem UTX0 0 to be valid).
• [Checksig PA] contains a representation (i.e. a hash) of the public key PA from a public- private key pair of Alice.
• the input 202 of Tx1 comprises a pointer pointing back to Tx1 (e.g. by means of its transaction ID, TxIDo, which in embodiments is the hash of the whole transaction Txo).
• the input 202 of Tx1 comprises an index identifying UTX0 0 within Txo, to identify it amongst any other possible outputs of Txo.
• the input 202 of Tx1 further comprises an unlocking script ⁇ Sig PA> which comprises a cryptographic signature of Alice, created by Alice applying her private key from the key pair to a predefined portion of data (sometimes called the "message" in cryptography).
• the data (or "message") that needs to be signed by Alice to provide a valid signature may be defined by the locking script, or by the node protocol, or by a combination of these.
• the node applies the node protocol. This comprises running the locking script and unlocking script together to check whether the unlocking script meets the condition defined in the locking script (where this condition may comprise one or more criteria). In embodiments this involves concatenating the two scripts:
• Tx1 will be invalid even if all the other conditions are met.
• the blockchain node 104 also needs to check whether the referenced UTXO in the preceding transaction Txo is already spent (i.e. whether it has already formed a valid input to another valid transaction). This is one reason why it is important for the blockchain 150 to impose a defined order on the transactions 152.
• a given blockchain node 104 may maintain a separate database marking which UTXOs 203 in which transactions 152 have been spent, but ultimately what defines whether a UTXO has been spent is whether it has already formed a valid input to another valid transaction in the blockchain 150.
• UTXO-based transaction models a given UTXO needs to be spent as a whole. It cannot "leave behind" a fraction of the amount defined in the UTXO as spent while another fraction is spent. However the amount from the UTXO can be split between multiple outputs of the next transaction. E.g. the amount defined in UTX0 0 in Txo can be split between multiple UTXOs in Tx1. Hence if Alice does not want to give Bob all of the amount defined in UTX0 0 , she can use the remainder to give herself change in a second output of Tx1, or pay another party.
• the transaction fee does not require its own separate output 203 (i.e. does not need a separate UTXO). Instead any difference between the total amount pointed to by the input(s) 202 and the total amount of specified in the output(s) 203 of a given transaction 152 is automatically given to the blockchain node 104 publishing the transaction.
• the assets of a given party 103 are scattered throughout the UTXOs of various transactions 152 throughout the blockchain 150.
• the locking script is sometimes called "scriptPubKey” referring to the fact that it typically comprises the public key of the party to whom the respective transaction is locked.
• the unlocking script is sometimes called “scriptSig” referring to the fact that it typically supplies the corresponding signature.
• the scripting language could be used to define any one or more conditions. Hence the more general terms “locking script” and “unlocking script” may be preferred.
• the client application on each of Alice and Bob's computer equipment 102a, 120b, respectively, may comprise additional communication functionality.
• This additional functionality enables Alice 103a to establish a separate side channel 107 with Bob 103b (at the instigation of either party or a third party).
• the side channel 107 enables exchange of data separately from the blockchain network.
• Such communication is sometimes referred to as "off-chain" communication.
• this may be used to exchange a transaction 152 between Alice and Bob without the transaction (yet) being registered onto the blockchain network 106 or making its way onto the chain 150, until one of the parties chooses to broadcast it to the network 106.
• Sharing a transaction in this way is sometimes referred to as sharing a "transaction template".
• a transaction template may lack one or more inputs and/or outputs that are required in order to form a complete transaction.
• the side channel 107 may be used to exchange any other transaction related data, such as keys, negotiated amounts or terms, data content, etc.
• FIG 3A illustrates an example implementation of the client application 105 for implementing embodiments of the presently disclosed scheme.
• the client application 105 comprises a transaction engine 401 and a user interface (UI) layer 402.
• the transaction engine 401 is configured to implement the underlying transaction-related functionality of the client 105, such as to formulate transactions 152, receive and/or send transactions and/or other data over the side channel 301, and/or send transactions to one or more nodes 104 to be propagated through the blockchain network 106, in accordance with the schemes discussed above and as discussed in further detail shortly.
• the Ul layer 402 is configured to render a user interface via a user input/output (I/O) means of the respective user's computer equipment 102, including outputting information to the respective user 103 via a user output means of the equipment 102, and receiving inputs back from the respective user 103 via a user input means of the equipment 102.
• the user output means could comprise one or more display screens (touch or non- touch screen) for providing a visual output, one or more speakers for providing an audio output, and/or one or more haptic output devices for providing a tactile output, etc.
• the user input means could comprise for example the input array of one or more touch screens (the same or different as that/those used for the output means); one or more cursor-based devices such as mouse, trackpad or trackball; one or more microphones and speech or voice recognition algorithms for receiving a speech or vocal input; one or more gesture-based input devices for receiving the input in the form of manual or bodily gestures; or one or more mechanical buttons, switches or joysticks, etc.
• the various functionality herein may be described as being integrated into the same client application 105, this is not necessarily limiting and instead they could be implemented in a suite of two or more distinct applications, e.g. one being a plug-in to the other or interfacing via an API (application programming interface).
• the functionality of the transaction engine 401 may be implemented in a separate application than the Ul layer 402, or the functionality of a given module such as the transaction engine 401 could be split between more than one application.
• some or all of the described functionality could be implemented at, say, the operating system layer.
• Figure 3B gives a mock-up of an example of the user interface (Ul) 500 which may be rendered by the Ul layer 402 of the client application 105a on Alice's equipment 102a. It will be appreciated that a similar Ul may be rendered by the client 105b on Bob's equipment 102b, or that of any other party.
• Ul user interface
• FIG. 3B shows the Ul 500 from Alice's perspective.
• the Ul 500 may comprise one or more Ul elements 501, 502, 502 rendered as distinct Ul elements via the user output means.
• the Ul elements may comprise one or more user-selectable elements 501 which may be, such as different on-screen buttons, or different options in a menu, or such like.
• the user input means is arranged to enable the user 103 (in this case Alice 103a) to select or otherwise operate one of the options, such as by clicking or touching the Ul element on-screen, or speaking a name of the desired option (N.B. the term "manual” as used herein is meant only to contrast against automatic, and does not necessarily limit to the use of the hand or hands).
• the options enable the user (Alice) to generate a signature to be embedded within a transaction.
• the Ul elements may comprise one or more data entry fields 502, through which the user can enter data to be embedded within a signature. These data entry fields are rendered via the user output means, e.g. on-screen, and the data can be entered into the fields through the user input means, e.g. a keyboard or touchscreen. Alternatively the data could be received orally for example based on speech recognition.
• the Ul elements may comprise one or more information elements 503 output to output information to the user. E.g. this/these could be rendered on screen or audibly.
• ECDSA - Elliptic Curve Groups is a cyclic elliptic curve group over finite field where p is prime.
• the number of elements in E is n where n is prime.
• G G E is the generator point of the elliptic curve group, meaning:
• the group operation is standard elliptic curve point addition and i ⁇ G denotes i repetitions of the group operation on G
• Sig Y [r y ,s y ], where [r Y , s y ] is a valid signature when verified using the public key Y.
• each participant agrees on the unique label i for each participant.
• Each participant i generates (t + 1) random numbers where ⁇ R means a randomly generated element of the set where is notation for the set ⁇ 1, ... , n — 1 ⁇ .
• a shared secret share is a point with the form (i, a i ), where i is the participants label in the scheme.
• JVRSS typically stands for "Joint verification random secret sharing” and includes steps 4 and 5 as well.
• JVRSS is taken to mean performing at least steps 1 to 3, where steps 4 and 5 are optional steps.
• Each participant i checks that each participant j has correctly calculated the polynomial point f j (i) by calculating fj(i) ⁇ G and verifying that If all participants find that this equation holds for each polynomial, then the group can collectively be sure that they have all created the same shared polynomial.
• JVRSS(i) for i 1
• the shared secret polynomial has order t, meaning (t + 1) participants are required to recreate it.
• This method for calculating the inverse of shared secrets is denoted by for participant z.
• a group of size N with a shared private key a of threshold (t + 1) execute the following steps:
• the coordinator requests a signature on the message from at least 2t + 1 participants.
• the coordinator verifies the signature using the standard ECDSA verification. If this fails, at least one of the shares must be incorrect, and the signature generation algorithm should be run again.
• opad is the block-sized outer padding
• ipad is the block-sized inner padding.
• the corresponding equation for the child public key is derived by simply point multiplying this equation by the base point G.
• the equation for calculating a non-hardened child private key sk child from a parent public key pk parent and parent private key sk parent is sk child sk parent + HMAC SHA5X2 L (C parent , pk parent ⁇ ⁇ index) , where c parent is the parent chain code, 2 31 ⁇ index ⁇ 2 32 is the child index, and HMAC-SHA512 is the HMAC function calculated with the SHA-512 hash function. Similar to hardened keys, the child chain code c chi id for non-hardened keys is defined to be the right 32 bytes of the result of the HMAC function: c child HMAC SHA512 R (C parent ,pk parent ⁇ index).
• a HD wallet should generate some hierarchical tree-like structure of private- public key pairs. This provides a high number of key pairs that can all be regenerated from one seed.
• FIG. 4 illustrates an example system 400 for generating a digital signature according to some embodiments of the present invention.
• the system comprises a plurality of participants 401 who each have a respective share of a shared private key.
• the shared private key may have been generated using a secret sharing scheme, e.g. JVRSS or Shamir's secret sharing scheme.
• the shared private key may have been generated using a scheme with a dealer, or using a dealer-less scheme. Only three participants are shown in Figure 4, but in general the system may comprise any number of participants 401.
• the system also comprises a verifying party 402, i.e. a signature verifying party, and a coordinator 404.
• the coordinator 404 is configured to generate a signature based on a threshold number of signature shares, each signature share being generated by a respective participant. Whilst the coordinator 404 is shown as being distinct in Figure 4, in some examples the coordinator may be the same entity as one of the participants, e.g. the first participant 401a. In some examples, the system comprises one or more blockchain nodes 104.
• Each participant 401, verifying party 402, and coordinator 404 operates respective computing equipment (not shown).
• Each respective computing equipment comprises respective processing apparatus comprising one or more processors, e.g. one or more central processing units (CPUs), accelerator processors (GPUs), application specific processors and/or field programmable gate arrays (FPGAs).
• the respective computing equipment may also comprise memory, i.e. computer-readable storage in the form of a non-transitory computer-readable medium or media.
• the memory may comprise one or more memory units employing one or more memory media, e.g. a magnetic medium such as a hard disk; an electronic medium such as a solid-state drive (SSD), flash memory or EEPROM; and/or an optical medium such as an optical disk drive.
• Each other participant e.g. the second and third participants 401b, 401c, also generate a respective ephemeral private key share.
• the other participants Preferably the other participants generate their respective ephemeral private key shares based on a hash of a respective external data item, but that is not essential.
• the participants may use the JVRSS scheme described above, where participants share polynomials evaluated at an index of the other participants.
• the JVRSS scheme is modified slightly by computing the zeroth order coefficient of the polynomial as based on the external data item, as opposed to being generated randomly. This is discussed in more detail below.
• the hash function used to generate the hash of the external data item may be any suitable hash function, e.g. SHA256, SHA512, and may comprise applying one or more hash functions multiple times.
• JVRSS-A in step 1) the participants set the zeroth-order coefficient a i0 of their respective private polynomial as being equal to the hash (e.g. double-hash) of the respective data item.
• the other polynomial coefficients may be chosen at random as in the normal JVRSS.
• the remaining steps of 1) to 5) of JVRSS are then followed as normal.
• Each participant then has a respective ephemeral private key share, and a set of obfuscated data items (i.e. public keys corresponding to the data items), one for each other participant.
• JVRSS, or rather JVRSS-A is a particular example of a secret sharing scheme and other scheme may be used, e.g. Shamir's secret sharing scheme.
• the signature therefore incorporates an external data item known, at this point, only to Alice 401a, e.g. a personal identifier.
• the external data item itself need not be a secret. It is preferred that the fact that the external data item is embedded within the signature is initially kept secret, but this is not essential.
• the external data item may be a certified public key of Alice's which itself is known to one or more parties, but its use as the external data item is not known.
• Alice 401a may make the signature available to Carol 402.
• Alice 401a may send the signature to Carol 402, or Alice may publish or otherwise broadcast the signature.
• Carol 402 may obtain the signature from a different party, e.g. the coordinator 404.
• Alice 401a may also send the message to Carol 402.
• the signature and the message are sent or published together.
• Alice 401a may also make the external data item available to Carol 402, either at the same time as the signature or at a different time, e.g. at a later time.
• the external data item may be made available in the same way as the signature or in a different way.
• Alice 401a may send the external data item to Carol 402 via a secure communication channel.
• Carol 402 requires the respective public keys corresponding to the respective data items generated by the other participants 401 (e.g. the public keys that obfuscate the zeroth-order coefficients).
• Alice 401 may send these to Carol 402, or the other participants may send their respective ephemeral public key shares to Carol 402.
• the external data item may be, or at least include, another signature.
• Alice 401a obtains a second message and generates a second signature based on at least the second message and a "main private key".
• main private key may be any private key owned by Alice 401a.
• Alice 401 may generate at least part of the second message herself. Additionally or alternatively, Alice 401a may receive or otherwise obtain at least part of the second message from another party, e.g. Carol 402. That is, Carol 402 may send some or all of the second message to Alice 401a, or Alice 401a and Carol 402 may have previously agreed upon at least part of the second message. For instance, Alice 401a and Carol 402 may have agreed to include an indication of the data and/or time at which the second signature is generated.
• the second message may comprise or be generated based on the first message. For instance, the second message may comprise the first message with additional data concatenated onto the start or end of the first message.
• each participant 401 uses the same second message to generate a respective second signature. That is, each participant 401 generates a respective second signature based on the second message and a receptive main private key.
• the ephemeral private key share is based on (i.e. is a function of) at least a hash of the external data item, e.g. a double-hash of the second signature.
• the ephemeral private key share may also be based on a randomly generated salt value, i.e. a value added to the hash of the external data item. More specifically, the data item used to generate Alice's ephemeral private key share may be based on the salt value.
• a salt value is used only once, i.e. a different salt value is used to generate different instances of the first signature.
• Alice 401a may generate a third signature based on a third message and the salt value.
• the salt value is used as a private key for generating the third signature.
• the third message may be generated based on the first and/or second messages.
• the third message may be the same as the second message.
• Alice 401a may send the third signature to Carol 402. If Alice 401a has generated the third message, she may also send it to Carol 402. Or, Carol 402 may have sent the third message to Alice 401a in which case Alice 401a does not need to re-send it to Carol 402, although she may choose to do so.
• Alice 103a may instead prove knowledge of the random salt value using a zero-knowledge proof (ZKP).
• ZKP zero-knowledge proof
• Alice 401a may generate a hash tree, e.g. a Merkle tree, using the respective public keys corresponding to the data items, i.e. the public key generated by Alice 401a and the public key obtained from the other participants. Each of these public keys is hashed to form a respective leaf hash of the hash tree.
• Alice 401a may transmit the resulting hash root (e.g. a Merkle root) to Carol 402, or she may publish the hash root.
• Alice 401a may send a hash proof (e.g. a Merkle proof) to Carol 402 to prove that Alice's public key is an element of the hash tree.
• the first message includes the hash root and so each participant that generates a signature share attests to the same hash root. That is, they attest to the public keys that have been used to generate the hash root.
• An example hash root is shown in Figure 7.
• the first message may be a blockchain transaction.
• Alice 401a may generate a share of a signature that is used to sign some or all of a blockchain transaction, e.g. one or more inputs and/or one or more outputs of the transaction.
• the coordinator 404 may then include the first signature in an input of the transaction that she has not signed.
• the transaction may comprise an output that is locked to a different party, e.g. Bob 103b and/or Carol 402, e.g.
• the output may be a pay-to- public-key (P2PK) or pay-to-public-key-hash (P2PKH) output locked a public key owned by Bob 103b.
• the second message may comprise the transaction.
• the second message may also comprise data relating to the blockchain 150, e.g. a current block height of the blockchain at the time the transaction is generated.
• Alice 401a or the coordinator 404 may make the first message available to Carol 402 by transmitting the transaction to the blockchain 150, from which Carol 402 may then access. This is illustrated in Figure 4.
• the hash root may be included in an output of the blockchain transaction.
• FIG. 5 illustrates an example sequence of steps which may be taken by Alice 401a to generate a signature share according to some embodiments of the present invention. It will be appreciated that some of the steps may be performed in a different order.
• Alice 401a obtains a first message, e.g. a blockchain transaction.
• Alice 401a obtains an external data item, e.g. a second signature.
• Alice 401a generates an ephemeral private key share based on the external data item, e.g. based on a hash of the second signature.
• Alice 401a generates an ephemeral public key which corresponds to the shared ephemeral private key.
• step S505 Alice 401a generates a signature share and in step S506 she sends it to the coordinator 404. After the coordinator 404 has generated the signature and it is available to Carol 402, Alice 401a sends at least the external data item to Carol 402.
• Carol 402 would like Alice 401a to prove that Alice 401a generated a share of the first signature.
• Carol 402 obtains the first signature.
• Alice 401a may send the first signature to Carol 402, or the first signature may be publicly accessible, e.g. recorded on the blockchain 150.
• Carol 402 obtains the first signature by extracting it from the transaction.
• Carol 402 also obtains a candidate external data item from Alice 401a.
• “candidate” is used to refer to an external data item that Alice 401a claims to have been embedded within the first signature, i.e. in her respective signature share. If that is indeed the case, the candidate external data item is the same as the external data item discussed above. However at this point Carol 402 cannot confirm that to be the case, hence the term "candidate”.
• Carol 402 uses the candidate external data item to generate a candidate ephemeral public key. To do this, Carol obtains Alice's external data item (or the first data item, if it is generated based on more than just the external data item) and generates a corresponding public key. Carol 402 also obtains public keys corresponding to the other participants data items. Carol 402 generates the candidate ephemeral public key using the candidate and obtains public keys.
• the candidate ephemeral public key comprises a first component and a second component, e.g. an x value and a y value.
• the first signature obtained by Carol 401 comprises a first signature component and a second signature component.
• Carol 402 compares the candidate first signature component to the first component of the candidate ephemeral public key. If they match, Carol 402 can be sure that Alice 401a did indeed generate a share of the first signature. That is, in order for the first component of the candidate ephemeral public key (which comprises an x-component equivalent to a candidate first signature component) and the first signature component to be a match, the candidate external data item must be the external data item used to generate Alice's signature share. Since Alice 401a provided Carol 402 with the candidate external data item, this proves that Alice 401a generated a share of the signature. This process is illustrated in steps S601 to S605 of Figure 6.
• Carol 402 may also verify that the first signature is a valid signature when validated against the corresponding public key. If the first signature is used to sign a blockchain transaction and that transaction has been recorded on the blockchain, Carol 401 may assume that the first signature is a valid signature (i.e. the transaction would not have been accepted by a blockchain node if the signature was not valid). However Carol 401 may still verify that the unlocking script that is being spent contains a signature check (i.e. to make sure that a blockchain node has performed a signature check on the signature during transaction validation). To do this, Carol 401 may check that the unlocking script of the spent transaction includes an OP_CHECKSIG script.
• the external data item may itself by a signature, i.e. a second signature.
• Carol 402 may obtain a second message, e.g. from Alice 401a, and verify that the second signature is a valid signature when verified using a public key provided by or otherwise linked to Alice 401a, e.g. a certified public key.
• Alice 401a may provide Carol 402 with a public key corresponding to the salt value.
• Carol 402 may then generate the candidate first signature component based on the "salt public key", e.g. based on a combination of the candidate ephemeral public key share and the salt public key. The x-value of said combination may be used to generate the candidate first signature component.
• Alice 401a may also provide Carol 402 with a third signature and a third message.
• Carol 402 may verify that the third signature is a valid signature when verified using the salt public key.
• Alice 401a may provide Carol 402 with a ZKP which Carol 402 may use to verify that Alice 401a knows the salt value.
• a group of N participants A 1 , ... , A N agree to form a threshold signature group.
• JVRSS-A modified JVRSS
• the public key PK Ai may be a certified public key, or derived from a certified public key.
• the group agree on an attest message M attest ("second message") which is public and will be used for attestation at a later point in time.
• second message an attest message
• Each group member 401 signs the attest message to generate a "second signature" (i.e. the external data item):
• the signature and hashed data will be used in both the threshold secret sharing and attest algorithm.
• a shared secret between N participants can be generated using a secret sharing scheme, e.g. the JVRSS method described above.
• the algorithm is modified by prescribing the zeroth-order (y-intercept).
• Step 1) each participant 401 computes the zeroth-order of their private polynomials (instead of choosing the value at random):
• the inverse of a shared secret between N participants can be calculated using the INVSS method described above.
• INVSS can be used to generate an N group ephemeral key and 2t + 1 inverse shares.
• INVSS is modified to incorporate ID embedding. This is simply so that to generate the shared ephemeral private key k (or rather, shares of the shared ephemeral private key, since the full private key itself is not actually generated), the participants 401 use the JVRSS-A method instead of the usual JVRSS.
• the participants also create a Merkle tree using the public key corresponding to the zeroth order of the polynomial. The participants take the following steps.
• the participants 401 can then confirm that everyone has the same Merkle root by broadcasting this value to all participants 401. This Merkle root can then be included in the message that is signed using the corresponding ephemeral key.
• N independent participants A 1 , ... ,A N agree to participate in a threshold secret sharing group. They also agree to use a trustless setup that enables future attestation.
• the participants use the attest message setup for the group of N particpants and also generate the attest message dependent group ephemeral key r (based on the sum of r i0 ). Note if the group want the attest message to be a transaction that is being signed, this step needs to be completed during the creation of the signature, once the message is known.
• the public key is calculated by adding the obfuscated zeroth-order values of the private polynomials
• Each participant 401 computes signature shares mod n, where (the inverse of the respective ephemeral private key share) and r (the public key corresponding to the shared ephemeral private key) are derived using the method described above.
• first signature [r, s] and the transaction can be signed (see table below for the complete transaction).
• M attest which may be provided or publicly known
• a participant 401 can prove that they are a member of a threshold group.
• the verifier 402 knows the number of participants N and Tx threshotd with first signature [r, s] .
• the threshold signer proof may be vulnerable to spoofing unless the Merkle proof is provided. If the Merkle proof is not included as part of the attestation, and if the attest message is publicly known a non-group member can reverse engineer the proof data.
• Eve can use the calculated data to pretend she was a participant in a group signing event. No secret information from the actual group signers will be leaked, but a third party can pretend that they participated in a group signing event.
• the blockchain network 106 is the bitcoin network and bitcoin nodes 104 perform at least all of the described functions of creating, publishing, propagating and storing blocks 151 of the blockchain 150. It is not excluded that there may be other network entities (or network elements) that only perform one or some but not all of these functions. That is, a network entity may perform the function of propagating and/or storing blocks without creating and publishing blocks (recall that these entities are not considered nodes of the preferred Bitcoin network 106).
• any reference to the term "bitcoin node” 104 above may be replaced with the term “network entity” or “network element”, wherein such an entity/element is configured to perform some or all of the roles of creating, publishing, propagating and storing blocks.
• the functions of such a network entity/element may be implemented in hardware in the same way described above with reference to a blockchain node 104. It will be appreciated that the above embodiments have been described by way of example only. More generally there may be provided a method, apparatus or program in accordance with any one or more of the following Statements.
• a computer-implemented method of generating a share of a digital signature wherein each participant of a group of participants has a respective share of a first shared private key, and wherein the method is performed by a first participant of the group and comprises: obtaining a first message; generating a first data item based on at least a hash of a first external data item; generating a first ephemeral private key share of an ephemeral private key, wherein the first ephemeral private key share is generated based on the first data item and a respective data item generated by each other participant; generating an ephemeral public key corresponding to the ephemeral private key; generating a first signature share based on the first message, the first ephemeral private key share, a first share of the first shared private key, and the ephemeral public key; and making the first signature share available to a coordinator for generating a first signature based on at least a threshold number of respective signature shares
• the external data item may comprise an identifier of the first party, e.g. a name, address, phone number, national insurance number, passport number, public key, etc.
• the first signature is an ECDSA signature.
• the "ephemeral public key” is used as shorthand for "x-component of the ephemeral public key”.
• each other participant Preferably each other participant generates their respective ephemeral public key shares in the same way and based on a respective external data item.
• Statement 2 The method of statement 1, wherein the generating of the first ephemeral private key share comprise performing a secret sharing scheme with each of the other participants.
• Statement 3 The method of statement 2, wherein the secret sharing scheme is a joint verifiable secret sharing (JVRSS) scheme.
• JVRSS joint verifiable secret sharing
• Statement 4 The method of statement 3, wherein the first data item is a zeroth-order coefficient of a first polynomial, and wherein the JVRSS scheme comprises: transmitting a respective instance of the first polynomial to each of the other participants, wherein the respective instance of the first polynomial is generated based on a respective index of the respective participant; and obtaining a respective polynomial from each other participant, wherein the respective polynomial is generated based on a respective index of the first participant and the respective data item generated by that other participant.
• Statement 6 The method of statement 5, comprising making the first external data item and the obtained respective public keys corresponding to the respective data items available to a verifying party for proving that the first participant generated the first signature.
• Statement 7. The method of any preceding statement, wherein obtaining the first message comprises generating the first message, and wherein the method comprising making the first message available to the verifying party.
• Statement 8 The method of any preceding statement, comprising: obtaining a second message; and generating a second signature based on at least the second message and a main private key of the first participant, and wherein the external data item comprises the second signature.
• Statement 9 The method of statement 8, wherein each participant generates their respective external data item based on the same second message.
• Statement 10 The method of statement 8 or statement 9, wherein the main private key of the first participant corresponds to a main public key linked to an identity of the first participant.
• Statement 11 The method of any preceding statement, wherein the first share of the first shared private key is generated using a secret sharing scheme.
• Statement 12 The method of any preceding statement, wherein the first participant is the coordinator, and wherein the method comprises: receiving at least the threshold number of respective signature shares; and generating the first signature comprising first and second signature components, wherein the first signature component is generated based on the ephemeral public key, and wherein the second signature component is generated based on at least the threshold number of respective signature shares.
• Statement 13 The method of any preceding statement, wherein the first data item is generated based on a random salt value.
• Statement 14 The method of statement 13, wherein the method comprises providing the verifying party with a zero-knowledge proof for proving knowledge of the random salt value.
• Statement 15 The method of statement 13 or statement 14, wherein the random salt value is a private key, and wherein the method comprises: obtaining a third message; generating a third signature based on at least the random salt value and the third message; and making the third signature, the third message and a public key corresponding to the random salt value available to the verifying party for proving that the third signature is a valid signature for the third message when verified using the public key corresponding to the random salt value.
• the third message may be the same as the second message.
• Statement 17 The method of any preceding statement, comprising: generating a root hash of a hash tree, wherein each respective public key corresponding to the respective data item is hashed to generate a respective leaf hash of the hash tree; and transmitting the root of the hash tree to one or more of the participants and/or the verifying party.
• Statement 18 The method of statement 15, comprising transmitting a hash proof to the verifying party for verifying that the first public key corresponding to the first data item is an element of the hash tree.
• the hash tree is a Merkle tree
• the hash root is a Merkle root
• the hash proof is a Merkle proof.
• Statement 19 The method of any preceding statement, wherein the first message comprises at least part of a blockchain transaction.
• the first signature may be used to sign the blockchain transaction.
• Statement 20 The method of statement 18 and statement 19, wherein the blockchain transaction comprises the hash root.
• Statement 21 The method of statement 19 or statement 20, wherein the blockchain transaction comprises the first signature.
• Statement 22 The method of any of statements 19 to 21, wherein making the first message available to the verifying party comprises transmitting the blockchain transaction to the blockchain network.
• Statement 23 The method of any preceding statement, wherein the hash of the external data item is a double-hash of the external data item.
• Statement 25 The method of statement 24, wherein the first signature signs a first message, and wherein the method comprises: obtaining a shared public key corresponding to a shared private key used to generate the first signature; and verifying that the first signature is a valid signature for the first message when verified using the first public key.
• Statement 26 The method of statement 24 or statement 25, wherein the candidate external data item is a second signature.
• Statement 27 The method of any of statements 24 to 26, wherein the second signature signs a second message, and wherein the method comprises: obtaining a second public key corresponding to a private key used to generate the second signature; and verifying that the second signature is a valid signature for the second message when verified using the second public key.
• Statement 28 The method of any of statements 24 or statement 27, wherein the candidate public key is generated based on a random salt value, and wherein the method comprises: receiving a zero-knowledge proof for proving knowledge of the random salt value; and verifying that the first participant has knowledge of the random salt value.
• Statement 29 The method of any of statements 24 to 28, wherein the candidate public key is generated based on a random salt value, and wherein the method comprises: obtaining a third message; obtaining a third signature; and verifying that the third signature is a valid signature for the third message when verified using a public key corresponding to the random salt value.
• Statement 31 The method of any of statements 24 to 30, wherein the first signature is received from the first party.
• Statement 32 The method of any of statements 24 to 31, wherein the first message is received from the first participant.
• Statement 33 The method of any of statements 24 to 31, wherein the first message is generated by the verifying party.
• Statement 34 The method of any of statements 24 to 33, wherein the first message comprises at least part of a blockchain transaction.
• Statement 36 The method of statement 35, wherein obtaining the first signature comprises extracting the first signature from the blockchain transaction.
• Statement 37 The method of any of statements 33 to 36, wherein an input of the blockchain transaction comprises the first signature, and wherein the method comprises: verifying that an output of a previous blockchain transaction referenced by the input of the blockchain transaction comprises a signature verification script.
• Statement 38. Computer equipment comprising: memory comprising one or more memory units; and processing apparatus comprising one or more processing units, wherein the memory stores code arranged to run on the processing apparatus, the code being configured so as when on the processing apparatus to perform the method of any of statements 1 to 37.
• Statement 39 A computer program embodied on computer-readable storage and configured so as, when run on one or more processors, to perform the method of any of statements 1 to 37.
• a method comprising the actions of the first participant and the verifying party.
• a system comprising the computer equipment of the first participant and the verifying party.

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