Digital signatures
A computer-implemented method of generating a share of a digital signature of a message, wherein a threshold number of different signature shares from respective participants of a group of participants are required to generate the digital signature, wherein each participant has a respective private key share, the method being performed by a first one of the participants and comprising: generating a first message-independent component and a first message-dependent component, wherein the message-independent component is generated based on a first private key share and wherein the message-dependent component is generated based on the message; causing the first message-independent component to be made available to a coordinator; and causing a first signature share to be made available to the coordinator for generating the signature based on at least the threshold number of signature shares, wherein the first signature share comprises at least the message-dependent component.
1 . A method of jointly generating a digital signature by distributed nodes in a computing network, the computing network including a set of at least 2t+1 nodes including a first node and a coordinating node, wherein the digital signature is generated by the coordinating node through joint participation of at least t+1 of the nodes in the set, where t>1, the method including a signature phase that comprises:
receiving, by the first node, a request for a signature share from the coordinating node;
calculating, by the first node, the signature share, wherein the first node does not receive communications relating to generation of the digital signature from any other nodes of the set during the signature phase except for the coordinating node; and
transmitting, by the first node, the signature share to the coordinating node to enable the coordinating node to generate the digital signature through interpolation of respective signature shares received from the at least t nodes, but fewer than 2t nodes, of the nodes in the set.
2 . The method claimed in claim 1 , wherein the first node does not receive a communication relating to generation of the digital signature from the coordinating node other than the request during the signature phase.
3 . The method claimed in claim 2 , wherein the first node does not receive any communication from the coordinating node during the signature phase other than the request.
4 . The method claimed in claim 1 , wherein the signature phase starts with transmission of the request by the coordinating node.
5 . The method claimed in claim 1 , wherein the first node does not employ joint verifiable random secret sharing during the signature phase.
6 . The method claimed in claim 1 , wherein the first node does not perform a zero knowledge proof during the signature phase.
7 . The method claimed in claim 1 , wherein the first node does not use homomorphic encryption during the signature phase.
8 . The method claimed in claim 1 , wherein the calculating the signature share includes hashing a message to generate a message digest and calculating the signature share using the message digest and a pre-signature share stored at the first node.
9 . The method claimed in claim 8 , wherein the pre-signature share is an intermediary value minus a blinding secret share.
10 . The method claimed in claim 1 , further comprising a pre-signature phase prior to the signature phase, wherein the pre-signature phase includes jointly generating and verifying at least three secret shares with the at least t nodes of the set.
11 . The method claimed in claim 10 , wherein the at least three secret shares include a private key share, an ephemeral key share, and a blinding secret share.
12 . The method claimed in claim 11 , wherein jointly generating and verifying includes using joint verifiable random secret sharing.
13 . A computing device implementing a first node in a computing network for jointly generating a digital signature, the computing network including a set of at least 2t+1 nodes including the first node and a coordinating node, wherein the digital signature is generated by the coordinating node through joint participation of at least t+1 of the nodes in the set, where t>1, the computing device comprising:
one or more processing units; and
memory storing processor-executable instructions that, when executed by the one or more processing units, are to cause the one or more processing units to, during a signature phase:
receive, by the first node, a request for a signature share from the coordinating node;
calculate the signature share, wherein the first node does not receive communications relating to generation of the digital signature from any other nodes of the set during the signature phase except for the coordinating node; and
transmit the signature share to the coordinating node to enable the coordinating node to generate the digital signature through interpolation of respective signature shares received from the at least t nodes, but fewer than 2t nodes, of the nodes in the set.
14 . The computing device claimed in claim 13 , wherein the first node does not receive a communication relating to generation of the digital signature from the coordinating node other than the request during the signature phase.
15 . The computing device claimed in claim 14 , wherein the first node does not receive any communication from the coordinating node during the signature phase other than the request.
16 . The computing device claimed in claim 13 , wherein the instructions, when executed, are to cause the one or more processing units to calculate the signature share by at least hashing a message to generate a message digest and calculating the signature share using the message digest and a pre-signature share stored at the first node.
17 . The computing device claimed in claim 16 , wherein the pre-signature share is an intermediary value minus a blinding secret share.
18 . A computer-readable storage medium having stored thereon processor-executable instructions for jointly generating a digital signature by distributed nodes in a computing network, the computing network including a set of at least 2t+1 nodes including a first node and a coordinating node, wherein the digital signature is generated by the coordinating node through joint participation of at least t+1 of the nodes in the set, where t>1, and wherein the instructions, when executed by one or more processors, are to cause the one or more processors to, during a signature phase:
receive, by the first node, a request for a signature share from the coordinating node;
calculate the signature share, wherein the first node does not receive communications relating to generation of the digital signature from any other nodes of the set during the signature phase except for the coordinating node; and
transmit the signature share to the coordinating node to enable the coordinating node to generate the digital signature through interpolation of respective signature shares received from the at least t nodes, but fewer than 2t nodes, of the nodes in the set.