Granted Patent B2

US 12,476,826 · App. 18/682,085 · Granted Nov 18, 2025

Inventor: Michaella Pettit (London, GB)

Assignee: nChain Licensing AG

H04L9/3255

Abstract

Claims (29)

1 . A computer-implemented method, performed by a first participant of a group of a participants, of proving that a target sub-group of the group generated a digital signature, wherein the signature can only be generated based on at least a threshold number of respective signature shares, wherein each participant of the group has a respective private key share of a shared private key, wherein the group is divisible into a plurality of unique sub-groups where each sub-group comprises at least the threshold number of participants, and wherein the method comprises:

for each respective sub-group to which the first participant belongs, generating a respective first ephemeral private key share of a respective shared ephemeral private key, wherein each other participant of each respective sub-group generates a respective ephemeral private key share of the respective shared ephemeral private key;

for each respective shared ephemeral private key, generating a respective shared ephemeral public key;

generating a first signature share of the signature, wherein the first signature share is generated based on a first private key share of the shared private key, the first ephemeral private key share of a target one of the respective shared ephemeral private keys, and a message; and

making the first signature share available to a coordinator for generating the signature based on at least the threshold number of respective signature shares, wherein each respective signature share is based on respective private key share of the shared private key and a respective ephemeral private key share of the target one of the respective shared ephemeral private keys, and wherein the signature comprises a component based on the respective shared ephemeral public key corresponding to the target one of the respective shared ephemeral private keys.

2 . The method of claim 1 , wherein the first participant is the coordinator, and wherein the method comprises:

obtaining at least the threshold number of respective signature shares; and

generating the signature based on at least the threshold number of respective signature shares.

3 . The method of claim 1 , comprising:

making available, to a verifying party, a list of respective participants belonging to the sub-group associated with the respective shared ephemeral public key corresponding to the target one of the respective shared ephemeral private keys.

4 . The method of claim 3 , comprising sending the message to the verifying party.

5 . The method of claim 1 , wherein the message comprises at least part of a blockchain transaction.

6 . The method of claim 2 , wherein the message comprises at least part of a blockchain transaction, and wherein the method comprises submitting the blockchain transaction to one or more nodes of a blockchain network.

7 . The method of claim 1 , wherein the message comprises a digital certificate.

8 . The method of claim 1 , wherein each respective first ephemeral private key share is generated using a joint verifiable secret sharing scheme.

9 . The method of claim 1 , wherein each respective first ephemeral private key share is generated using Shamir's secret sharing scheme.

10 . The method of claim 1 , wherein the group is divided into all possible unique sub-groups.

11 . 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 run on the processing apparatus, the processing apparatus performs a method, performed by a first participant of a group of a participants, of proving that a target sub-group of the group generated a digital signature, wherein the signature can only be generated based on at least a threshold number of respective signature shares, wherein each participant of the group has a respective private key share of a shared private key, wherein the group is divisible into a plurality of unique sub-groups where each sub-group comprises at least the threshold number of participants, and wherein the method comprises:

for each respective sub-group to which the first participant belongs, generating a respective first ephemeral private key share of a respective shared ephemeral private key, wherein each other participant of each respective sub-group generates a respective ephemeral private key share of the respective shared ephemeral private key;

for each respective shared ephemeral private key, generating a respective shared ephemeral public key;

generating a first signature share of the signature, wherein the first signature share is generated based on a first private key share of the shared private key, the first ephemeral private key share of a target one of the respective shared ephemeral private keys, and a message; and

making the first signature share available to a coordinator for generating the signature based on at least the threshold number of respective signature shares, wherein each respective signature share is based on respective private key share of the shared private key and a respective ephemeral private key share of the target one of the respective shared ephemeral private keys, and wherein the signature comprises a component based on the respective shared ephemeral public key corresponding to the target one of the respective shared ephemeral private keys.

12 . A computer program embodied on non-transitory computer-readable storage media and configured so as, when run on computer equipment, the computer equipment performs a method, performed by a first participant of a group of a participants, of proving that a target sub-group of the group generated a digital signature, wherein the signature can only be generated based on at least a threshold number of respective signature shares, wherein each participant of the group has a respective private key share of a shared private key, wherein the group is divisible into a plurality of unique sub-groups where each sub-group comprises at least the threshold number of participants, and wherein the method comprises:

for each respective sub-group to which the first participant belongs, generating a respective first ephemeral private key share of a respective shared ephemeral private key, wherein each other participant of each respective sub-group generates a respective ephemeral private key share of the respective shared ephemeral private key;

for each respective shared ephemeral private key, generating a respective shared ephemeral public key;

generating a first signature share of the signature, wherein the first signature share is generated based on a first private key share of the shared private key, the first ephemeral private key share of a target one of the respective shared ephemeral private keys, and a message; and

making the first signature share available to a coordinator for generating the signature based on at least the threshold number of respective signature shares, wherein each respective signature share is based on respective private key share of the shared private key and a respective ephemeral private key share of the target one of the respective shared ephemeral private keys, and wherein the signature comprises a component based on the respective shared ephemeral public key corresponding to the target one of the respective shared ephemeral private keys the method of claims 1 to 10 .

Priority Claims (1)

Continuity (1)

References Cited (118)