Digital signatures

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 of generating 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, wherein each participant has a respective ephemeral private key share, the method being performed by a coordinator and comprising:
• obtaining at least a threshold number of respective message-independent components, wherein each respective message-independent component is generated based on a respective private key share;
• obtaining at least the threshold number of respective signature shares, wherein each respective signature share is based on at least a respective message-dependent component, and wherein each respective message-dependent component is generated based on the message;
• and
• generating the signature of the message based on each of the obtained signature shares and each of the obtained message-independent components, wherein each message-independent component and/or message-dependent component is based on a respective ephemeral private key share.

A computer program embodied on computer-readable storage and configured so as, when run on computer equipment, to perform a method of generating 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, wherein each participant has a respective ephemeral private key share, the method being performed by a coordinator and comprising:

• obtaining at least a threshold number of respective message-independent components, wherein each respective message-independent component is generated based on a respective private key share;
• obtaining at least the threshold number of respective signature shares, wherein each respective signature share is based on at least a respective message-dependent component, and wherein each respective message-dependent component is generated based on the message;
• and
• generating the signature of the message based on each of the obtained signature shares and each of the obtained message-independent components, wherein each message-independent component and/or message-dependent component is based on a respective ephemeral private key share.