Digital signature system, and method

A digital signature method comprising:

• by a first apparatus:
• acquiring and storing in a storage:
• a first helper key generated using first secret information corresponding to a verification key and first biometric information;
• helper data generated using second secret information for distributed signature generation and the first biometric information;
• and
• third secret information for distributed signature generation;
• generating a second distributed key;
• and
• generating a second distributed signature for the message to be signed by using the second distributed key and the third secret information, and sending/receiving information with a second apparatus,
• the method comprising:
• by the second apparatus:
• acquiring second biometric information;
• acquiring the helper data;
• restoring the second secret information using the second biometric information and the helper data;
• generating a first distributed key;
• and
• generating a first distributed signature for the message, by using the first distributed key and the second secret information and sending/receiving information with the first apparatus,
• the method further comprising
• by one of the first apparatus or the second apparatus,
• generating a signature for the message using:
• one of the first distributed signature or the second distributed signature generated by the one of the first apparatus or the second apparatus;
• and
• other of the first distributed signature or the second distributed signature generated by other of the first apparatus or the second apparatus.

A non-transitory storage medium storing a program causing a first processing apparatus to execute processing including:

• acquiring and storing in a storage:
• a first helper key generated using first secret information corresponding to a verification key and first biometric information;
• helper data generated using second secret information for distributed signature generation and the first biometric information;
• and
• third secret information for distributed signature generation;
• generating a second distributed key;
• and
• generating a second distributed signature for the message to be signed by using the second distributed key and the third secret information, and sending/receiving information with a second processing apparatus,
• wherein the non-transitory storage medium stores a program causing a second processing apparatus to execute processing including:
• acquiring second biometric information;
• acquiring the helper data;
• restoring the second secret information using the second biometric information and the helper data;
• generating the first distributed key;
• and
• generating the first distributed signature for the message by using the first distributed key and the second secret information and sending/receiving information with the first processing apparatus,
• wherein the non-transitory storage medium stores the program causing one of the first processing apparatus or the second processing apparatus to execute processing including
• generating a signature for the message using:
• one of the first distributed signature or the second distributed signature generated by the one of the first processing apparatus or the second processing apparatus;
• and
• other of the first distributed signature or the second distributed signature generated by other of the first processing apparatus and the second processing apparatus.