Lightweight distributed signature protocol for mobile computing and IoT devices

A system comprising a processor, memory accessible by the processor, and computer program instructions stored in the memory and executable by the processor to perform:

• generating, at a key generation center, a first partial private cryptographic key for a user ID and a second partial private cryptographic key for the user ID;
• transmitting the first partial private cryptographic key to a first other device;
• transmitting the second partial private cryptographic key to a second other device;
• and
• generating a distributed cryptographic signature for a message using the first partial private cryptographic key and the second partial private cryptographic key
• wherein, when the first partial private cryptographic key and the second partial private cryptographic key are combined, a valid private cryptographic key is formed;
• and
• wherein generating the distributed cryptographic signature for the message comprises:
• transmitting a request for a cryptographic signature from the first other device to the second other device;
• generating at the second other device, in response to receiving the request from the first other device, a first plurality of intermediate values using a plurality of random numbers and the first partial private cryptographic key;
• generating at the first other device, in response to receiving the first plurality of intermediate values from the second other device, a second plurality of intermediate values using a plurality of random numbers and the message;
• generating, at the second other device, in response to receiving the second plurality of intermediate values from the first other device, a third plurality of intermediate values using the second partial private cryptographic key;
• and
• generating, at the first other device, in response to receiving the third plurality of intermediate values from the second other device, the distributed cryptographic signature using the first partial private cryptographic key.

A computer program product for cryptography, the computer program product comprising a non-transitory computer readable storage having program instructions embodied therewith, the program instructions executable by a computer, to cause the computer to perform a method comprising:

• generating, at a key generation center, a first partial private cryptographic key for a user ID and a second partial private cryptographic key for the user ID;
• transmitting the first partial private cryptographic key to a first other device;
• transmitting the second partial private cryptographic key to a second other device;
• and
• generating a distributed cryptographic signature for a message using the first partial private cryptographic key and the second partial private cryptographic key
• wherein, when the first partial private cryptographic key and the second partial private cryptographic key are combined, a valid private cryptographic key is formed;
• and
• wherein generating the distributed cryptographic signature for the message comprises:
• transmitting a request for a cryptographic signature from the first other device to the second other device;
• generating at the second other device, in response to receiving the request from the first other device, a first plurality of intermediate values using a plurality of random numbers and the first partial private cryptographic key;
• generating at the first other device, in response to receiving the first plurality of intermediate values from the second other device, a second plurality of intermediate values using a plurality of random numbers and the message;
• generating, at the second other device, in response to receiving the second plurality of intermediate values from the first other device, a third plurality of intermediate values using the second partial private cryptographic key;
• and
• generating, at the first other device, in response to receiving the third plurality of intermediate values from the second other device, the distributed cryptographic signature using the first partial private cryptographic key.