Key exchange system, method and program for generating a shared key for secure communication

A communication device for generating a shared key for performing encrypted communication with another communication device by an authenticated key exchange protocol using an ID based encryption, the communication device comprising:

• a memory;
• and
• a processor configured to:
• generate a short term private key by using a private key of the communication device;
• generate a short term public key of the communication device using the short term private key and a pairing group G1 being one of asymmetric pairing groups G1 and G2 used for the ID based encryption;
• and
• generate a shared key for performing encrypted communication with the other communication device by performing a first pairing operation using the private key of the communication device and a short term public key generated in the other communication device, and performing a second pairing operation using the short term private key of the communication device and public information used in generating a private key of the other communication device,
• wherein the private key of the communication device is generated using the pairing group G2 being another one of the asymmetric pairing groups G1 and G2, and
• wherein the processor is further configured to:
• randomly select an element of a residue class Zq with q as a prime number to generate the short term private key using a predetermined function having, as an input, a string obtained by coupling strings representing the selected element and the private key of the communication device;
• generate the short term public key by computing the short term private key and the pairing group G1;
• and
• generate the shared key by using a computation result of the first pairing operation, a computation result of the second pairing operation, a result of computing the short term private key and the short term public key generated in the other communication device, and a shared session ID between the communication device and the other communication device.

A key exchange method for generating a shared key for performing encrypted communication between a plurality of communication devices by an authenticated key exchange protocol using an ID based encryption, the key exchange method comprising, performed by each of the plurality of communication devices:

• generating a short term private key by using a private key of a communication device;
• generating a short term public key of the communication device using the short term private key and a pairing group G1 being one of asymmetric pairing groups G1 and G2 used for the ID based encryption;
• and
• generating a shared key for performing encrypted communication with another communication device by performing a first pairing operation using the private key of the communication device and a short term public key generated in the other communication device, and performing a second pairing operation using the short term private key of the communication device and public information used in generating a private key of the other communication device,
• wherein the private key of the communication device is generated using the pairing group G2 being another one of the asymmetric pairing groups G1 and G2, and
• wherein the method is further configured to:
• randomly select an element of a residue class Zq with q as a prime number to generate the short term private key using a predetermined function having, as an input, a string obtained by coupling strings representing the selected element and the private key of the communication device;
• generate the short term public key by computing the short term private key and the pairing group G1;
• and
• generate the shared key by using a computation result of the first pairing operation, a computation result of the second pairing operation, a result of computing the short term private key and the short term public key generated in the other communication device, and a shared session ID between the communication device and the other communication device.