Key exchange system, communication apparatus, key exchange method and program

A communication apparatus for generating a shared key for executing encrypted communication with another communication apparatus according to an authenticated key exchange protocol using ID-based encryption, the communication apparatus comprising:

• a memory;
• and
• a processor configured to execute operations comprising:
• generating a short-term private key by using a first element on coset modulo a prime number from a private key of the communication apparatus;
• generating a short-term public key of the communication apparatus by using a second element on coset modulo the prime number from the short-term private key;
• generating private information associated with the communication apparatus by using a third element on coset modulo the prime number from the short-term private key, a short-term public key generated by said another communication apparatus, public information associated with the communication apparatus and said another communication apparatus;
• and
• generating the shared key for executing encrypted communication with said another communication apparatus by executing a pairing operation, wherein the pairing operation comprises computing on an elliptic curve using the private key of the communication apparatus and the private information associated with the communication apparatus.

A method for generating a shared key for executing encrypted communication between a communication apparatus and another communication apparatus from among a plurality of communication apparatuses according to an authenticated key exchange protocol using ID-based encryption, the method comprising:

• generating a short-term private key by using a first element on coset modulo a prime number from a private key of the communication apparatus;
• generating a short-term public key of the communication apparatus by using a second element on coset modulo the prime number from the short-term private key;
• generating private information associated with the communication apparatus by using a third element on coset modulo the prime number from the short-term private key, a short-term public key generated by said another communication apparatus, public information associated with the communication apparatus and said another communication apparatus;
• and
• generating the shared key for executing encrypted communication with said another communication apparatus by executing a pairing operation, wherein the pairing operation comprises computing on an elliptic curve using the private key of the communication apparatus and the private information associated with the communication apparatus.