AUTHENTICATION KEY EXCHANGE SYSTEM, EQUIPMENT, SERVER, METHOD, AND PROGRAM

1 . An authentication key exchange system comprising:

a key generation device; and

a plurality of equipment,

wherein the key generation device includes:

a first processor; and

a first memory storing program instructions that cause the first processor to:

receive a security parameter λ and a total number N of the equipment as inputs, and output a master private key MSK, a master public key MPK, and an initial revoked user list RL;

receive the master private key MSK, the master public key MPK, and an identifier ID of the equipment as inputs, and output a static private key ssk ID corresponding to the identifier ID;

receive the master public key MPK and a new revoked user list RL as inputs, increment a current time T, and update a revoked user list RL T at the current time T to the revoked user list RL; and

receive the master private key MSK, the master public key MPK, the current time T, and the revoked user list RL as inputs, and output key update information ku T at the current time T by using a KUNode algorithm, and

wherein the equipment includes:

a second processor; and

a second memory storing program instructions that cause the second processor to:

receive the master public key MPK, the static private key ssk ID corresponding to its own identifier ID, and the key update information ku T at the current time T as inputs, and output a latest private key csk ID,T at the current time T without using pairing calculation;

receive the master public key MPK and the latest private key csk ID,T corresponding to its own identifier ID at the current time T as inputs, and output a temporary private key esk ID and a temporary public key epk ID ; and

receive the master public key MPK, its own identifier ID, an identifier ID′ of a communication partner, the latest private key csk ID,T corresponding to its own identifier ID at the current time T, the temporary private key esk ID corresponding to its own identifier ID, and a temporary public key epk ID′ corresponding to the identifier ID′ of the communication partner as inputs, and output a session key SK shared with the communication partner.

2 . The authentication key exchange system as claimed in claim 1 , wherein the program instructions cause the second processor to receive the master public key MPK, the static private key ssk ID , and the key update information ku T as the inputs, and output the latest private key csk ID,T by using a Schnorr signature.

3 . The authentication key exchange system as claimed in claim 2 , wherein the program instructions cause the second processor to output the latest private key csk ID,T by providing a signature to a hash value of information including the identifier ID and the current time T by using the Schnorr signature that uses, as a signature key, a sum or a linear combination of a value s ID included in the static private key ssk ID and a value s T∥θ corresponding to a value θ uniquely determined based on its own identifier ID among a plurality of values s T∥θ included in the key update information ku T .

4 . Equipment sharing a session key with another equipment that is a communication partner, the equipment comprising:

a processor; and

a memory storing program instructions that cause the processor to:

receive a master public key MPK, a static private key ssk ID corresponding to its own identifier ID, and key update information ku T at a current time T as inputs, and output a latest private key csk ID,T at the current time T without using pairing calculation;

receive the master public key MPK and the latest private key csk ID,T corresponding to its own identifier ID at the current time T as inputs, and output a temporary private key esk ID and a temporary public key epk ID ; and

receive the master public key MPK, its own identifier ID, an identifier ID′ of the communication partner, the latest private key csk ID,T corresponding to its own identifier ID at the current time T, the temporary private key esk ID corresponding to its own identifier ID, and a temporary public key epk ID′ corresponding to the identifier ID′ of the communication partner as inputs, and output a session key SK shared with the communication partner.

5 . A server that functions as a key generation device, comprising:

a processor; and

a memory storing program instructions that cause the processor to:

receive a security parameter 1 λ and a total number N of equipment as inputs, and output a master private key MSK, a master public key MPK, and an initial revoked user list RL;

receive the master private key MSK, the master public key MPK, and an identifier ID of the equipment as inputs, and output a static private key ssk ID corresponding to the identifier ID;

receive the master public key MPK and a new revoked user list RL as inputs, increment a current time T, and update a revoked user list RL T at the current time T to the revoked user list RL; and

receive the master private key MSK, the master public key MPK, the current time T, and the revoked user list RL as inputs, and output key update information ku T at the current time T by using a KUNode algorithm.

6 . An authentication key exchange method used by an authentication key exchange system including a key generation device and a plurality of equipment, the authentication key exchange method comprising:

receiving, by the key generation device, a security parameter 1 λ and a total number N of the equipment as inputs, and outputting a master private key MSK, a master public key MPK, and an initial revoked user list RL;

receiving, by the key generation device, the master private key MSK, the master public key MPK, and an identifier ID of the equipment as inputs, and outputting a static private key ssk ID corresponding to the identifier ID;

receiving, by the key generation device, the master public key MPK and a new revoked user list RL as inputs, increment a current time T, and updating a revoked user list RL T at the current time T to the revoked user list RL; and

receiving, by the key generation device, the master private key MSK, the master public key MPK, the current time T, and the revoked user list RL as inputs, and outputting key update information ku T at the current time T by using a KUNode algorithm,

receiving, by the equipment, the master public key MPK, the static private key ssk ID corresponding to its own identifier ID, and the key update information ku T at the current time T as inputs, and outputting a latest private key csk ID,T at the current time T without using pairing calculation;

receiving, by the equipment, the master public key MPK and the latest private key csk ID,T corresponding to its own identifier ID at the current time T as inputs, and outputting a temporary private key esk ID and a temporary public key epk ID ; and

receiving, by the equipment, the master public key MPK, its own identifier ID, an identifier ID′ of a communication partner, the latest private key csk ID,T corresponding to its own identifier ID at the current time T, the temporary private key esk ID corresponding to its own identifier ID, and a temporary public key epk ID′ corresponding to the identifier ID′ of the communication partner as inputs, and outputting a session key SK shared with the communication partner.

7 . A non-transitory computer-readable recording medium having stored therein a program for causing a computer to perform the authentication key exchange method as claimed in claim 6 .