Information processing method and information processing system

1. A method for an information processing system including a first device, the first device including a processor and a memory, the method comprising:

the memory storing a plurality of second encrypted feature values generated by encrypting each of a plurality of reference feature values calculated from a plurality of pieces of privacy data acquired in advance by using inner product encryption, each of the plurality of reference feature values being represented as an n-dimensional vector, and n being an integer equal to or larger than 1;

the processor receiving, from a second device connected to the first device, a query including a first encrypted feature value provided with confidential information unique to a user, the first encrypted feature value being generated by encrypting a first feature value calculated from privacy data of the user by using inner product encryption and the first feature value being represented as an n-dimensional vector;

the processor acquiring a plurality of inner product values by computing an inner product of the first encrypted feature value and each of the plurality of second encrypted feature values;

the processor transmitting, to the second device, privacy data of the plurality of pieces of privacy data having an inner product value of the first encrypted feature value and a second encrypted feature value with an encrypted reference feature value calculated from the privacy data, the inner product value being equal to or smaller than a predetermined threshold;

the processor identifying a secret key of the user by using the confidential information included in the query when an unauthorized access to the first device is detected; and

the processor outputting identification information for identifying the secret key of the user to the second device.

2. The method according to claim 1 , wherein

the secret key of the user is a signature generation key for a group signature of a group to which the user belongs,

the confidential information includes the group signature, and

the identifying includes identifying the signature generation key from the group signature by using a tracing key of the group signature included in the confidential information included in the query.

3. The method according to claim 1 , wherein

the secret key of the user is a unique secret key as a secret key unique to the user in traitor tracing assigned to the second device,

the first encrypted feature value provided with the confidential information is encrypted by inner product encryption using the unique secret key,

the second encrypted feature value is encrypted by inner product encryption using a system secret key, and

the identifying includes

acquiring a first inner product value as an inner product value of the second encrypted feature value and the first encrypted feature value included in the query,

generating, for each of plurality of users, a verification secret key with one of elements of the system secret key corresponding to a user of the plurality of users changed to a random number,

acquiring, for each of the plurality of users, a second inner product value as an inner product value of a verification value generated by encrypting the reference feature value by inner product encryption using the verification secret key and the first encrypted feature value included in the query, and

identifying a secret key of a user from among the plurality of users, the secret key having the first inner product value and the second inner product value not matching each other.

4. The method according to claim 1 , wherein

the privacy data of the user includes vital data of the user.

5. The method according to claim 1 , wherein

the privacy data of the user includes log information indicating history of operation of a device or vehicle by the user.

6. The method according to claim 1 , wherein

the first feature value includes a component indicating an index regarding at least one of a shape, size, weight, state, and movement of an entire or part of a body of the user.

7. The method according to claim 1 , wherein

the plurality of pieces of privacy data includes vital data of a plurality of different persons.

8. An information processing system including a first device, the information processing system comprising:

a memory storing a plurality of second encrypted feature values generated by encrypting each of a plurality of reference feature values calculated from a plurality of pieces of privacy data acquired in advance by using inner product encryption, each of the plurality of reference feature values being represented as an n-dimensional vector and n being an integer equal to or larger than 1; and

a processor that, in operation, performs operations including

receiving, from a second device connected to the first device, a query including a first encrypted feature value provided with confidential information unique to a user, the first encrypted feature value being generated by encrypting a first feature value calculated from privacy data of the user by using inner product encryption and the first feature value being represented as an n-dimensional vector,

acquiring a plurality of inner product values by computing an inner product of the first encrypted feature value and each of the plurality of second encrypted feature values,

transmitting, to the second device, privacy data of the plurality of pieces of privacy data having an inner product value of the first encrypted feature value and a second encrypted feature value with an encrypted reference feature value calculated from the privacy data, the inner product value being equal to or smaller than a predetermined threshold,

identifying a secret key of the user by using the confidential information included in the query when an unauthorized access to the first device is detected, and

outputting identification information for identifying the secret key of the user to the second device.