# US 11,909,867 B2 · Key exchange system, method and program for generating a shared key for secure communication

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- Number: US 11,909,867 B2
- Document ID: US11909867B2
- Status: Granted
- Kind: B2
- Application number: 17/607,776
- Filed: 2019-05-29
- Published: 2022-07-14
- Granted: 2024-02-20
- Earliest claimed: 2019-05-29
- Assignees: Nippon Telegraph and Telephone Corporation
- Applicants: Nippon Telegraph and Telephone Corporation
- Inventors: Junichi Tomida; Fumitaka Hoshino; Akira Nagai
- Web page: https://patentgrep.com/patent/US11909867B2

## CPC

- H04L 9/0825: {using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates}
- H04L 9/0847: {involving identity based encryption [IBE] schemes}
- H04L 9/0827: {involving distinctive intermediate devices or communication paths (network architectures or network communication protocols using different networks H04L63/18)}
- H04L 9/3073: {involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

A key exchange system, for generating a shared key for performing encrypted communication between multiple communication devices, includes the multiple communication devices. Each of the multiple communication devices includes a memory, and a processor configured to generate a short term private key by using a private key, generate a short term public key on one of asymmetric pairing groups used for the ID based encryption, by using the short term private key, and generate a shared key for performing encrypted communication with another communication device by performing a first pairing operation using a private key generated on another one of the asymmetric pairing groups 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.

## Claims

### Claim 1

A key exchange system 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 system comprising:
the plurality of communication devices,
wherein each of the plurality of communication devices includes:
a memory, and
a processor configured to:
generate a short term private key by using a private key of a 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 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 pair 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 string 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.

### Claim 2

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.

### Claim 3

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.