System and method for generating scalable group key based on homomorphic encryption with trust server

1. An operating method of a communication system, comprising:

sharing, by a plurality of electronic devices for forming a group, a homomorphic encryption (HE) key;

generating, by a server, a Boolean circuit for performing an operation based on input values corresponding to a number of the electronic devices;

transmitting, by each of the electronic devices, an encrypted session ephemeral key to the server through HE;

calculating, by the server, an HE-evaluated value by applying the encrypted session ephemeral keys as the input values of the Boolean circuit;

transmitting, by the server, the HE-evaluated value and a given random number to each of the electronic devices; and

generating, by each of the electronic devices, a common session key for the group based on the HE key, the HE-evaluated value and the given random number through homomorphic decryption,

wherein the HE key comprises at least any one of a homomorphic secret key or a homomorphic public key, and

wherein the encrypted session ephemeral key is generated from the homomorphic public key and the session ephemeral key of each of the electronic devices through the HE.

2. The operating method of claim 1 , wherein the generating of the session key comprises:

obtaining a homomorphic decryption value from the homomorphic secret key and the HE-evaluated value through the homomorphic decryption; and

obtaining the session key by adding the homomorphic decryption value and the given random number.

3. The operating method of claim 2 , wherein the transmitting of the HE-evaluated value and the given random number comprises:

generating an encryption message, comprising the HE-evaluated value and the encrypted random number, by encrypting the given random number using a communication secret key; and

transmitting the encryption message to each of the electronic devices.

4. The operating method of claim 3 , wherein the generating of the session key further comprises:

obtaining the HE-evaluated value and the given random number by decrypting the encrypted random number within the encryption message using the communication secret key.

5. The operating method of claim 1 , further comprising:

detecting, by the server and the electronic devices, at least another electronic device to be added to the group;

providing, by at least any one of the electronic devices, the HE key to the another electronic device; and

updating, by the server, the Boolean circuit based on a number of the electronic devices and the another electronic device,

wherein each of the transmitting of the encrypted session ephemeral key, the calculating of the HE-evaluated value, the transmitting of the HE-evaluated value and the given random number, and the generating of the session key is performed by the server or the electronic devices and the another electronic device again.

6. The operating method of claim 1 , further comprising:

detecting, by the server, any one of the electronic devices removed from the group; and

updating, by the server, the Boolean circuit based on a number of remaining electronic devices of the electronic devices,

wherein each of the transmitting of the encrypted session ephemeral key, the calculating of the HE-evaluated value, the transmitting of the HE-evaluated value and the given random number, and the generating of the session key is performed by the server or the remaining electronic devices again.

7. A communication system comprising:

a plurality of electronic devices configured to share a homomorphic encryption (HE) key in order to form a group; and

a server configured to generate a Boolean circuit for performing an operation based on input values corresponding to a number of the electronic devices,

wherein the server is configured to:

receive an encrypted session ephemeral key from each of the electronic devices through HE,

calculate an HE-evaluated value by applying the encrypted session ephemeral keys as the input values of the Boolean circuit, and

transmit the HE-evaluated value and a given random number to each of the electronic devices, and

wherein each of the electronic devices is configured to generate a common session key for the group based on the HE key, the HE-evaluated value and the given random number through homomorphic decryption

wherein the HE key comprises at least any one of a homomorphic secret key or a homomorphic public key, and

wherein the encrypted session ephemeral key is generated from the homomorphic public key and the session ephemeral key of each of the electronic devices through the HE.

8. The communication system of claim 7 , wherein each of the electronic devices is configured to:

obtain a homomorphic decryption value by decrypting the homomorphic secret key and the HE-evaluated value through the homomorphic decryption, and

obtain the session key by adding the homomorphic decryption value and the given random number.

9. The communication system of claim 8 , wherein the server is configured to:

generate an encryption message, comprising the HE-evaluated value and the encrypted random number, by encrypting the given random number using a communication secret key; and

transmit the encryption message to each of the electronic devices.

10. The communication system of claim 9 , wherein each of the electronic devices is configured to:

obtain the HE-evaluated value and the given random number by decrypting the encrypted random number within the encryption message using the communication secret key.

11. The communication system of claim 7 , wherein the server is configured to:

detect at least another electronic device to be added to the group and update the Boolean circuit based on a number of the electronic devices and the another electronic device,

receive another encrypted session ephemeral key from each of the electronic devices and the another electronic device through the HE,

calculating another HE-evaluated value by applying the another encrypted session ephemeral keys as he input values of the Boolean circuit, and

transmit the another HE-evaluated value and another given random number to each of the electronic devices and the another electronic device using a communication secret key of the electronic devices and the another electronic device.

12. The communication system of claim 11 ,

wherein at least any one of the electronic devices is configured to provide the HE key to the another electronic device, and

wherein each of the electronic devices and the another electronic device is configured to generate the common session key for the group again based on the HE key, the another HE-evaluated value and the another given random number through the homomorphic decryption.

13. The communication system of claim 7 , wherein the server is configured to:

detect any one of the electronic devices removed from the group,

update the Boolean circuit based on a number of remaining electronic devices of the electronic devices,

receive another encrypted session ephemeral key from the remaining electronic devices through the HE,

calculate another HE-evaluated value by applying the another encrypted session ephemeral keys as the input values of the Boolean circuit, and

transmit the another HE-evaluated value and another given random number to each of the remaining electronic devices using a communication secret key of each of the remaining electronic devices.

14. The communication system of claim 13 , wherein the remaining electronic devices are configured to:

generate a common session key for the group again based on the HE key, the another HE-evaluated value and the another given random number through the homomorphic decryption.

15. An operating method of a communication system, comprising: sharing, by a plurality of electronic devices for forming a group, a homomorphic encryption (HE) key;

generating, by a server, a Boolean circuit for performing an operation based on input values corresponding to a number of the electronic devices;

transmitting, by each of the electronic devices, an encrypted session ephemeral key to the server through HE;

calculating, by the server, an HE-evaluated value by applying the encrypted session ephemeral keys as the input values of the Boolean circuit;

transmitting, by the server, the HE-evaluated value to each of the electronic devices; and

generating, by each of the electronic devices, a common session key for the group based on the HE key and the HE-evaluated value through homomorphic decryption

wherein the HE key comprises at least any one of a homomorphic secret key or a homomorphic public key,

wherein the encrypted session ephemeral key is generated from the homomorphic public key and the session ephemeral key of each of the electronic devices through the HE, and

wherein the session key is generated from the homomorphic secret key and the HE-evaluated value through the homomorphic decryption.

16. A communication system comprising:

a plurality of electronic devices configured to share a homomorphic encryption (HE) key in order to form a group; and

a server configured to generate a Boolean circuit for performing an operation based on input values corresponding to a number of the electronic devices,

wherein the server is configured to:

receive an encrypted session ephemeral key from each of the electronic devices through HE,

calculating an HE-evaluated value by applying the encrypted session ephemeral keys as the input values of the Boolean circuit, and

transmit the HE-evaluated value to each of the electronic devices,

wherein each of the electronic devices is configured to generate a common session key for the group based on the HE key and the HE-evaluated value through homomorphic decryption

wherein the HE key comprises at least any one of a homomorphic secret key or a homomorphic public key,

wherein the encrypted session ephemeral key is generated from the homomorphic public key and the session ephemeral key of each of the electronic devices through HE, and

wherein the session key is generated from the homomorphic secret key and the HE-evaluated value through the homomorphic decryption.