Data communication between a group of users

1. A method for implementing communication of data between a group of users in a communication system, comprising:

generating, by a server of the communication system, a plurality of quorum portions of a group signing key;

providing, by the server, at least one of said plurality of quorum portions of the group signing key to each of a plurality of devices of the group of users, to configure each device to become operable to generate an encrypted portion of a group digital signature using a corresponding quorum portion of the group signing key;

receiving, by the server, a predetermined minimum number of encrypted portions of the group digital signature, each generated by a respective device of the group of users; and

combining, by the server, the predetermined minimum number of encrypted portions of the group digital signature to construct an encrypted group digital signature.

2. The method of claim 1 , further comprising decrypting, by the server, the encrypted group digital signature.

3. The method of claim 1 , further comprising:

generating, by the server, a plurality of quorum portions of a group decryption key;

providing, by the server, at least one of said plurality of quorum portions of the group decryption key to each of a plurality of devices of a decryption group;

transmitting, by the server, the predetermined minimum number of encrypted portions of the group digital signature to the decryption group; and

receiving, by the server, a decrypted group digital signature from the decryption group.

4. The method of claim 1 , wherein the group signing key is a private group signing key, the method further comprising verifying the encrypted group digital signature using a corresponding public group signing key.

5. The method of claim 4 , wherein each quorum portion of the group signing key comprises respective contributing shares of first and second components of the private group signing key.

6. The method of claim 5 , wherein the predetermined minimum number of encrypted portions of the group digital signature are each generated from the respective contributing shares of each user in the group of users.

7. The method of claim 1 , wherein a predefined minimum number of devices of the group of users form a chain of quorum devices to generate a quorum signature component using their respective quorum portions of the group signing key.

8. The method of claim 7 , further comprising receiving a quorum-signed group signature quorum portion, generated by one of the predefined minimum number of devices of the group of users using the quorum signature component to digitally sign group data that is output by the group of users.

9. The method of claim 8 , wherein the group data comprises one or more data files and/or communication events produced by the group of users.

10. The method of claim 1 , wherein the plurality of quorum portions of the group signing key are generated using secret parameters that are not communicated by the server or each user in the group of users.

11. The method of claim 1 , wherein the group signing key and the plurality of quorum portions of the group signing key are purged from the server after provision to each of the plurality of devices of the group of users.

12. The method of claim 1 , further comprising generating and verifying, by the server, check ciphertexts to determine that the predetermined minimum number of encrypted portions of the group digital signature are constructed correctly.

13. A method according to claim 1 , wherein the group of users are selected from devices that have returned an irrevocable message that is generated by digitally signing a commitment message with a cryptographic signature.

14. A computer-implemented method, comprising:

receiving, by a device of a user in a group of users in a communication system, a quorum portion of a group signing key;

communicating, by the device, a group data output to devices of other users in the group of users;

generating, by the device, a portion of a group digital signature by digitally signing the group data output based at least on the received quorum portion of the group signing key;

encrypting, by the device, the generated portion of a group digital signature using a public group encryption key; and

transmitting, by the device, the encrypted portion of the group digital signature to a server in the communication system, wherein the server reconstructs a group digital signature from a predetermined minimum number of encrypted portions of the group digital signature generated by respective devices of the group of users.

15. The computer-implemented method of claim 14 , further comprising:

receiving, by the device, a public group encryption key based on a homomorphic encryption scheme; and

encrypting, by the device, the generated portion of the group digital signature using the public group encryption key to output a malleable encrypted portion of the group digital signature.

16. The computer-implemented method of claim 14 , further comprising generating, by a chain of quorum devices including the device, a quorum signature component using respective quorum portions of the group signing key, wherein the quorum signature component is used to sign the group data output by the group of users to generate the portion of the group digital signature.

17. A system for implementing communication of data between a group of users in a communication system, the system comprising a computer processor configured to perform a method of:

generating, by a server of the communication system, a plurality of quorum portions of a group signing key;

providing, by the server, at least one of said plurality of quorum portions of the group signing key to each of a plurality of devices of the group of users, to configure each device to become operable to generate an encrypted portion of a group digital signature using a corresponding quorum portion of the group signing key;

receiving, by the server, a predetermined minimum number of encrypted portions of the group digital signature, each generated by a respective device of the group of users; and

combining, by the server, the predetermined minimum number of encrypted portions of the group digital signature to construct an encrypted group digital signature.

18. A non-transitory computer-readable medium comprising computer-executable instructions that when executed on a computing device perform a method for implementing communication of data between a group of users in a communication system, the method comprising:

generating, by a server of the communication system, a plurality of quorum portions of a group signing key;

providing, by the server, at least one of said plurality of quorum portions of the group signing key to each of a plurality of devices of the group of users, to configure each device to become operable to generate an encrypted portion of a group digital signature using a corresponding quorum portion of the group signing key;

receiving, by the server, a predetermined minimum number of encrypted portions of the group digital signature, each generated by a respective device of the group of users; and

combining, by the server, the predetermined minimum number of encrypted portions of the group digital signature to construct an encrypted group digital signature.