Methods and devices for computing a shared encryption key

A mobile device for computing a shared encryption key (k) in a group of n mobile devices, the group of n mobile devices comprising at least three mobile devices, the mobile device comprising:

• a processor;
• and
• a memory;
• wherein the processor is configured to
• compute a public key (Xi) for the mobile device for transmission to at least one first other mobile device of the group of n mobile devices, wherein the public key (Xi) for the mobile device is a function of at least a private key (xi) associated with the mobile device and of a shared password (π) known to all mobile devices of the group of n mobile devices;
• compute a public value (Ki) for the mobile device for transmission to each of all other mobile devices of the group of n mobile devices, wherein the public value (Ki) for the mobile device is a function of at least the private key (xi) associated with the mobile device and of a public key of at least one second other mobile device of the group of n mobile devices;
• and
• use the public value (K1, . . . Ki−1, Ki+1, . . . Kn) of each of all other mobile devices of the group of n mobile devices to compute the shared encryption key (k) in accordance with a group key establishment protocol.

A non-transitory computer readable storage medium having stored therein a computer program which, when executed by a processor of a mobile device, causes the processor to perform a method of computing a shared encryption key (k) for a group of n mobile devices, the group of n mobile devices comprising at least three mobile devices, wherein the method comprises:

• for an i-th mobile device of the group of n mobile devices:
• computing a public key (Xi) for the mobile device for transmission to at least one first other mobile device of the group of n mobile devices, wherein the public key (Xi) for the mobile device is a function of at least a private key (xi) associated with the mobile device and of a shared password (π) known to all mobile devices of the group of n mobile devices;
• computing a public value (Ki) for the mobile device for transmission to each of all other mobile devices of the group of n mobile devices, wherein the public value (Ki) for the mobile device is a function of at least the private key (xi) associated with the mobile device and of a public key of at least one second other mobile device of the group of n mobile devices;
• and
• using the public value (K1, . . . Ki−1, Ki+1, . . . Kn) of each of all other mobile devices of the group of n mobile devices to compute the shared encryption key (k) in accordance with a group key establishment protocol.