A method includes, by a key server: identifying a group of devices; accessing secret values pre-provisioned to devices in the group of devices; accessing prime numbers pre-provisioned to devices in the group of devices; generating a cryptographic key for communication among the group of devices; generating a message based on the secret values, the prime numbers, and the cryptographic key; and transmitting the message to a device in the group of devices. The method also includes, by a first device in the group of devices: in response to receiving the message, deriving the cryptographic key from the message based on a first secret value, pre-provisioned to the first device, and a first prime number pre-provisioned to the first device; and associating the cryptographic key with communication among the group of devices.