Decentralised authentication

A communication system comprising:

• a first device;
• a second device;
• and
• a proxy device,
• wherein:
• the first device stores first-device data and a first-device private key;
• the second device stores second-device data and a second-device private key;
• the proxy device stores proxy data and a proxy-device private key;
• the first-device data is additionally stored by the second device and by the proxy device;
• the second-device data is additionally stored by the first device and by the proxy device;
• and
• the proxy data is additionally stored by the first device and by the second device;
• wherein the first device is configured, in a commitment phase, to:
• use the first-device data and first-device secret-key information to generate a one-time first-device commitment value, the first-device secret-key information comprising, or being derived from, the first-device private key and a first random nonce;
• and
• send the one-time first-device commitment value to the proxy device,
• wherein the second device is configured, in the commitment phase, to:
• use the second-device data and second-device secret-key information to generate a one-time second-device commitment value, the second-device secret-key information comprising, or being derived from, the second-device private key and a second random nonce;
• and
• send the one-time second-device commitment value to the proxy device,
• wherein the proxy device is configured, in the commitment phase, to:
• use the proxy data and proxy-device secret-key information to generate a one-time proxy-device commitment value, the proxy-device secret-key information comprising, or being derived from, the proxy-device private key and a third random nonce;
• and
• send the one-time proxy device commitment value to the first device and to the second device;
• wherein:
• the first device is configured, in a checking phase, performed after the commitment phase, to communicate the first-device secret-key information to the proxy device and to the second device;
• the second device is configured, in the checking phase, to communicate the second-device secret-key information to the proxy device;
• the proxy device is configured, in the checking phase, to use the first-device data stored by the proxy device, and the first-device secret-key information received from the first device, to verify the one-time first-device commitment value received from the first device;
• and
• the proxy device is further configured, in the checking phase, to use the second-device data stored by the proxy device, and the second-device secret-key information received from the second device, to verify the one-time second-device commitment value received from the second device and to communicate the proxy-device secret-key information to the first device and to the second device;
• the first device is further configured to use the proxy data stored in the first device, and the proxy-device secret-key information received from the proxy device, to verify the one-time proxy-device commitment value received from the proxy device;
• and
• the second device is further configured to use the proxy data stored in the second device, and the proxy-device secret-key information received from the proxy device, to verify the one-time proxy-device commitment value received from the proxy device;
• and wherein:
• the proxy device is configured to enter a digest phase in response to a successful verification of the one-time first-device commitment value and of the one-time second-device commitment value in the commitment phase;
• the proxy device is configured, when in the digest phase, to calculate a one-time digest from i) the first-device data stored by the proxy device, ii) the second-device data stored by the proxy device, iii) the first-device secret-key information received from the first device, and iv) the second-device secret-key information received from the second device, and to send the one-time digest to the second device;
• the second device is configured to authenticate the first device by using at least i) the first-device data stored by the second device, ii) the second-device data stored by the second device, iii) the first-device secret-key information received from the first device, and iv) the second-device secret-key information, to verify the one-time digest received from the proxy device;
• and
• wherein the proxy device is further configured to send the one-time digest to the first device, wherein the second device is further configured to communicate the second-device secret-key information to the first device and the first device is configured to authenticate the second device by using at least i) the first-device data stored by the first device, ii) the second-device data stored by the first device, iii) the first-device secret-key information, and iv) the second-device secret-key information received from the second device, to verify the one-time digest received from the proxy device.