Abstract: First and second devices store respective device data and private keys. The first-device data is additionally stored by the second device and by a proxy; and the second-device data is additionally stored by the first device and by the proxy. In a commitment phase, each of the first and second devices uses its respective device data, private key and a random nonce to generate a respective one-time first-device or second-device commitment value, which it sends to the proxy. In a checking phase, the devices communicate secret-key information to the proxy, which verifies the received one-time commitment values. In a digest phase, the proxy calculates a one-time digest, which it sends to the second device. The second device then verifies the received one-time digest to authenticate the first device.