Fast Secret Key Generation in Static Environments Using Induced Randomness

摘要

Secret key agreement in distributed low-power networks, such as Internet of Things (IoT) networks, is a major requirement for deploying cryptographic protocols to protect the security of sensitive data. However, due to the distributed nature of such networks, the devices need to be able to generate secret keys locally from some common source of randomness. The randomness in the characteristics of the physical layer channel provides such sources, however, this can be quite limited if the devices operate in a static environment and experience static or very slow fading channel. Therefore, fast secret key generation in such environments while keeping a low complexity architecture for the network nodes, such as IoT devices, remains a challenging task. We design a low-complexity protocol for fast secret key generation in static environments. To this end, we propose to use a limited number of random bits independently generated by the legitimate parties, referred to as Alice and Bob, in combination with the fading parameter to create a common source of randomness. In the proposed protocol, Alice and Bob share their random bits over the public channel, assumed to be a fading channel, and then construct a common random sequence. Then they perform several steps for recovery from errors in the shared sequence, privacy amplification to limit the chances of a successful attack, and consistency checking by exploiting universal hash functions. We characterize the reliability of the proposed protocol and provide an upper bound on the probability of accepting a mismatched key by Alice and Bob. The eavesdropper Eve is assumed to be passive and a successful attack by her is the event of guessing the key right based on her observations. We provide an analytical upper bound, that can be numerically evaluated, on the probability of a successful attack by Eve using the cryptographic notion of semantic security. In the simulations, the proposed protocol achieves a bit generation rate of 64-96 bits/packet, bit mismatch rate of 11-24%, bit error rate of 0.005%, 50% randomness efficiency, the probability of successful attack of at most 2^{-31, and the probability of consistency checking failure of at most 2-16.}