  Two legitimate parties, referred to as Alice and Bob, wish to generate secret
keys from the wireless channel in the presence of an eavesdropper, referred to
as Eve, in order to use such keys for encryption and decryption. In general,
the secret key rate highly depends on the coherence time of the channel. In
particular, a straightforward method of generating secret keys in static
environments results in ultra-low rates. In order to resolve this problem, we
introduce a low-complexity method called induced randomness. In this method,
Alice and Bob independently generate local randomness to be used together with
the uniqueness of the wireless channel coefficients in order to enable
high-rate secret key generation. In this work, two scenarios are considered:
first, when Alice and Bob share a direct communication channel, and second,
when Alice and Bob do not have a direct link and communicate through an
untrusted relay. After exchanging the induced randomness, post-processing is
done by Alice and Bob to generate highly-correlated samples that are used for
the key generation. Such samples are then converted into bits, disparities
between the sequences generated by Alice and Bob are mitigated, and the
resulting sequences are then hashed to compensate for the information leakage
to the eavesdropper and to allow consistency checking of the generated key bit
sequences. We utilize semantic security measures and information-theoretic
inequalities to upper bound the probability of successful eavesdropping attack
in terms of the mutual information measures that can be numerically computed.
Given certain reasonable system parameters this bound is numerically evaluated
to be $2^{-31}$ and $2^{-10.57}$ in the first and the second scenario,
respectively.
