Based on the quotes below I belive paper relies explicitly on the GE channel's hardness to break:
"On Our Modeling Assumptions. Our model considers a relatively powerful adversary
that, for example, has the ability to choose the encryption scheme using which all parties must
communicate, and to decrypt all such communications. We believe that this can be very realistic
in certain scenarios, but it is also important to note the limitations that our model places on
The most obvious limitation is that the encryption scheme chosen by the adversary must
be semantically secure (against third parties that do not have the ability to decrypt)."
"All known constructions of such undetectable random string embedding rely on the sampling
of a public random seed after the adversarial strategy is fixed. In this paper, however, we are
interested in bootstrapping hidden communications from the very ground up, and we are not
willing to assume that the parties start from a state where such a seed is already present."
" We begin with the following simple
idea: for each consecutive pair of ciphertexts c and c0, a single hidden (random) bit b is defined
by b = f(c, c0) where f is some two-source extractor. It is initially unclear why this should work
because (1) c and c0 are encryptions of messages m and m0 which are potentially dependent,
and two-source extractors are not guaranteed to work without independence; ..."
"We overcome difficulty (1) by relying on the semantic security of the ciphertexts of the
adversarially chosen encryption scheme. Paradoxically, even though the adversary knows the
decryption key, we exploit the fact that semantic security still holds against the extractor, which
does not have the decryption key."