Reversible computing is a computational model that only allows thermodynamically reversible operations. According to Landauer's principle, which states that erasing a bit of information releases $kT \ln(2)$ joules of heat, this rules out transition functions that are not one-to-one (e.g., the Boolean AND and OR operators). It is well known that quantum computation is inherently reversible because the allowed operations in quantum computation are represented by unitary matrices.
This question is about cryptography. Informally, the notion of "reversibility" seems anathema to the fundamental goals of cryptography, thus suggesting the question: "Does cryptography have an inherent thermodynamic cost?"
I believe that this is a different question than, "Can everything be done in quantum?"
In his lecture notes, Dr. Preskill states, "There is a general strategy for simulating an irreversible computation on a reversible computer. Each irreversible gate can be simulated by a Toffoli gate by fixing inputs and ignoring outputs. We accumulate and save all 'garbage' output bits that are needed to reverse the steps of the computation."
This suggests that these reversible quantum simulations of irreversible operations take an input as well as some "scratch" space. Then, the operation generates output along with some "dirty" scratch bits. The operations are all reversible with respect to the output plus garbage bits, but at some point, the garbage bits are "thrown away" and not considered further.
Since cryptography depends on the existence of trapdoor one-way functions, an alternative statement of the question might be, "Are there any trapdoor one-way functions that can be implemented using only reversible logical operations, without additional scratch space?" If so, is it also possible to COMPUTE an arbitrary trapdoor one-way function using only reversible operations (and no scratch space)?