Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructive Post-Quantum Reductions   Is it possible to convert classical cryptographic reductions into
post-quantum ones? It is customary to argue that while this is problematic in
the interactive setting, non-interactive reductions do carry over. However,
when considering quantum auxiliary input, this conversion results in a
non-constructive post-quantum reduction that requires duplicating the quantum
auxiliary input, which is in general inefficient or even impossible. This
violates the win-win premise of provable cryptography: an attack against a
cryptographic primitive should lead to an algorithmic advantage.
  We initiate the study of constructive quantum reductions and present positive
and negative results for converting large classes of classical reductions to
the post-quantum setting in a constructive manner. We show that any
non-interactive non-adaptive reduction from assumptions with a polynomial
solution space (such as decision assumptions) can be made post-quantum
constructive. In contrast, assumptions with super-polynomial solution space
(such as general search assumptions) cannot be generally converted.
  Along the way, we make several additional contributions:
  1. We put forth a framework for reductions (or general interaction) with
stateful solvers for a computational problem, that may change their internal
state between consecutive calls. We show that such solvers can still be
utilized. This framework and our results are meaningful even in the classical
setting.
  2. A consequence of our negative result is that quantum auxiliary input that
is useful against a problem with a super-polynomial solution space cannot be
generically ``restored'' post-measurement. This shows that the novel rewinding
technique of Chiesa et al. (FOCS 2021) is tight in the sense that it cannot be
extended beyond a polynomial measurement space.

32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol