7 research outputs found
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata
After an apparent hiatus of roughly 30 years, we revisit a seemingly
neglected subject in the theory of (one-dimensional) cellular automata:
sublinear-time computation. The model considered is that of ACAs, which are
language acceptors whose acceptance condition depends on the states of all
cells in the automaton. We prove a time hierarchy theorem for sublinear-time
ACA classes, analyze their intersection with the regular languages, and,
finally, establish strict inclusions in the parallel computation classes
and (uniform) . As an addendum, we introduce and
investigate the concept of a decider ACA (DACA) as a candidate for a decider
counterpart to (acceptor) ACAs. We show the class of languages decidable in
constant time by DACAs equals the locally testable languages, and we also
determine as the (tight) time complexity threshold for DACAs
up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202
Asymptotically Compact Adaptively Secure Lattice IBEs and Verifiable Random Functions via Generalized Partitioning Techniques
In this paper, we focus on the constructions of adaptively secure identity-based encryption (IBE) from lattices and verifiable random function (VRF) with large input spaces. Existing constructions of these primitives suffer from low efficiency, whereas their counterparts with weaker guarantees (IBEs with selective security and VRFs with small input spaces) are reasonably efficient. We try to fill these gaps by developing new partitioning techniques that can be performed with compact parameters and proposing new schemes based on the idea.
- We propose new lattice IBEs with poly-logarithmic master public key sizes, where we count the number of the basic matrices to measure the size. Our constructions are proven secure under the LWE assumption with polynomial approximation factors. They achieve the best asymptotic space efficiency among existing schemes that depend on the same assumption and achieve the same level of security.
- We also propose several new VRFs on bilinear groups. In our first scheme, the size of the proofs is poly-logarithmic in the security parameter, which is the smallest among all the existing schemes with similar properties. On the other hand, the verification keys are long. In our second scheme, the size of the verification keys is poly-logarithmic, which is the smallest among all the existing schemes. The size of the proofs is sub-linear, which is larger than our first scheme, but still smaller than all the previous schemes