3,039 research outputs found
Chasing diagrams in cryptography
Cryptography is a theory of secret functions. Category theory is a general
theory of functions. Cryptography has reached a stage where its structures
often take several pages to define, and its formulas sometimes run from page to
page. Category theory has some complicated definitions as well, but one of its
specialties is taming the flood of structure. Cryptography seems to be in need
of high level methods, whereas category theory always needs concrete
applications. So why is there no categorical cryptography? One reason may be
that the foundations of modern cryptography are built from probabilistic
polynomial-time Turing machines, and category theory does not have a good
handle on such things. On the other hand, such foundational problems might be
the very reason why cryptographic constructions often resemble low level
machine programming. I present some preliminary explorations towards
categorical cryptography. It turns out that some of the main security concepts
are easily characterized through the categorical technique of *diagram
chasing*, which was first used Lambek's seminal `Lecture Notes on Rings and
Modules'.Comment: 17 pages, 4 figures; to appear in: 'Categories in Logic, Language and
Physics. Festschrift on the occasion of Jim Lambek's 90th birthday', Claudia
Casadio, Bob Coecke, Michael Moortgat, and Philip Scott (editors); this
version: fixed typos found by kind reader
Secure and Privacy-Preserving Average Consensus
Average consensus is fundamental for distributed systems since it underpins
key functionalities of such systems ranging from distributed information
fusion, decision-making, to decentralized control. In order to reach an
agreement, existing average consensus algorithms require each agent to exchange
explicit state information with its neighbors. This leads to the disclosure of
private state information, which is undesirable in cases where privacy is of
concern. In this paper, we propose a novel approach that enables secure and
privacy-preserving average consensus in a decentralized architecture in the
absence of any trusted third-parties. By leveraging homomorphic cryptography,
our approach can guarantee consensus to the exact value in a deterministic
manner. The proposed approach is light-weight in computation and communication,
and applicable to time-varying interaction topology cases. A hardware
implementation is presented to demonstrate the capability of our approach.Comment: 7 pages, 4 figures, paper is accepted to CPS-SPC'1
On the Cryptographic Hardness of Local Search
We show new hardness results for the class of Polynomial Local Search problems (PLS):
- Hardness of PLS based on a falsifiable assumption on bilinear groups introduced by Kalai, Paneth, and Yang (STOC 2019), and the Exponential Time Hypothesis for randomized algorithms. Previous standard model constructions relied on non-falsifiable and non-standard assumptions.
- Hardness of PLS relative to random oracles. The construction is essentially different than previous constructions, and in particular is unconditionally secure. The construction also demonstrates the hardness of parallelizing local search.
The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property
- …