SearcharxivSearch

arXiv · 1501.03872

The Dead Cryptographers Society Problem

Abstract

This paper defines The Dead Cryptographers Society Problem - DCS (where several great cryptographers created many polynomial-time Deterministic Turing Machines (DTMs) of a specific type, ran them on their proper descriptions concatenated with some arbitrary strings, deleted them and left only the results from those running, after they died: if those DTMs only permute and sometimes invert the bits on input, is it possible to decide the language formed by such resulting strings within polynomial time?), proves some facts about its computational complexity, and discusses some possible uses on Cryptography, such as into distance keys distribution, online reverse auction and secure communication.

Explore related subjects

Keep this discovery

BibTeXRIS

André Luiz Barbosa. 2018-12-21. The Dead Cryptographers Society Problem. https://arxiv.org/abs/1501.03872

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC