Related papers: A cryptographic application of the Thurston norm
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
The configuration-space topology in canonical General Relativity depends on the choice of the initial data 3-manifold. If the latter is represented as a connected sum of prime 3-manifolds, the topology receives contributions from all…
We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial bandstructure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a non-trivial…
We show that the Thurston norm of any irreducible 3-manifold can be detected using twisted Reidemeister torsions corresponding to integral representations and also corresponding to representations over finite fields. In particular our…
This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…
We present a three-stage quantum cryptographic protocol guaranteeing security in which each party uses its own secret key. Unlike the BB84 protocol, where the qubits are transmitted in only one direction and classical information exchanged…
While QKD ensures information-theoretic security at the link level, real-world deployments depend on trusted repeaters, creating potential vulnerabilities. In this paper, we thus introduce a topology-hiding connectivity assurance protocol…
The improvements on quantum technology are threatening our daily cybersecurity, as a capable quantum computer can break all currently employed asymmetric cryptosystems. In preparation for the quantum-era the National Institute of Standards…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positve integral multiple represented by an…
This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
This is an exposition of results on the existence problem of $\pi_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are…
An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is…
Traditional risk measures in finance, predominantly based on the second moment of return distributions or tail risk heuristics (VaR/CVaR), fail to account for the intrinsic geometric structure of market dynamics. This paper introduces a…
In 1976 Thurston associated to a $3$-manifold $N$ a marked polytope in $H_1(N;\mathbb{R}),$ which measures the minimal complexity of surfaces representing homology classes and determines all fibered classes in $H^1(N;\mathbb{R})$. Recently…
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels,…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
We show that if M is a hyperbolic 3-manifold which admits a quasigeodesic flow, then pi_1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that…