Related papers: A cryptographic application of the Thurston norm
For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of…
By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users…
For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting…
A scheme is presented based on numbers that represent a manifold in $d$ dimensions for generalizations of textbook cryptosystems. The interlocking or intersection of geometries, requiring the addition of a series of integers $q_j$, can be…
Threshold cryptography has gained momentum in the last decades as a mechanism to protect long term secret keys. Rather than having a single secret key, this allows to distribute the ability to perform a cryptographic operation such as…
Quantum cryptography has been recently extended to continuous variable systems, e.g., the bosonic modes of the electromagnetic field. In particular, several cryptographic protocols have been proposed and experimentally implemented using…
Quantum cryptography is going to find practically useful applications. Recently some first quantum cryptographic solutions became available on the market. For clients it is important to be able to compare the quality and properties of the…
We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number bigger than one generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
This book provides a self-contained introduction to the topology and geometry of surfaces and three-manifolds. The main goal is to describe Thurston's geometrisation of three-manifolds, proved by Perelman in 2002. The book is divided into…
Encrypted control is a promising method for the secure outsourcing of controller computation to a public cloud. However, a feasible method for security proofs of control has not yet been developed in the field of encrypted control systems.…
We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…
This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$…
We study the geometry and topology of Riemannian 3-orbifolds which are locally volume collapsed with respect to a curvature scale. We show that a sufficiently collapsed closed 3-orbifold without bad 2-suborbifolds either admits a metric of…
We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed…