Related papers: A cryptographic application of the Thurston norm

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and is essential to privacy-preserving computing, such as neural network inference, medical diagnosis, and financial data analysis. Only addition and…

We study when the Thurston norm is detected by twisted Alexander polynomials associated to representations of the 3-manifold group to SL(2, C). Specifically, we show that the hyperbolic torsion polynomial determines the genus for a large…

Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted data without knowing its corresponding plaintext. For…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…

We discuss the isometry group structure of three-dimensional black holes and Chern-Simons invariants. Aspects of the holographic principle relevant to black hole geometry are analyzed.

We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence of universal limit laws for the topologies; namely, the…

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by…

Homomorphic encryption (HE) is a promising cryptographic technique for enabling secure collaborative machine learning in the cloud. However, support for homomorphic computation on ciphertexts under multiple keys is inefficient. Current…

We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse)…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

We follow existing distributed systems frameworks employing methods from algebraic topology to formally define primitives of blockchain technology. We define the notion of cross chain liquidity, sharding and probability spaces between and…

Threshold cryptography is a powerful and well-known technique with many applications to systems relying on distributed trust. It has recently emerged also as a solution to challenges in blockchain: frontrunning prevention, managing wallet…

With the rapid development of cloud computing, the privacy security incidents occur frequently, especially data security issues. Cloud users would like to upload their sensitive information to cloud service providers in encrypted form…

Two different kinds of synchronization have been applied to cryptography: Synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the…

For a closed orientable connected 3-manifold $M$, its complexity $\boldsymbol{T}(M)$ is defined to be the minimal number of tetrahedra in its triangulations. Under the assumption that $M$ is prime (but not necessarily atoroidal), we…

At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In this paper, we show that there is a big difference between…

This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run…

In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…