Related papers: GB-hash : Hash Functions Using Groebner Basis

We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…

Graph neural networks (GNNs) are deep learning models designed specifically for graph data, and they typically rely on node features as the input to the first layer. When applying such a type of network on the graph without node features,…

We develop a method for approximating the Gr\"obner basis of the ideal of polynomials which vanish at a finite set of points, when the coordinates of the points are known with only limited precision. The method consists of a preprocessing…

The computation of Gr\"obner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robust. In this paper, we frame and present results on the…

Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully…

Fully Homomorphic Encryption (FHE) enables the processing of encrypted data without decrypting it. FHE has garnered significant attention over the past decade as it supports secure outsourcing of data processing to remote cloud services.…

In recent years, deep hashing methods have been proved to be efficient since it employs convolutional neural network to learn features and hashing codes simultaneously. However, these methods are mostly supervised. In real-world…

In this study, we evaluated four binarization methods. Locality-Sensitive Hashing (LSH), Iterative Quantization (ITQ), Kernel-based Supervised Hashing (KSH), and Supervised Discrete Hashing (SDH) on the ODIR dataset using deep feature…

Security systems relying on passwords are vulnerable to being forgotten, guessed, or breached. Likewise, biometric systems that operate independently are at risk of template spoofing and replay incidents. This paper introduces a…

Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process,…

We study the complexity of Gr\"obner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We give a bound on the number of polynomials of degree $d$…

Fully Homomorphic Encryption (FHE) enables computations on encrypted data, preserving confidentiality without the need for decryption. However, FHE is often hindered by significant performance overhead, particularly for high-precision and…

This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the…

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function…

As an approximate nearest neighbor search technique, hashing has been widely applied in large-scale image retrieval due to its excellent efficiency. Most supervised deep hashing methods have similar loss designs with embedding learning,…

While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…

Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we…

Fully Homomorphic Encryption (FHE) allows computations to be performed on encrypted data, significantly enhancing user privacy. However, the I/O challenges associated with deploying FHE applications remains understudied. We analyze the…

Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(\alpha)$, a…

Binary optimization is a fundamental area in computational science, with wide-ranging applications from logistics to cryptography, where the tasks are often formulated as Quadratic or Polynomial Unconstrained Binary Optimization problems…