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

Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used,…

We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new…

Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most…

Bloom filter is a compact memory-efficient probabilistic data structure supporting membership testing, i.e., to check whether an element is in a given set. However, as Bloom filter maps each element with uniformly random hash functions, few…

Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…

Face recognition models operate in a client-server setting where a client extracts a compact face embedding and a server performs similarity search over a template database. This raises privacy concerns, as facial data is highly sensitive.…

In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive…

Deep hashing has shown promising performance in large-scale image retrieval. However, latent codes extracted by Deep Neural Networks (DNNs) will inevitably lose semantic information during the binarization process, which damages the…

Protecting sensitive program content is a critical issue in various situations, ranging from legitimate use cases to unethical contexts. Obfuscation is one of the most used techniques to ensure such protection. Consequently, attackers must…

The F5 algorithm is generally believed as one of the fastest algorithms for computing Gr\"{o}bner bases. However, its termination problem is still unclear. Recently, an algorithm GVW and its variant GVWHS have been proposed, and their…

There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes…

Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Groebner basis with its reduced…

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

Fully Homomorphic Encryption (FHE) is one of the most promising technologies for privacy protection as it allows an arbitrary number of function computations over encrypted data. However, the computational cost of these FHE systems limits…

Homomorphic encryption (HE) enables computations directly on encrypted data, offering strong cryptographic guarantees for secure and privacy-preserving data storage and query execution. However, despite its theoretical power, practical…

Consistent hashing is a technique for distributing data across a network of nodes in a way that minimizes reorganization when nodes join or leave the network. It is extensively applied in modern distributed systems as a fundamental…

Given a set S of n keys, a k-perfect hash function (kPHF) is a data structure that maps the keys to the first m integers, where each output integer can be hit by at most k input keys. When m=n/k, the resulting function is called a minimal…

The compression-complexity trade-off of lossy compression algorithms that are based on a random codebook or a random database is examined. Motivated, in part, by recent results of Gupta-Verd\'{u}-Weissman (GVW) and their underlying…