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

It is known that for binary codes one can use Gr\"obner bases to obtain a subset of codewords of minimal support that can be used to determine the second generalized Hamming weight of the code. In this paper we establish conditions on a…

The era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in…

The Sparsest Permutation (SP) algorithm is accurate but limited to about 9 variables in practice; the Greedy Sparest Permutation (GSP) algorithm is faster but less weak theoretically. A compromise can be given, the Best Order Score Search,…

Since the first theoretically feasible full homomorphic encryption (FHE) scheme was proposed in 2009, great progress has been achieved. These improvements have made FHE schemes come off the paper and become quite useful in solving some…

Recently Hashemi and Kapur published an algorithm [1] for Groebner basis conversion by truncating polynomials according to a source and a target monomial order. Here we present a counterexample to this algorithm.

A contemporary and exciting application of Groebner bases is their use in computational biology, particularly in the reverse engineering of gene regulatory networks from experimental data. In this setting, the data are typically limited to…

We define a new type of ideal basis called the proper basis that improves both Gr\"obner basis and Buchberger's algorithm. Let $x_1$ be the least variable of a monomial ordering in a polynomial ring $K[x_1,\dotsc,x_n]$ over a field $K$. The…

Many different approaches for neural network based hash functions have been proposed. Statistical analysis must correlate security of them. This paper proposes novel neural hashing approach for gray scale image authentication. The suggested…

We revisit the classical problem of designing optimally efficient cryptographically secure hash functions. Hash functions are traditionally designed via applying modes of operation on primitives with smaller domains. The results of…

We present a Compression Tool, "GenBit Compress", for genetic sequences based on our new proposed "GenBit Compress Algorithm". Our Tool achieves the best compression ratios for Entire Genome (DNA sequences) . Significantly better…

One way of investigating how genes affect human traits would be with a genome-wide association study (GWAS). Genetic markers, known as single-nucleotide polymorphism (SNP), are used in GWAS. This raises privacy and security concerns as…

Recent years have seen more and more demand for a unified framework to address multiple realistic image retrieval tasks concerning both category and attributes. Considering the scale of modern datasets, hashing is favorable for its low…

A feature selection algorithm should ideally satisfy four conditions: reliably extract relevant features; be able to identify non-linear feature interactions; scale linearly with the number of features and dimensions; allow the…

We extend the method of Ghasemi and Marshall [SIAM. J. Opt. 22(2) (2012), pp 460-473], to obtain a lower bound $f_{{\rm gp},M}$ for a multivariate polynomial $f(x) \in \mathbb{R}[x]$ of degree $ \le 2d$ in $n$ variables $x = (x_1,...,x_n)$…

Hashing has been widely used for large-scale search due to its low storage cost and fast query speed. By using supervised information, supervised hashing can significantly outperform unsupervised hashing. Recently, discrete supervised…

Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary's nature and inspiral kinematics. Using the lalinference\_mcmc Markov-chain Monte Carlo parameter estimation code, we use two…

We aim to advance the state-of-the-art in Quadratic Unconstrained Binary Optimization formulation with a focus on cryptography algorithms. As the minimal QUBO encoding of the linear constraints of optimization problems emerges as the…

Let T(x) in k[x] be a monic non-constant polynomial and write R=k[x] / (T) the quotient ring. Consider two bivariate polynomials a(x, y), b(x, y) in R[y]. In a first part, T = p^e is assumed to be the power of an irreducible polynomial p. A…

We construct geohashing procedure based on using of space-filling H-curve. This curve provides a way to construct geohash with less computations than the construction based on usage of Hilbert curve. At the same time, H-curve has better…

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH$^*$, which was shown to be $\Delta$-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function…