Related papers: Gr\"obner Basis Cryptanalysis of Ciminion and Hydr…
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
Rowhammer is a hardware-based bug that allows the attacker to modify the data in the memory without accessing it, just repeatedly and frequently accessing (or hammering) physically adjacent memory rows. So that it can break the memory…
At CRYPTO 2017, Bela\"id et al presented two new private multiplication algorithms over finite fields, to be used in secure masking schemes. To date, these algorithms have the lowest known complexity in terms of bilinear multiplication and…
Ensuring the safety and alignment of large language models (LLMs) with human values is crucial for generating responses that are beneficial to humanity. While LLMs have the capability to identify and avoid harmful queries, they remain…
In this paper we are interested in the problem of learning an over-complete basis and a methodology such that the reconstruction or inverse problem does not need optimization. We analyze the optimality of the presented approaches, their…
Regulatory frameworks such as GDPR increasingly require that ML predictions be accompanied by post-hoc explanations, even when raw data and trained models cannot be released. Differential privacy (DP) is the standard mitigation for the…
Let $(f\_1,\dots, f\_s) \in \mathbb{Q}\_p [X\_1,\dots, X\_n]^s$ be a sequence of homogeneous polynomials with $p$-adic coefficients. Such system may happen, for example, in arithmetic geometry. Yet, since $\mathbb{Q}\_p$ is not an effective…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
Rivest-Shamir-Adleman (RSA) cryptosystem uses modular multiplication for encryption and decryption. So, performance of RSA can be drastically improved by optimizing modular multiplication. This paper proposes a new parallel, high-radix…
Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…
We consider the problem of computing critical points of the restriction of a polynomial map to an algebraic variety. This is of first importance since the global minimum of such a map is reached at a critical point. Thus, these points…
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of $T/T^{\dagger}$-gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains 3 qubits. The…
We cryptanalyse here two variants of the McEliece cryptosystem based on quasi-cyclic codes. Both aim at reducing the key size by restricting the public and secret generator matrices to be in quasi-cyclic form. The first variant considers…
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our…
Despite their appealing flexibility, deep neural networks (DNNs) are vulnerable against adversarial examples. Various adversarial defense strategies have been proposed to resolve this problem, but they typically demonstrate restricted…
Deep hashing improves retrieval efficiency through compact binary codes, yet it introduces severe and often overlooked privacy risks. The ability to reconstruct original training data from hash codes could lead to serious threats such as…
Orthogonal and quasi-orthogonal matrices have a long history of use in digital image processing, digital and wireless communications, cryptography and many other areas of computer science and coding theory. The practical benefits of using…
We construct neural network regression models to predict key metrics of complexity for Gr\"obner bases of binomial ideals. This work illustrates why predictions with neural networks from Gr\"obner computations are not a straightforward…
In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gr\"obner basis, due to combinatorial properties of the polyomino itself. Moreover, we…