相关论文: Gr\"obner Basis Cryptanalysis of Ciminion and Hydr…

A new version of the Graeffe algorithm for finding all the roots of univariate complex polynomials is proposed. It is obtained from the classical algorithm by a process analogous to renormalization of dynamical systems. This iteration is…

The restarted primal-dual hybrid gradient method (rPDHG) is a first-order method that has recently received significant attention for its computational effectiveness in solving linear program (LP) problems. Despite its impressive practical…

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.…

Large-degree polynomial multiplication is an integral component of post-quantum secure lattice-based cryptographic algorithms like CRYSTALS-Kyber and Dilithium. The computational complexity of large-degree polynomial multiplication can be…

Deep Neural Networks (DNN) applications are increasingly becoming a part of our everyday life, from medical applications to autonomous cars. Traditional validation of DNN relies on accuracy measures, however, the existence of adversarial…

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes…

The Legendre Pseudorandom Function (PRF) is a highly efficient cryptographic primitive built upon the Legendre symbol, valued for its low multiplicative complexity in Multi-Party Computation (MPC) and Zero-Knowledge Proof (ZKP) protocols.…

In this article explicit formulas for the recurrence equation p_{n+1}(x) = (A_n x + B_n) p_n(x) - C_n p_{n-1}(x) and the derivative rules sigma(x) p'_n(x) = alpha_n p_{n+1}(x) + beta_n p_n(x) + gamma_n p_{n-1}(x) and sigma(x) p'_n(x) =…

We present a concrete oracle construction for bilinear Diophantine equations of the form $f(x,y) = Axy + Bx + Cy + D$, together with its application as a scalable, hardware-agnostic benchmark for digital quantum computers. The oracle can be…

Side-channel analysis attacks, especially horizontal DPA and DEMA attacks, are significant threats for cryptographic designs. In this paper we investigate to which extend different multiplication formulae and randomization of the field…

In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of…

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

Federated Learning (FL) in 5G and edge network environments face severe security threats from adversarial clients. Malicious participants can perform label flipping, inject backdoor triggers, or launch Sybil attacks to corrupt the global…

Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…

We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…

There has been recent interest in the deployment of ab initio density matrix renormalization group computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio…

In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe in the new results an approach to attacking a RSA-type modulus based on continued fractions, independent…

We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…

Large language models (LLMs) are increasingly used to assist developers with code, yet their implementations of cryptographic functionality often contain exploitable flaws. Minor design choices (e.g., static initialization vectors or…

Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present…