Related papers: An Algebraic Attack on Rank Metric Code-Based Cryp…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
The McEliece scheme is a generic frame which allows to use any error correcting code of which there exists an efficient decoding algorithm to design an encryption scheme by hiding the generator matrix code. Similarly, the Niederreiter frame…
The subset cover problem for $k \geq 1$ hash functions, which can be seen as an extension of the collision problem, was introduced in 2002 by Reyzin and Reyzin to analyse the security of their hash-function based signature scheme HORS. The…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…
In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate…
The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for…
We present some new and recent algorithmic results concerning polynomial system solving over various rings. In particular, we present some of the best recent bounds on: (a) the complexity of calculating the complex dimension of an algebraic…
Modern analyst agents must reason over complex, high token inputs, including dozens of retrieved documents, tool outputs, and time sensitive data. While prior work has produced tool calling benchmarks and examined factuality in knowledge…
Adversarial prompts generated using gradient-based methods exhibit outstanding performance in performing automatic jailbreak attacks against safety-aligned LLMs. Nevertheless, due to the discrete nature of texts, the input gradient of LLMs…
In the \textsc{Maximum Degree Contraction} problem, input is a graph $G$ on $n$ vertices, and integers $k, d$, and the objective is to check whether $G$ can be transformed into a graph of maximum degree at most $d$, using at most $k$ edge…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
Most problems in Machine Learning cater to classification and the objects of universe are classified to a relevant class. Ranking of classified objects of universe per decision class is a challenging problem. We in this paper propose a…
Arithmetic circuit complexity studies the complexity of computing polynomials using only arithmetic operations such as addition, multiplication, subtraction, and division. Polynomials over rings of integers model counting problems.…
In parameterized complexity, it is a natural idea to consider different generalizations of classic problems. Usually, such generalization are obtained by introducing a "relaxation" variable, where the original problem corresponds to setting…
A critical problem in the emerging high-throughput genotyping protocols is to minimize the number of polymerase chain reaction (PCR) primers required to amplify the single nucleotide polymorphism loci of interest. In this paper we study PCR…
The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum…
With the boom of Large Language Models (LLMs), the research of solving Math Word Problem (MWP) has recently made great progress. However, there are few studies to examine the security of LLMs in math solving ability. Instead of attacking…
As Large Language Models (LLMs) are widely used, understanding them systematically is key to improving their safety and realizing their full potential. Although many models are aligned using techniques such as reinforcement learning from…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…