Related papers: An Algebraic Attack on Rank Metric Code-Based Cryp…
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems…
In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography. These applications raised…
Adversarial ranking attacks have gained increasing attention due to their success in probing vulnerabilities, and, hence, enhancing the robustness, of neural ranking models. Conventional attack methods employ perturbations at a single…
A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau's encryption scheme, based on rank-metric codes, for some parameters. The secret matrix component of Loidreau's scheme is chosen over a…
Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Faugere's F4 is a well-known Grobner bases algorithm to solve this problem. However, a serious drawback exists in the Grobner bases based…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
We introduce a new rank-based key encapsulation mechanism (KEM) with public key and ciphertext sizes around 3.5 Kbytes each, for 128 bits of security, without using ideal structures. Such structures allow to compress objects, but give…
The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on…
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of…
Post-Quantum Cryptography PQC attempts to find cryptographic protocols resistant to attacks using Shors polynomial time algorithm for numerical field problems or Grovers algorithm to find the unique input to a black-box function that…
We present a polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters.
Recently, $\alpha$-Rank, a graph-based algorithm, has been proposed as a solution to ranking joint policy profiles in large scale multi-agent systems. $\alpha$-Rank claimed tractability through a polynomial time implementation with respect…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes. When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose…
With the advancement of quantum computing, symmetric cryptography faces new challenges from quantum attacks. These attacks are typically classified into two models: Q1 (classical queries) and Q2 (quantum superposition queries). In this…
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…
Large Reasoning Models (LRMs) have advanced rapidly; however, existing benchmarks in mathematics, code, and common-sense reasoning remain limited. They lack long-context evaluation, offer insufficient challenge, and provide answers that are…
Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…
We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the…
The ring and polynomial learning with errors problems (Ring-LWE and Poly-LWE) have been proposed as hard problems to form the basis for cryptosystems, and various security reductions to hard lattice problems have been presented. So far…