Related papers: Ring-LWE Cryptography for the Number Theorist

Let $P_k:= \mathbb F_2[x_1,x_2,\ldots,x_k]$ be the polynomial algebra over the prime field of two elements, $\mathbb F_2$, in $k$ variables $x_1, x_2, \ldots, x_k$, each of degree 1. We are interested in the Peterson hit problem of finding…

We show direct and conceptually simple reductions between the classical learning with errors (LWE) problem and its continuous analog, CLWE (Bruna, Regev, Song and Tang, STOC 2021). This allows us to bring to bear the powerful machinery of…

Backdoor learning has become an emerging research area towards building a trustworthy machine learning system. While a lot of works have studied the hidden danger of backdoor attacks in image or text classification, there is a limited…

The ever-growing big data and emerging artificial intelligence (AI) demand the use of machine learning (ML) and deep learning (DL) methods. Cybersecurity also benefits from ML and DL methods for various types of applications. These methods…

We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the…

The recent success of machine learning (ML) has been fueled by the increasing availability of computing power and large amounts of data in many different applications. However, the trustworthiness of the resulting models can be compromised…

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without too much technicality one can look for analytic solutions to Witten's open string field theory. This is an…

Much is known about the adele ring of an algebraic number field from the perspective of Harmonic Analysis and Class Field Theory. However, its ring-theoretical aspects are often ignored. Here we present a description of the prime spectrum…

The assumed hardness of the Linear Code Equivalence problem (LCE) lies at the core of the security of the LESS signature scheme and other signature schemes with advanced functionalities. The LCE problem asks to determine whether two linear…

We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.

Large language models (LLMs) remain vulnerable to a slew of adversarial attacks and jailbreaking methods. One common approach employed by white-hat attackers, or red-teamers, is to process model inputs and outputs using string-level…

Designing privacy-preserving deep learning models is a major challenge within the deep learning community. Homomorphic Encryption (HE) has emerged as one of the most promising approaches in this realm, enabling the decoupling of knowledge…

Large Language Models (LLMs) are increasingly popular, powering a wide range of applications. Their widespread use has sparked concerns, especially through jailbreak attacks that bypass safety measures to produce harmful content. In this…

In this paper we present an attack on a recently proposed code-based Private Information Retrieval (PIR) scheme. Indeed, the server can retrieve the index of the desired file with high probability in polynomial time. The attack relies on…

Split Learning (SL) is a collaborative learning approach that improves privacy by keeping data on the client-side while sharing only the intermediate output with a server. However, the distributed nature of SL introduces new security…

We associate to a semisimple complex Lie algebra $\mathfrak{g}$ a sequence of polynomials $P_{\ell,\mathfrak{g}}(x)\in\mathbb{Q}[x]$ in $r$ variables, where $r$ is the rank of $\mathfrak{g}$ and $\ell=0,1,2,\ldots $. The polynomials…

We give a precise description of how the class group of a number field measures the failure of unique factorization in its ring of integers. Specifically, following ideas of Kummer, we determine the structure of all irreducible…

We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended…

Secret sharing allows distributing a secret among several parties such that only authorized subsets, specified by an access structure, can reconstruct the secret. Sehrawat and Desmedt (COCOON 2020) introduced hidden access structures, that…