Related papers: Provably weak instances of Ring-LWE
Lattices have many significant applications in cryptography. In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem…
We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method…
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 deployment of large language models (LLMs) on third-party devices requires new ways to protect model intellectual property. While Trusted Execution Environments (TEEs) offer a promising solution, their performance limits can lead to a…
The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…
The Rank Decoding problem (RD) is at the core of rank-based cryptography. This problem can also be seen as a structured version of MinRank, which is ubiquitous in multivariate cryptography. Recently, \cite{BBBGNRT20,BBCGPSTV20} proposed…
Wireless sensor networks are vulnerable to several attacks, one of them being the black hole attack. A black hole is a malicious node that attracts all the traffic in the network by advertising that it has the shortest path in the network.…
Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the…
The Learning With Errors ($\mathsf{LWE}$) problem asks to find $\mathbf{s}$ from an input of the form $(\mathbf{A}, \mathbf{b} = \mathbf{A}\mathbf{s}+\mathbf{e}) \in (\mathbb{Z}/q\mathbb{Z})^{m \times n} \times…
Developers and organizations are using Large Language Models (LLMs) to generate security-critical code more frequently than ever, including cryptographic solutions for their products. This study presents an empirical evaluation of…
In this paper we study skew Poincar\'e-Birkhoff-Witt extensions over weak symmetric and $(\Sigma,\Delta)$-weak symmetry rings. Since these extensions generalize Ore extensions of injective type and another noncommutative rings of polynomial…
We investigate security properties of the Anshel-Anshel-Goldfeld commutator key-establishment protocol used with certain polycyclic groups. We show that despite low success of the length based attack the protocol can be broken by a…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Let $R$ be a ring. An $R$-module $M$ is said to be a weak $w$-projective module if ${\rm Ext}_R^1(M,N)=0$ for all $N \in \mathcal{P}_{w}^{\dagger_\infty}$ (see, \cite{FLQ}). In this paper, we introduce and study some properties of weak…
We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures…
Rank-metric code-based cryptography relies on the hardness of decoding a random linear code in the rank metric. The Rank Support Learning problem (RSL) is a variant where an attacker has access to N decoding instances whose errors have the…
The Longest Common Weakly Increasing Subsequence problem (LCWIS) is a variant of the classic Longest Common Subsequence problem (LCS). Both problems can be solved with simple quadratic time algorithms. A recent line of research led to a…
We consider the median procedure (Barthelemy and Monjardet, 1981) that aggregates a sequence n of binary relations from some input class into a single binary relation from some (possibly different) output class, minimizing the number of…
Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009)…
These lecture notes have been written for courses given at \'Ecole normale sup\'erieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general…