Related papers: On Ring Learning with Errors over the Tensor Produ…

The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often…

The Learning with Errors (\LWE) problem has been widely utilized as a foundation for numerous cryptographic tools over the years. In this study, we focus on an algebraic variant of the \LWE problem called \emph{Group ring} \LWE ($\GRLWE$).…

Lattice-based cryptography is a foundation for post-quantum security, with the Learning with Errors (LWE) problem as a core component in key exchange, encryption, and homomorphic computation. Structured variants like Ring-LWE (RLWE) and…

We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems, even with polynomial modulus. Previously this was only known under quantum reductions. Our techniques capture the…

The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms…

Multidimensional signals like 2-D and 3-D images or videos are inherently sensitive signals which require privacy-preserving solutions when processed in untrustworthy environments, but their efficient encrypted processing is particularly…

As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to quantum attacks is paramount. Some leading candidate cryptosystems use the Learning with Errors (LWE) problem, attractive for its…

The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and…

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…

Recent work showed that ML-based attacks on Learning with Errors (LWE), a hard problem used in post-quantum cryptography, outperform classical algebraic attacks in certain settings. Although promising, ML attacks struggle to scale to more…

In this work, we unveil an analogy between well-known lattice based learning with error problem and ill-posed inverse problems. We show that LWE problem is a structured inverse problem. Further, we propose a symmetric encryption scheme…

Some hard problems from lattices, like LWE (Learning with Errors), are particularly suitable for application in Cryptography due to the possibility of using worst-case to average-case reductions as evidence of strong security properties. In…

We introduce a continuous analogue of the Learning with Errors (LWE) problem, which we name CLWE. We give a polynomial-time quantum reduction from worst-case lattice problems to CLWE, showing that CLWE enjoys similar hardness guarantees to…

The Ring Learning-With-Errors (RLWE) problem shows great promise for post-quantum cryptography and homomorphic encryption. We describe a new attack on the non-dual search RLWE problem with small error widths, using ring homomorphisms to…

The Learning with Errors (LWE) problem is a hard math problem in lattice-based cryptography. In the simplest case of binary secrets, it is the subset sum problem, with error. Effective ML attacks on LWE were demonstrated in the case of…

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…

At ASIACRYPT 2018, a digital attack based on linear least squares was introduced for a variant of the learning with errors (LWE) problem which omits modular reduction known as the integer learning with errors problem (ILWE). In this paper,…

Modern information communications use cryptography to keep the contents of communications confidential. RSA (Rivest-Shamir-Adleman) cryptography and elliptic curve cryptography, which are public-key cryptosystems, are widely used…

Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures. Prior work proposed new machine learning (ML)-based attacks on LWE problems…

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…