Related papers: LWE from Non-commutative Group Rings

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…

Our main result is a quantum public-key encryption scheme based on the Extrapolated Dihedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number…

The shortest vector problem (SVP) over ideal lattices is closely related to the Ring-LWE problem, which is widely used to build post-quantum cryptosystems. Power-of-two cyclotomic fields are frequently adopted to instantiate Ring-LWE. Pan…

The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the three cryptosystems standardized in August 2024 by the National Institute of Standards and Technology to replace non-quantum resistant current…

Currently deployed public-key cryptosystems will be vulnerable to attacks by full-scale quantum computers. Consequently, "quantum resistant" cryptosystems are in high demand, and lattice-based cryptosystems, based on a hard problem known as…

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,…

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round…

The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model 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…

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…

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus,…

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…

This paper introduces a privacy-preserving distributed learning framework via private-key homomorphic encryption. Thanks to the randomness of the quantization of gradients, our learning with error (LWE) based encryption can eliminate the…

In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller…

Learning with Errors (LWE) is a hard math problem used in post-quantum cryptography. Homomorphic Encryption (HE) schemes rely on the hardness of the LWE problem for their security, and two LWE-based cryptosystems were recently standardized…

Sparse binary LWE secrets are under consideration for standardization for Homomorphic Encryption and its applications to private computation. Known attacks on sparse binary LWE secrets include the sparse dual attack and the hybrid sparse…

We construct a strong PUF with provable security against ML attacks on both classical and quantum computers. The security is guaranteed by the cryptographic hardness of learning decryption functions of public-key cryptosystems, and the…

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 present a quantum attack on ML-KEM and related 2-power cyclotomic lattice schemes. Combining with Parts I-III, we provide an algorithm and verify the resulting approximation factor satisfies $\gamma\le 21 < q/2=1664.5$ for ML-KEM-1024,…

This study proposes post-quantum encrypted control systems based on dynamic-key Learning with Errors (LWE) encryption schemes. The proposed method develops update maps that simultaneously update the private key and ciphertexts within the…