Related papers: Classical Hardness of Learning with Errors

We prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $\mathbb{Q}(\zeta_n)$ are not equivalent. Precisely, we show that reducing one problem to the other…

The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques,…

In this work, we study the solution of shortest vector problems (SVPs) arising in terms of learning with error problems (LWEs). LWEs are linear systems of equations over a modular ring, where a perturbation vector is added to the right-hand…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

Learning by examples, which learns to solve a new problem by looking into how similar problems are solved, is an effective learning method in human learning. When a student learns a new topic, he/she finds out exemplar topics that are…

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…

One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…

Arora & Ge introduced a noise-free polynomial system to compute the secret of a Learning With Errors (LWE) instance via linearization. Albrecht et al. later utilized the Arora-Ge polynomial model to study the complexity of Gr\"obner basis…

In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisentr\"ager-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] gives rise to…

We present a new perspective on the popular multi-class algorithmic techniques of one-vs-all and error correcting output codes. Rather than studying the behavior of these techniques for supervised learning, we establish a connection between…

This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…

When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the…

Large language models exhibit a puzzling inconsistency: they solve complex problems yet frequently fail on seemingly simpler ones. We investigate whether LLMs internally encode problem difficulty in a way that aligns with human judgment,…

Edge probing tests are classification tasks that test for grammatical knowledge encoded in token representations coming from contextual encoders such as large language models (LLMs). Many LLM encoders have shown high performance in EP…

Modern cryptographic methods for implementing privacy-preserving LLMs such as \gls{HE} require the LLMs to have a polynomial form. Forming such a representation is challenging because transformers include non-polynomial components, such as…

Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…

We propose a strong physical unclonable function (PUF) provably secure against machine learning (ML) attacks with both classical and quantum computers. Its security is derived from cryptographic hardness of learning decryption functions of…

Although encrypted control systems ensure confidentiality of private data, it is challenging to detect anomalies without the secret key as all signals remain encrypted. To address this issue, we propose a homomorphic encryption scheme for…

Recent advancements in Large Language Model (LLM) safety have primarily focused on mitigating attacks crafted in natural language or common ciphers (e.g. Base64), which are likely integrated into newer models' safety training. However, we…

Contrastive learning (CL) is a popular technique for self-supervised learning (SSL) of visual representations. It uses pairs of augmentations of unlabeled training examples to define a classification task for pretext learning of a deep…