RLWE and PLWE over cyclotomic fields are not equivalent

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 increases the noise by a factor that is more than polynomial in $n$. We do so by providing a lower bound, holding for infinitely many positive integers $n$, for the condition number of the Vandermonde matrix of the $n$th cyclotomic polynomial

Lattice-Based proof of a shuffle

In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft

Approximate Voronoi cells for lattices, revisited

We revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis-Laarhoven-De Weger [PQCrypto, 2019] of determining exact asymptotics on the volume of these Voronoi cells under the Gaussian heuristic. As a result, we obtain improved upper bounds on the time complexity of the randomized iterative slicer when using less than $2^{0.076d + o(d)}$ memory, and we show how to obtain time-memory trade-offs even when using less than $2^{0.048d + o(d)}$ memory. We also settle the open problem of obtaining a continuous trade-off between the size of the advice and the query time complexity, as the time complexity with subexponential advice in our approach scales as $d^{d/2 + o(d)}$, matching worst-case enumeration bounds, and achieving the same asymptotic scaling as average-case enumeration algorithms for the closest vector problem.Comment: 18 pages, 1 figur

A Homomorphic Encryption Framework for Privacy-Preserving Spiking Neural Networks

Machine learning (ML) is widely used today, especially through deep neural networks (DNNs); however, increasing computational load and resource requirements have led to cloud-based solutions. To address this problem, a new generation of networks has emerged called spiking neural networks (SNNs), which mimic the behavior of the human brain to improve efficiency and reduce energy consumption. These networks often process large amounts of sensitive information, such as confidential data, and thus privacy issues arise. Homomorphic encryption (HE) offers a solution, allowing calculations to be performed on encrypted data without decrypting them. This research compares traditional DNNs and SNNs using the Brakerski/Fan-Vercauteren (BFV) encryption scheme. The LeNet-5 and AlexNet models, widely-used convolutional architectures, are used for both DNN and SNN models based on their respective architectures, and the networks are trained and compared using the FashionMNIST dataset. The results show that SNNs using HE achieve up to 40% higher accuracy than DNNs for low values of the plaintext modulus t, although their execution time is longer due to their time-coding nature with multiple time steps

LNCS

We extend a commitment scheme based on the learning with errors over rings (RLWE) problem, and present efficient companion zeroknowledge proofs of knowledge. Our scheme maps elements from the ring (or equivalently, n elements fro