Related papers: A new Hybrid Lattice Attack on Galbraith's Binary …
Due to the rapid advances in the development of quantum computers and their susceptibility to errors, there is a renewed interest in error correction algorithms. In particular, error correcting code-based cryptosystems have reemerged as a…
Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
Lattice Boltzmann method (LBM) is a promising approach to solving Computational Fluid Dynamics (CFD) problems, however, its nature of memory-boundness limits nearly all LBM algorithms' performance on modern computer architectures. This…
We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has…
Federated learning is a method used in machine learning to allow multiple devices to work together on a model without sharing their private data. Each participant keeps their private data on their system and trains a local model and only…
Weber's conjecture (1886) governs three aspects of lattice-based cryptography: the solvability of the Principal Ideal Problem, the freeness of modules over rings of integers, and the tightness of worst-case-to-average-case reductions in…
We present an efficient reduction from the Bounded integer programming (BIP) to the Subspace avoiding problem (SAP) in lattice theory. The reduction has some special properties with some interesting consequences. The first is the new upper…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Homomorphic encryption (HE) offers data confidentiality by executing queries directly on encrypted fields in the database-as-a-service (DaaS) paradigm. While fully HE exhibits great expressiveness but prohibitive performance overhead, a…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
Many modern applications that deal with sensitive data, such as healthcare and government services, outsource computation to cloud platforms. In such untrusted environments, privacy is of vital importance. One solution to this problem is…
We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asymptotic formula, where its main term coincides with the full…
Shor's algorithm contains a classical post-processing part for which we aim to create an efficient, understandable method aside from continued fractions. Let r be an unknown positive integer. Assume that with some constant probability we…
Homomorphic encryption (HE) is a promising cryptographic technique for enabling secure collaborative machine learning in the cloud. However, support for homomorphic computation on ciphertexts under multiple keys is inefficient. Current…
The imminent threat of quantum computing necessitates quantum-resistant cryptosystems. This paper establishes tight security bounds for two NIST PQC finalists: SPHINCS+ (hash-based) and NTRU (lattice-based). Our key contributions include:…
By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehl\'{e}, we obtain improved asymptotic quantum results for solving the shortest vector…
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the…
As machine learning (ML) models become increasingly deployed through cloud infrastructures, the confidentiality of user data during inference poses a significant security challenge. Homomorphic Encryption (HE) has emerged as a compelling…