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IEEE Access, 2021 Polynomial-time attacks designed to run on quantum computers and capable of breaking RSA and AES are already known. It is imperative to develop quantum-resistant algorithms before quantum computers become available.
Ricardo Neftali Pontaza Rodas +3 more
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Higher-order topolectrical semimetal realized via synthetic gauge fields
APL Photonics, 2021 Classical bosonic systems may be tailored to support topological order and unidirectional edge transport exploiting gauge fields. Here, we theoretically explore how synthetic gauge fields may be used to induce higher-order topological phases and zero ...
Xiang Ni, Andrea Alù
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Bosonic double ring lattice under artificial gauge fields [PDF]
Physical Review A, 2018 We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete non-linear Schrödinger equations at mean field level. At varying inter-ring tunnel coupling, flux and interactions we identify the vortex, Meissner and biased ...
Victorin, Nicolas +2 more
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Security Impact Analysis of Degree of Field Extension in Lattice Attacks on Ring-LWE Problem
2023 IEEE 47th Annual Computers, Software, and Applications Conference (COMPSAC), 2023 accepted in COMPSAC 2023 Workshop DSML: The 1st IEEE International Workshop on Data Science & Machine Learning for Cybersecurity, IoT & Digital ...
Yuri Lucas Direbieski +5 more
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Constructions of Dense Lattices of Full Diversity
Trends in Computational and Applied Mathematics, 2020 A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions.
A. A. Andrade +3 more
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The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields [PDF]
Compositio Mathematica, 2016 For $n=3$ , $4 ...
Bhargava, Manjul, Harron, Piper
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Constructing lattice-ordered fields and division rings [PDF]
Bulletin of the Australian Mathematical Society, 1989 Neumann's totally ordered power series fields and division rings may be tipped over to form archimedean lattice-ordered fields and division rings. This process is described and then generalised to produce non-archimedean lattice-ordered fields and division rings in which 1 > 0 and, as well, ones in which 1 ≯ 0.
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Neutrosophic Multigroups and Applications
Mathematics, 2019 In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices.
Derya Bakbak +2 more
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Codes over rings of size
Finite Fields and Their Applications, 2010 Let $\ell>0$ be a square-free integer congruent to 3 mod 4 and $Ø_K$ the ring of integers of the imaginary quadratic field $K=Q(\sqrt{-\ell})$. Codes $C$ over rings $Ø_K / p Ø_K$ determine lattices $Λ_\ell (C) $ over $K$. If $ p \nmid \ell$ then the ring $\R:=Ø_K / p Ø_K$ is isomorphic to $\F_{p^2}$ or $\F_p \times \F_p$. Given a code $C$ over $\R$,
Tony Shaska, C. Shor, G. S. Wijesiri
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, 2022 A portion of the Muon g-2 Storage Ring electric system, which provides vertical beam focusing, exhibited an unexpected time dependence that produced a characteristic evolution of the stored beam during Run-1 of the Muon g-2 Experiment at Fermilab (E989).
Tarazona, David +8 more
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