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Concept

Root of unity

Related publications (21)

K3 surfaces, cyclotomic polynomials and orthogonal groups

Eva Bayer Fluckiger

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Revisiting Multivariate Ring Learning with Errors and Its Applications on Lattice-Based Cryptography

Juan Ramón Troncoso-Pastoriza

The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Ring Learning with Errors (RLWE), introducing efficiency improvements with respect to the RLWE counterpart thanks to its multivariate structure. Nevertheless, the rec ...

2021

Remarks on the derived center of small quantum groups

Anna Lachowska

Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on th ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Davide Pradovera

We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...

2020

Multiquadratic Rings and Walsh-Hadamard Transforms for Oblivious Linear Function Evaluation

Juan Ramón Troncoso-Pastoriza

The Ring Learning with Errors (RLWE) problem has become one of the most widely used cryptographic assumptions for the construction of modern cryptographic primitives. Most of these solutions make use of power-of-two cyclotomic rings mainly due to its simpl ...

IEEE2020

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Short Stickelberger Class Relations and Application to Ideal-SVP

Benjamin Pierre Charles Wesolowski

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...

Springer International Publishing Ag2017

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Jeanine Marie Van Order

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

2012

Low-strain interface models for epitaxial graphene on SiC(0001)

Alfredo Pasquarello, Gabriele Sclauzero

A set of low-strain commensurate interface structures for epitaxial graphene on SiC(0001) are obtained by combining rotated graphene supercells with m x m or m root 3 x m root 3R30 degrees SiC cells. For two among the interfaces with lowest strain, corresp ...

Elsevier2012

Terephthalic acid adsorption on Si(111)-(root 3x root 3)-Bi surfaces: Effect of Bi coverage

Klaus Kern

The influence of the density of metallic atoms on the formation of supramolecular structures onto Si surface alloys is investigated by scanning tunneling microscopy. Terephthalic acid (TPA) adsorption experiments are performed on the Si(111) alpha- and bet ...

2011

A high-reflectivity atom-focusing mirror stable at room temperature

It is shown that the Pb(root 3x root 3)R30/Si(111) ordered layer is an excellent mirror for neutral He atoms. It focuses more than 15% of the incoming He atoms into the specular peak, and is stable up to 450 K. Moreover, the reflectivity remains almost unc ...

American Institute of Physics2010

Explicit construction of self-dual integral normal bases for the square-root of the inverse different

Erik Jarl Pickett

Let K be a finite extension of Q(p), let L/K be a finite abelian Galois extension of odd degree and let D-L be the valuation ring of L. We define A(L/K) to be the unique fractional D-L-ideal with square equal to the inverse different of L/K. For p an odd p ...

2009

Assessing the atomic contribution to the Rashba spin-orbit splitting in surface alloys: Sb/Ag(111)

Klaus Kern, Marco Grioni, Luca Moreschini

We have studied the electronic structure of the Ag(111)(root 3x root 3)R30 degrees-Sb surface alloy by angle-resolved photoemission. We find two hybrid surface bands, similar to the isostructural Ag(111)-Bi interface. The spin-orbit coupling induced spin s ...

2009

Higher-Order Riesz Transforms And Steerable Wavelet Frames

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce an Nth-order extension of the Riesz transform in d dimensions. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing con ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

On the essential dimension of cyclic p-groups

Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have edℚ(ℤ/8ℤ)=4, a result which ...

Springer-Verlag2008

The link between the infinite mapping class group of the disk and the braid group on infinitely many strands

φ For all finite n ∈ N, there is a well-known isomorphism between the standard braid group Bn and the mapping class group π0Hn. This isomorphism has been exhaustively studied in literature, and generalized in many ways. For some basic topological reason, t ...

EPFL2008

Minimum euclidien des ordres maximaux dans les algèbres centrales à division

Jérôme Chaubert

This work concerns the study of Euclidean minima of maximal orders in central simple algebras. In the first part, we define the concept of ideal lattice in the non-commutative case. Let A be a semi-simple algebra over Q. An ideal lattice over A is a triple ...

EPFL2007

Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

2006

Discrete logarithm variants of VSH

Arjen Lenstra, Martijn Stam

Recent attacks on standardised hash functions such as SHA1 have reawakened interest in design strategies based on techniques common in provable security. In presenting the VSH hash function, a design based on RSA-like modular exponentiation, the authors in ...

2006