Publications related to Cyclotomic polynomial

Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

We consider Isogeometric Analysis (IGA) for the numerical solution of the electrophysiology of the atria, which in this work is modeled by means of the bidomain equations on thin surfaces. First, we consider the bidomain equations coupled with the Roger-Mc ...

ELSEVIER SCIENCE SA2019

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

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Jan Sickmann Hesthaven, Boris Bonev

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

2018

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

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

A novel technique is proposed for the simultaneous measurement of all three components of displacement from a single recording of the interference field in digital holographic interferometry. The interference field is divided into a number of rectangular s ...

Optical Soc Amer2015

TCHo: A Code-Based Cryptosystem

Serge Vaudenay, Alexandre Raphaël Duc

TCHo is a public-key cryptosystem based on the hardness of finding a multiple polynomial with low weight and on the hardness of distinguishing between the output of an LFSR with noise and some random source. An early version was proposed in 2006 by Finiasz ...

Springer Berlin Heidelberg2013

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Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

Arithmetic and geometric structures in cryptography

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Short Stickelberger Class Relations and Application to Ideal-SVP

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

On the discrete logarithm problem in finite fields of fixed characteristic

On The Exponent Of Distribution Of The Ternary Divisor Function

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

TCHo: A Code-Based Cryptosystem

TCHo: A Code-Based Cryptosystem

Isogeometric Analysis of the electrophysiology in the human heart: Numerical simulation of the bidomain equations on the atria

Arithmetic and geometric structures in cryptography

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Short Stickelberger Class Relations and Application to Ideal-SVP

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

On the discrete logarithm problem in finite fields of fixed characteristic

On The Exponent Of Distribution Of The Ternary Divisor Function