IEEE TRANSACTIONS ON COMPUTERS, VOL. ??, NO. ??, ??? A New Range-Reduction Algorithm N. Brisebarre, D. Defour, P. Kornerup, J.-M Muller and N. Revol

Source URL: perso.ens-lyon.fr

• Mathematics
• Algebra
• Abstract algebra
• Finite fields
• Field theory
• Angle
• Sine
• Factorial
• XTR
• Valuation
• Non-analytic smooth function
• Proof that is irrational

Certification of a Numerical Result: Use of Interval Arithmetic and Multiple Precision Hong Diep Nguyen and Nathalie Revol INRIA Universit´e de Lyon Laboratoire LIP (UMR 5668 CNRS - ENS Lyon - INRIA - UCBL)

Source URL: perso.ens-lyon.fr

• Numerical analysis
• Mathematics
• Applied mathematics
• Iterative refinement
• Iterative method
• Interval arithmetic
• Newton's method
• Condition number
• Residual
• Root-finding algorithm
• Affine arithmetic

On the Ring-LWE and Polynomial-LWE Problems Miruna Rosca1,2 , Damien Stehlé1 , and Alexandre Wallet1 1 ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL), France

Source URL: eprint.iacr.org

• Algebra
• Abstract algebra
• Mathematics
• Commutative algebra
• Lattice-based cryptography
• Post-quantum cryptography
• Cryptography
• Field theory
• Ring learning with errors
• Ring learning with errors key exchange
• Ring learning with errors signature

Formal Correctness of Comparison Algorithms between Binary64 and Decimal64 Floating-point Numbers Arthur Blot ENS Lyon, France NSV, July 22-23, 2017

Source URL: www.cs.ox.ac.uk

• Computer arithmetic
• Arithmetic
• Computing
• Binary arithmetic
• Theory of computation
• Data types
• IEEE standards
• Decimal64 floating-point format
• IEEE 754
• Double-precision floating-point format
• cole normale suprieure de Lyon
• Algorithm

On Computing the Resultant of Generic Bivariate Polynomials Gilles Villard Univ Lyon, CNRS, ENS de Lyon, Inria, Université Claude Bernard Lyon 1, LIP UMR 5668, FLyon, France ABSTRACT An algorithm is presented for

Source URL: perso.ens-lyon.fr

A New View on HJLS and PSLQ: Sums and Projections of Lattices Jingwei Chen†,‡ Chengdu Institute of Computer Application, CAS

Source URL: perso.ens-lyon.fr

• Algebra
• Mathematics
• Representation theory of Lie groups
• Lie algebras
• Matrix theory
• Spectral theory
• Lattice
• Weight
• Jordan normal form
• Spectral theory of ordinary differential equations

Publication list We list below the publications acknowledging Milyon. They are sorted by • Papers published in peer-reviewed journals extracted from Web of Science database and mentioning Milyon in the text. • Paper

Source URL: milyon.universite-lyon.fr

MATHEMATICS OF COMPUTATION Volume 81, Number 279, July 2012, Pages 1487–1511 SArticle electronically published on February 17, 2012 PERTURBATION ANALYSIS OF THE QR FACTOR R

Source URL: perso.ens-lyon.fr

• Algebra
• Mathematics
• Linear algebra
• Rank
• QR decomposition
• Matrix
• Determinant

Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits In memory of Wen-tsun Wu–Jean-Guillaume Dumas

Source URL: perso.ens-lyon.fr

Recent Progress in Linear Algebra and Lattice Basis Reduction Gilles Villard CNRS, ENS de Lyon, INRIA, UCBL, Université de Lyon Laboratoire LIP

Source URL: perso.ens-lyon.fr

• Mathematics
• Algebra
• Cryptography
• Computational number theory
• Lattice points
• Linear algebra
• Lattice-based cryptography
• Lattice reduction
• LenstraLenstraLovsz lattice basis reduction algorithm
• Hermite normal form
• Euclidean algorithm
• Integer relation algorithm