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» Bounds for Real Roots and Applications to Orthogonal Polynom...
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TCS
2008
13 years 8 months ago
On the complexity of real root isolation using continued fractions
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algeb...
Elias P. Tsigaridas, Ioannis Z. Emiris
PKC
2010
Springer
138views Cryptology» more  PKC 2010»
14 years 11 days ago
Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA
We present an elementary method to construct optimized lattices that are used for finding small roots of polynomial equations. Former methods first construct some large lattice i...
Mathias Herrmann, Alexander May
AISC
2006
Springer
14 years 5 days ago
An Algorithm for Computing the Complete Root Classification of a Parametric Polynomial
Abstract. The Complete Root Classification for a univariate polynomial with symbolic coefficients is the collection of all the possible cases of its root classification, together w...
Songxin Liang, David J. Jeffrey
ESA
2001
Springer
61views Algorithms» more  ESA 2001»
14 years 28 days ago
A Separation Bound for Real Algebraic Expressions
Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for int...
Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, S...
EUROCRYPT
2005
Springer
14 years 1 months ago
A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers
We present a new and flexible formulation of Coppersmith’s method for finding small solutions of bivariate polynomials p(x, y) over the integers. Our approach allows to maximiz...
Johannes Blömer, Alexander May