Réseaux Euclidiens et Algorithmique, une liste de références

Réseaux et Algorithmique des Nombres

Retour à la page principale

Factorisation des polynômes:

Polynomial Factorization and Nonrandomness of Bits of Algebraic and Some Transcendental Numbers, STOC 1984, Kannan R. and Lenstra A. and Lovász L. (1984)
Factoring Polynomials and the Knapsack Problem, Van Hoeij M. (2001)

Racines de polynômes modulaires:

How to Guess l-th Roots Modulo n by Reducing Lattice Bases, AAECC, Girault M. and Toffin P. and Vallée B. (1988)
Computation of Approximate L-th Roots Modulo n and Application to Cryptography, CRYPTO 1988, Girault M. and Toffin P. and Vallée B. (1988)
Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known, Coppersmith D. (1996)
Finding a Small Root of a Univariate Modular Equation, Coppersmith D. (1996)
Finding Small Roots of Univariate Modular Equations Revisited, IMA Int. Conf., Howgrave-Graham N. (1997)
Finding Small Solutions to Small Degree Polynomials, Coppersmith D. (2001)

Factorisation des entiers:

Provably Fast Integer Factoring with Quasi-Uniform Small Quadratic Residues, STOC 1989, Vallée B. (1989)
Factoring Integers and Computing Discrete Logarithms via Diophantine Approximation, Schnorr C.P. (1993)
Factoring via Strong Lattice Reduction Algorithm, Ritter H. and Rössner C. (1997)
Factoring N=prq for large r , Boneh D. and Durfee G. and Howgrave-Graham N. (1999)

Équations linéaires a coefficients entiers:

Solving Simultaneous Modular Equations of Low Degree, Håstad J. (1988)
Polynomial Time algorithms for Finding Integer Relations among real Numbers, SIAM Journal on Computing, Vol.18, Håstad J. and Just B. and Lagarias J. and Schnorr C.P. (1989)
Solving a Linear Diophantine Equation with Lower and Upper Bounds on the Variables, Aardal K. and Hurkens C. and Lenstra A. (1998)
Hard Equality Constrained Integer Knapsacks, Lenstra A. and Aardal K. (2002)

Restes Chinois:

Autres:

Disproof of the Mertens conjecture, Odlyzko A. and te Riele H. (1985)
Lattice sieving and trial division, ANTS 1994, Golliver G. and Lenstra A. and MacCurley K. (1994)
Determining the small solutions to S-unit equations, Smart N.P. (1997)
Rational Points Near Curves and Small Nonzero |x3-y2| via Lattice Reduction, Elkies N.D. (1998)
Approximate Integer Common Divisors , Howgrave-Graham N. (2001)
Worst cases and lattice reduction , Stehlé D. and Lefèvre V. and Zimmermann P. (2003)

Dernière mise à jour le 31/10/2003. Page maintenue par Damien Stehlé: damien.stehle@loria.fr