J. Buchmann, Reducing lattice bases by means of approximations, Lecture Notes in Computer Science, vol.877, pp.160-168, 1994.
DOI : 10.1007/3-540-58691-1_54

J. J. Cannon and W. Bosma, « Handbook of Magma Functions, 2006.

X. Chang, D. Stehlé, and G. Villard, Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction, Mathematics of Computation, vol.81, issue.279, 2008.
DOI : 10.1090/S0025-5718-2012-02545-2
URL : https://hal.archives-ouvertes.fr/ensl-00529425

H. Cohen, A Course in Computational Algebraic Number Theory, 2ème édition, 1995.

Ú. Erlingsson, E. Kaltofen, and D. Musser, Generic Gram-Schmidt orthogonalization by exact division, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.275-282, 1996.
DOI : 10.1145/236869.237085
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.7908

L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, P. Zimmermann et al., a multiple-precision binary floating-point library with correct rounding, ACM Transactions on Mathematical Software, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00070266

N. Gama, N. Howgrave-graham, H. Koy, and P. Nguyen, « Rankin's Constant and Blockwise Lattice Reduction », Actes de la conférence Crypto, n?4117n?4117 in Lecture Notes in Computer Science, pp.112-130, 2006.
DOI : 10.1007/11818175_7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.415.2011

N. Gama and P. Nguyen, « Finding short lattice vectors within Mordell's inequality », Actes de la conférence STOC, pp.207-216, 2008.
DOI : 10.1145/1374376.1374408

G. Hanrot and «. Lll, LLL: A Tool for Effective Diophantine Approximation, 2008.
DOI : 10.1007/978-3-642-02295-1_6
URL : https://hal.archives-ouvertes.fr/inria-00187880

A. Hassibi and S. Boyd, Integer Parameter Estimation in Linear Models with Applications to GPS, IEEE Transactions on signal processing, vol.46, pp.11-11, 1998.

N. Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, 2002.
DOI : 10.1137/1.9780898718027

I. and «. Ieee, Standard 754-2008 for Floating-Point Arithmetic, 2008.

E. Kaltofen, On the complexity of finding short vectors in integer lattices, Lecture Notes in Computer Science, vol.162, pp.236-244, 1983.
DOI : 10.1007/3-540-12868-9_107

S. Khot, Hardness of approximating the shortest vector problem in lattices », Actes de la conférence FOCS, pp.126-135, 2004.

H. Koy and C. P. Schnorr, Segment LLL-Reduction of Lattice Bases, Actes de la conférence CALC'01, pp.67-80, 2001.
DOI : 10.1007/3-540-44670-2_7

H. Koy and C. P. Schnorr, Segment LLL-Reduction with Floating Point Orthogonalization, Actes de la conférence CALC'01, pp.81-96, 2001.
DOI : 10.1007/3-540-44670-2_8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.8677

B. A. Lamacchia, « Basis Reduction Algorithms and Subset Sum Problems, 1991.

A. K. Lenstra, L. H. Jr, and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.513-534, 1982.
DOI : 10.1007/BF01457454
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.318

A. May, Using LLL-Reduction for Solving RSA and Factorization Problems, 2008.
DOI : 10.1007/978-3-642-02295-1_10

R. Merkle and M. Hellman, Hiding information and signatures in trapdoor knapsacks, IEEE Transactions on Information Theory, vol.24, issue.5, pp.525-530, 1978.
DOI : 10.1109/TIT.1978.1055927

D. Micciancio and S. Goldwasser, Complexity of lattice problems: a cryptographic perspective, 2002.
DOI : 10.1007/978-1-4615-0897-7

I. Morel, D. Stehlé, and G. Villard, From an LLL-reduced basis to another, En préparation (Int. Symp. Symb. Alg. Comp. 2008 Poster presentation, 2008.
DOI : 10.1145/1504347.1504358
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.2519

W. H. Mow, Maximum likelihood sequence estimation from the lattice viewpoint, [Proceedings] Singapore ICCS/ISITA `92, pp.1591-1600, 1994.
DOI : 10.1109/ICCS.1992.254963

P. Nguyen, D. Stehlé, L. Floating-point, and . Revisited, Floating-Point LLL Revisited, Lecture Notes in Computer Science, vol.3494, pp.215-233, 2005.
DOI : 10.1007/11426639_13
URL : https://hal.archives-ouvertes.fr/inria-00000377

P. Nguyen, D. Stehlé, «. Lll-on-the-average, ». Actes-de-la-conférence, and A. Vii, LLL on the Average, Lecture Notes in Computer Science, vol.4076, pp.238-256, 2006.
DOI : 10.1007/11792086_18
URL : https://hal.archives-ouvertes.fr/hal-00107309

A. Novocin, Factoring univariate polynomials over the rationals, ACM SIGSAM Bulletin, vol.42, issue.3, 2008.
DOI : 10.1145/1504347.1504365

A. M. Odlyzko, Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's fast signature scheme, IEEE Transactions on Information Theory, vol.30, issue.4, pp.594-601, 1984.
DOI : 10.1109/TIT.1984.1056942

S. Oishi and M. Rump, Fast verification of solutions of matrix equations, Numerische Mathematik, pp.755-773, 2002.
DOI : 10.1007/s002110100310

X. Pujol and D. Stehlé, Rigorous and Efficient Short Lattice Vectors Enumeration, 2008.
DOI : 10.1007/BF01581144
URL : https://hal.archives-ouvertes.fr/hal-00550983

S. Rump, 10. Computer-Assisted Proofs and Self-Validating Methods, Handbook of Accuracy and Reliability in Scientific Computation, SIAM, pp.195-240, 2005.
DOI : 10.1137/1.9780898718157.ch10

S. Rump, Verification of Positive Definiteness, BIT Numerical Mathematics, vol.46, issue.2, pp.433-452, 2006.
DOI : 10.1007/s10543-006-0056-1

C. P. Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms, Theoretical Computer Science, vol.53, issue.2-3, pp.201-224, 1987.
DOI : 10.1016/0304-3975(87)90064-8

C. P. Schnorr, A more efficient algorithm for lattice basis reduction, Journal of Algorithms, vol.9, issue.1, pp.47-62, 1988.
DOI : 10.1016/0196-6774(88)90004-1

C. P. Schnorr, Fast LLL-type lattice reduction, Information and Computation, pp.1-25, 2006.
DOI : 10.1016/j.ic.2005.04.004
URL : http://doi.org/10.1016/j.ic.2005.04.004

C. P. Schnorr, « Hot Topics of LLL and lattice reduction, 2008.

C. P. Schnorr and M. Euchner, Lattice basis reduction: improved practical algorithms and solving subset sum problems, Mathematics of Programming, pp.181-199, 1994.
DOI : 10.1007/3-540-54458-5_51
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.3331

A. Schönhage, Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm, Lecture Notes in Computer Science, vol.172, pp.436-447, 1984.
DOI : 10.1007/3-540-13345-3_40

D. Stehlé, Algorithmique de la réduction de réseaux et application à la recherche de pires cas pour l'arrondi de fonctions mathématiques, 2005.

D. Stehlé, Floating-Point LLL: Theoretical and Practical Aspects, 2008.
DOI : 10.1007/978-3-642-02295-1_5

W. Stein and «. Sage, open source mathematics software, 2008.

A. Storjohann, Faster Algorithms for Integer Lattice Basis Reduction, Dpt. Comp. Sc, 1996.

J. Sun, Componentwise perturbation bounds for some matrix decompositions, BIT, vol.31, issue.2, pp.702-714, 1992.
DOI : 10.1007/BF01994852

M. Van-hoeij, Factoring Polynomials and 0???1 Vectors, Lecture Notes in Computer Science, vol.2146, pp.45-50, 2001.
DOI : 10.1007/3-540-44670-2_5

G. Villard, Certification of the QR factor R and of lattice basis reducedness, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.361-368, 2007.
DOI : 10.1145/1277548.1277597
URL : https://hal.archives-ouvertes.fr/hal-00127059

G. Villard, Certification of the QR Factor R, and of lattice basis reducedness, RR n?2007n?2007-03, 2007.