M. Ajtai, -hard for randomized reductions (extended abstract), Proceedings of the thirtieth annual ACM symposium on Theory of computing , STOC '98, pp.284-293, 1998.
DOI : 10.1145/276698.276705

M. Ajtai and C. Dwork, A public-key cryptosystem with worst-case/average-case equivalence, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing , STOC '97, pp.284-293, 1997.
DOI : 10.1145/258533.258604

M. Ajtai, R. Kumar, and D. Sivakumar, A sieve algorithm for the shortest lattice vector problem, Proc. of STOC, pp.601-610, 2001.

Y. Arbitman, G. Dogon, V. Lyubashevsky, D. Micciancio, C. Peikert et al., SWIFFTX: a proposal for the SHA-3 standard, 2008.

D. Cadé, X. Pujol, and D. Stehlé, fplll -a floating-point LLL implementation

D. Cash, D. Hofheinz, E. Kiltz, and C. Peikert, Bonsai trees, or how to delegate a lattice basis, 2010.

J. H. Conway and N. J. Sloane, Sphere Packings, Lattices and Groups, 1988.

D. Coppersmith, Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities, Journal of Cryptology, vol.10, issue.4, pp.233-260, 1997.
DOI : 10.1007/s001459900030

. Van-dijk, C. Gentry, S. Halevi, and V. Vaikuntanathan, Fully Homomorphic Encryption over the Integers, 2010.
DOI : 10.1007/978-3-642-13190-5_2

U. Fincke and M. Pohst, A procedure for determining algebraic integers of given norm, Proc. of EUROCAL, pp.194-202, 1983.
DOI : 10.1007/3-540-12868-9_103

N. Gama and P. Q. Nguyen, Finding short lattice vectors within mordell's inequality, Proceedings of the fourtieth annual ACM symposium on Theory of computing, STOC 08, pp.207-216, 2008.
DOI : 10.1145/1374376.1374408

N. Gama, P. Q. Nguyen, and O. Regev, Lattice Enumeration Using Extreme Pruning, 2010.
DOI : 10.1007/978-3-642-13190-5_13

URL : https://hal.archives-ouvertes.fr/hal-01083526

C. Gentry, Fully homomorphic encryption using ideal lattices, Proceedings of the 41st annual ACM symposium on Symposium on theory of computing, STOC '09, pp.169-178, 2009.
DOI : 10.1145/1536414.1536440

C. Gentry, C. Peikert, and V. Vaikuntanathan, Trapdoors for hard lattices and new cryptographic constructions, Proceedings of the fourtieth annual ACM symposium on Theory of computing, STOC 08, pp.197-206, 2008.
DOI : 10.1145/1374376.1374407

O. Goldreich, S. Goldwasser, and S. Halevi, Public-key cryptosystems from lattice reduction problems, Proc. of CRYPTO, pp.112-131, 1997.
DOI : 10.1007/BFb0052231

D. Goldstein and A. Mayer, On the equidistribution of Hecke points, Forum Mathematicum, vol.15, issue.2, pp.165-189, 2003.
DOI : 10.1515/form.2003.009

Z. Guo and P. Nilsson, VLSI architecture of the soft-output sphere decoder for MIMO systems, Proc. of MWSCAS, pp.1195-1198, 2005.

G. Hanrot and D. Stehlé, Improved Analysis of Kannan???s Shortest Lattice Vector Algorithm, Proc. of CRYPTO, pp.170-186, 2007.
DOI : 10.1007/978-3-540-74143-5_10

J. Hermans, M. Schneider, J. Buchmann, F. Vercauteren, and B. Preneel, Parallel Shortest Lattice Vector Enumeration on Graphics Cards, Proc. of AFRICACRYPT. LNCS, pp.52-68, 2010.
DOI : 10.1007/978-3-642-12678-9_4

J. Hoffstein, J. Pipher, and J. H. Silverman, NTRU: A ring-based public key cryptosystem, Proc. of ANTS, pp.267-288, 1998.
DOI : 10.1007/BFb0054868

N. Howgrave-graham, A Hybrid Lattice-Reduction and Meet-in-the-Middle Attack Against NTRU, Proc. of CRYPTO, pp.150-169, 2007.
DOI : 10.1007/978-3-540-74143-5_9

R. Kannan, Improved algorithms for integer programming and related lattice problems, Proceedings of the fifteenth annual ACM symposium on Theory of computing , STOC '83, pp.99-108, 1983.
DOI : 10.1145/800061.808749

A. K. Lenstra, J. Lenstra, H. W. Lovász, and L. , Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982.
DOI : 10.1007/BF01457454

L. Lovász, An Algorithmic Theory of Numbers Magma: The Magma computational algebra system, cBMS-NSF Regional Conference Series in Applied Mathematics 26, 1986.

A. May, Using LLL-Reduction for Solving RSA and Factorization Problems, chapter, 2009.
DOI : 10.1007/978-3-642-02295-1_10

D. Micciancio and O. Regev, Lattice-based cryptography, pp.147-191, 2009.

D. Micciancio and P. Voulgaris, A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations, 2010.

D. Micciancio and P. Voulgaris, Faster exponential time algorithms for the shortest vector problem, Proc. of SODA, pp.1468-1480, 2010.
DOI : 10.1137/1.9781611973075.119

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. Q. Nguyen, B.V.: The LLL algorithm, survey and applications, Information Security and Cryptography, 2010.
URL : https://hal.archives-ouvertes.fr/in2p3-00945236

P. Q. Nguyen and D. Stehlé, Floating-Point LLL Revisited, Proc. of EUROCRYPT, pp.215-233, 2005.
DOI : 10.1007/11426639_13

URL : https://hal.archives-ouvertes.fr/inria-00000377

P. Q. Nguyen and D. Stehlé, LLL on the Average, Proc. of ANTS, pp.238-256, 2006.
DOI : 10.1007/11792086_18

URL : https://hal.archives-ouvertes.fr/hal-00107309

P. Q. Nguyen and J. Stern, Cryptanalysis of the Ajtai-Dwork cryptosystem, Proc. of CRYPTO, pp.223-242, 1998.
DOI : 10.1007/BFb0055731

P. Q. Nguyen and J. Stern, The two faces of lattices in cryptology, Proc. of CALC, pp.146-180, 2001.

P. Q. Nguyen and T. Vidick, Sieve algorithms for the shortest vector problem are practical, Journal of Mathematical Cryptology, vol.2, issue.2, 2008.
DOI : 10.1515/JMC.2008.009

A. M. Odlyzko, The rise and fall of knapsack cryptosystems, Proceedings of Cryptology and Computational Number Theory. Proceedings of Symposia in Applied Mathematics, pp.75-88, 1989.
DOI : 10.1090/psapm/042/1095552

C. Peikert, Public-key cryptosystems from the worst-case shortest vector problem, Proceedings of the 41st annual ACM symposium on Symposium on theory of computing, STOC '09, pp.333-342, 2009.
DOI : 10.1145/1536414.1536461

X. Pujol and D. Stehlé, Rigorous and Efficient Short Lattice Vectors Enumeration, Proc. ASIACRYPT. LNCS, pp.390-405, 2008.
DOI : 10.1007/BF01581144

URL : https://hal.archives-ouvertes.fr/hal-00550983

X. Pujol and D. Stehlé, Solving the shortest lattice vector problem in time 2 2.465n . Cryptology ePrint Archive, Report, vol.605, p.605, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00550976

O. Regev, Lattices in computer science lecture notes of a course given at the Tel Aviv University, 2004.

O. Regev, On lattices, learning with errors, random linear codes, and cryptography, Proc. of STOC, pp.84-93, 2005.

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 and M. Euchner, Lattice basis reduction: Improved practical algorithms and solving subset sum problems, Mathematical Programming, vol.13, issue.1, pp.181-199, 1994.
DOI : 10.1007/BF01581144

C. P. Schnorr and H. H. Hörner, Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction, Proc. of EUROCRYPT, pp.1-12, 1995.
DOI : 10.1007/3-540-49264-X_1

V. Shoup, NTL, Number Theory C++ Library

N. P. Smart and F. Vercauteren, Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes, 2010.
DOI : 10.1007/978-3-642-13013-7_25

D. Stehlé, R. Steinfeld, K. Tanaka, and K. Xagawa, Efficient Public Key Encryption Based on Ideal Lattices, Proc. of ASIACRYPT, pp.617-635, 2009.
DOI : 10.1007/978-3-642-10366-7_36

C. Studer, A. Burg, and H. Bölcskei, Soft-output sphere decoding: algorithms and VLSI implementation, IEEE Journal on Selected Areas in Communications, vol.26, issue.2, pp.290-300, 2008.
DOI : 10.1109/JSAC.2008.080206

E. Viterbo and J. Boutros, A universal lattice code decoder for fading channels, IEEE Transactions on Information Theory, vol.45, issue.5, pp.1639-1642, 1999.
DOI : 10.1109/18.771234

. Xilinx, Virtex-5 family overview