Ajtai : Les entrées " grands, p.125 ,
129 6.2.3 Structure générale des réseaux uni-tas cryptographiques ,
133 6.3.1 Réseaux de Coppermith à une variable, p.134 ,
135 6.3.4 Indépendance des blocs des cfg 137 6.3.5 Nombre d'itérations dans le cas des réseaux de Coppersmith vérifiant la condition d'indépendance, p.138 ,
Lattice problems in NP ??? coNP, Journal of the ACM, vol.52, issue.5, pp.749-765, 2005. ,
DOI : 10.1145/1089023.1089025
Generating hard instances of lattice problems (extended abstract), Proceedings of the twenty-eighth annual ACM symposium on Theory of computing , STOC '96, pp.99-108, 1996. ,
DOI : 10.1145/237814.237838
-hard for randomized reductions (extended abstract), Proceedings of the thirtieth annual ACM symposium on Theory of computing , STOC '98, pp.10-19, 1998. ,
DOI : 10.1145/276698.276705
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
Sampling short lattice vectors and the closest lattice vector problem, Proceedings 17th IEEE Annual Conference on Computational Complexity, pp.53-76, 2002. ,
DOI : 10.1109/CCC.2002.1004339
Random lattices, threshold phenomena and efficient reduction algorithms, Theoretical Computer Science, vol.287, issue.2, pp.359-385, 2002. ,
DOI : 10.1016/S0304-3975(01)00251-1
The optimal LLL algorithm is still polynomial in fixed dimension, Theoretical Computer Science, vol.297, issue.1-3, pp.1-3, 2003. ,
DOI : 10.1016/S0304-3975(02)00616-3
On the reduction of a random basis, ANALCO, pp.265-270, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00022848
Average Bit-Complexity of Euclidean Algorithms, ICALP (2000), pp.373-387 ,
DOI : 10.1007/3-540-45022-X_32
noise, Physical Review Letters, vol.59, issue.4, pp.381-384, 1987. ,
DOI : 10.1103/PhysRevLett.59.381
Euclidean algorithms are gaussian. CoRR cs, p.307062, 2003. ,
DOI : 10.1016/j.jnt.2004.08.008
URL : https://hal.archives-ouvertes.fr/hal-00012771
Cryptanalysis of RSA with Private Key d Less than N 0.292, IEEE Transactions on Information Theory, vol.46, issue.66, pp.1339-1349, 2000. ,
DOI : 10.1007/3-540-48910-X_1
Dynamical analysis of ??-Euclidean algorithms, Journal of Algorithms, vol.44, issue.1, pp.246-285, 2002. ,
DOI : 10.1016/S0196-6774(02)00218-3
URL : https://hal.archives-ouvertes.fr/hal-00442421
Fully homomorphic encryption without bootstrapping, Electronic Colloquium on Computational Complexity (ECCC), vol.18, pp.111-54, 2011. ,
DOI : 10.1145/2090236.2090262
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.456.1531
Classical hardness of learning with errors, Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, STOC '13, pp.575-584 ,
DOI : 10.1145/2488608.2488680
URL : https://hal.archives-ouvertes.fr/hal-00922194
Ecient fully homomorphic encryption from (standard) LWE, FOCS (2011), pp.97-106 ,
DOI : 10.1109/focs.2011.12
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.6463
Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages, CRYPTO (2011), pp.505-524 ,
DOI : 10.1007/978-3-642-22792-9_29
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.4811
The densest lattice in twenty-four dimensions, Electron. Res. Announc. Am. Math. Soc, vol.10, pp.408174-58, 2004. ,
Finding a Small Root of a Univariate Modular Equation, pp.155-165, 1996. ,
DOI : 10.1007/3-540-68339-9_14
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
Lattice Attacks on NTRU, EUROCRYPT, pp.52-61, 1997. ,
DOI : 10.1007/3-540-69053-0_5
Improved low-density subset sum algorithms, Computational Complexity, vol.9, issue.1, pp.111-128, 1992. ,
DOI : 10.1007/BF01201999
The Design of Rijndael : AES -The Advanced Encryption Standard, 2002. ,
DOI : 10.1007/978-3-662-04722-4
The Lyapunov tortoise and the dyadic hare, AD of DMTCS Proceedings, Discrete Mathematics and Theoretical Computer Science, pp.71-94, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-01184044
Dynamical Analysis of the Parametrized Lehmer???Euclid Algorithm, Combinatorics, Probability and Computing, vol.13, issue.4-5, pp.4-5, 2004. ,
DOI : 10.1017/S0963548304006261
An Average-Case Analysis of the Gaussian Algorithm for Lattice Reduction, Combinatorics, Probability and Computing, vol.6, issue.4, pp.397-433, 1997. ,
DOI : 10.1017/S0963548397003258
An upper bound on the average number of iterations of the LLL algorithm, Theoretical Computer Science, vol.123, issue.1, pp.95-115, 1994. ,
DOI : 10.1016/0304-3975(94)90071-X
New directions in cryptography, IEEE Transactions on Information Theory, vol.22, issue.6, pp.644-654, 1976. ,
DOI : 10.1109/TIT.1976.1055638
Sur le nombre de divisions à eectuer pour obtenir le plus grand commun diviseur entre deux nombres entiers, Journal de Mathématiques Pures et Appliquées, vol.11, pp.41-74, 1846. ,
Partial Key Exposure Attacks on RSA up to Full Size Exponents, CRYPTO 2005, pp.371-386, 2005. ,
DOI : 10.1007/11426639_22
A procedure for determining algebraic integers of given norm, In EUROCAL, pp.194-202, 1983. ,
DOI : 10.1007/3-540-12868-9_103
Finding short lattice vectors within mordell's inequality Predicting lattice reduction, STOCCité pages 10 et 24.) [34] Gama EUROCRYPT, pp.207-216, 2008. ,
DOI : 10.1145/1374376.1374408
A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, vol.31, issue.52, pp.469-472, 1985. ,
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
Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp.107-109 ,
DOI : 10.1109/FOCS.2011.94
Fully Homomorphic Encryption with Polylog Overhead, EUROCRYPT (2012), pp.465-482 ,
DOI : 10.1007/978-3-642-29011-4_28
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
On the Limits of Nonapproximability of Lattice Problems, Journal of Computer and System Sciences, vol.60, issue.3, pp.540-563, 2000. ,
DOI : 10.1006/jcss.1999.1686
Eliminating decryption errors in the Ajtai-Dwork Cryptosystem, Advances in Cryptology -CRYPTO 97 17th Annual International Cryptology Conference, pp.105-111, 1997. ,
DOI : 10.1007/BFb0052230
Public-key cryptosystems from lattice reduction problems, CRYPTO, pp.112-131, 1997. ,
DOI : 10.1007/BFb0052231
Games on line graphs and sand piles, Theoretical Computer Science, vol.115, issue.2 ,
DOI : 10.1016/0304-3975(93)90122-A
URL : http://doi.org/10.1016/0304-3975(93)90122-a
Improved Analysis of Kannan???s Shortest Lattice Vector Algorithm, Proceedings of the 27th annual international cryptology conference on Advances in cryptology CRYPTO'07, pp.170-186, 2007. ,
DOI : 10.1007/978-3-540-74143-5_10
Solving Simultaneous Modular Equations of Low Degree, SIAM Journal on Computing, vol.17, issue.2, pp.336-341, 1988. ,
DOI : 10.1137/0217019
The Number of Steps in the Euclidean Algorithm, Journal of Number Theory, vol.49, issue.2, pp.49-149, 1994. ,
DOI : 10.1006/jnth.1994.1088
OEuvres : Publiées sous les auspices de l, Académie des Sciences, vol.1, issue.27, p.9, 1905. ,
NTRU: A ring-based public key cryptosystem, ANTS, pp.267-288, 1998. ,
DOI : 10.1007/BFb0054868
Finding small roots of univariate modular equations revisited, 1997. ,
DOI : 10.1007/BFb0024458
Self-organized criticality. Cambridge Lecture Notes in Physics Emergent complex behavior in physical and biological systems, 1998. ,
Improved algorithms for integer programming and related lattice problems, Proceedings of the fifteenth annual ACM symposium on Theory of computing , STOC '83, pp.193-206, 1983. ,
DOI : 10.1145/800061.808749
Reducibility among combinatorial problems, In Complexity of Computer Computations, pp.85-103, 1972. ,
DOI : 10.1007/978-3-540-68279-0_8
Perturbation Theory for Linear Operators, 1980. ,
Introduction to the Modern Theory of Dynamical Systems, 1995. ,
DOI : 10.1017/CBO9780511809187
Hardness of approximating the shortest vector problem in lattices, FOCS, pp.126-135, 2004. ,
Elliptic curve cryptosystems, Mathematics of Computation, vol.48, issue.177, pp.203-209, 1987. ,
DOI : 10.1090/S0025-5718-1987-0866109-5
Sur les formes quandratiques, Mathematishe Annalen, vol.6, issue.26, pp.336-389, 1873. ,
DOI : 10.1007/bf01442795
Worst-case complexity bounds for algorithms in the theory of integral quadratic forms, Journal of Algorithms, vol.1, issue.2, pp.142-186, 1980. ,
DOI : 10.1016/0196-6774(80)90021-8
The computational complexity of simultaneous diophantine approximation problems, FOCS, pp.32-39, 1982. ,
Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice, Combinatorica, vol.96, issue.4 (208), pp.4-333, 1990. ,
DOI : 10.1007/BF02128669
Solving low-density subset sum problems, Journal of the ACM, vol.32, issue.1, pp.229-246, 1985. ,
DOI : 10.1145/2455.2461
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.7057
Recherches d'arithmétiques. In Nouveaux mémoires de l'Académie royale des sciences et des belles-lettres de Berlin, pp.1773-1775 ,
Distribution de la constante d'Hermite et du plus court vecteur dans les r??seaux de dimension deux, Journal de Th??orie des Nombres de Bordeaux, vol.6, issue.1, pp.135-159, 1994. ,
DOI : 10.5802/jtnb.110
Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982. ,
DOI : 10.1007/BF01457454
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.318
Integer Programming with a Fixed Number of Variables, Mathematics of Operations Research, vol.8, issue.4, pp.538-548, 1983. ,
DOI : 10.1287/moor.8.4.538
Flags and lattice basis reduction, pp.37-52, 2001. ,
Gaussian Laws for the Main Parameters of the Euclid Algorithms, Algorithmica, vol.15, issue.1, pp.497-554, 2008. ,
DOI : 10.1007/s00453-007-9009-6
URL : https://hal.archives-ouvertes.fr/hal-00207680
An algorithmic theory of numbers, graphs and convexity, CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.50, pp.10-23, 1986. ,
DOI : 10.1137/1.9781611970203
On Ideal lattices and Learning with Errors over Rings, EUROCRYPT (2010), pp.1-23 ,
DOI : 10.1007/978-3-642-13190-5_1
URL : https://hal.archives-ouvertes.fr/hal-00921792
Modelling the LLL Algorithm by Sandpiles, Proceedings of the 9th Latin American conference on Theoretical Informatics et 126.) [72] Mahler, K. A theorem on inhomogeneous diophantine inequalities. Nederl. Akad. Wetensch ., Proc, pp.267-281, 1938. ,
DOI : 10.1007/978-3-642-12200-2_25
URL : https://hal.archives-ouvertes.fr/hal-01082028
Perfect lattices in Euclidean spaces Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 2003. ,
Using LLL-Reduction for Solving RSA and Factorization Problems, The LLL Algorithm, pp.315-348, 2010. ,
DOI : 10.1007/978-3-642-02295-1_10
A public-key cryptosystem based on algebraic number theory, Tech. rep, 1978. ,
Handbook of Applied Cryptography, 1996. ,
DOI : 10.1201/9781439821916
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
Improving Lattice Based Cryptosystems Using the Hermite Normal Form, CaLC, pp.126-145, 2001. ,
DOI : 10.1007/3-540-44670-2_11
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant, SIAM Journal on Computing, vol.30, issue.6, pp.2008-2035, 2001. ,
DOI : 10.1137/S0097539700373039
Cryptographic Functions from Worst-Case Complexity Assumptions, The LLL Algorithm, pp.427-452, 2010. ,
DOI : 10.1007/978-3-642-02295-1_13
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.119.5535
Lattice-based cryptography, Encyclopedia of Cryptography and Security, pp.713-715 ,
Complexity of Lattice Problems : a cryptographic perspective of The Kluwer International Series in Engineering and Computer Science, 2002. ,
DOI : 10.1007/978-1-4615-0897-7
Worst???Case to Average???Case Reductions Based on Gaussian Measures, SIAM Journal on Computing, vol.37, issue.1, pp.267-302, 2007. ,
DOI : 10.1137/S0097539705447360
Lattice-based cryptography, 2008. ,
Use of elliptic curves in cryptography In Lecture notes in computer sciences ; 218 on Advances in cryptology?CRYPTO 85, pp.417-426, 1986. ,
Symmetric bilinear forms, 1973. ,
DOI : 10.1007/978-3-642-88330-9
LLL on the Average, ANTS, pp.238-256, 2006. ,
DOI : 10.1007/11792086_18
URL : https://hal.archives-ouvertes.fr/hal-00107309
Cryptanalysis of the Ajtai-Dwork cryptosystem, Advances in Cryptology -CRYPTO 98, 18th Annual International Cryptology Conference, pp.223-242, 1998. ,
DOI : 10.1007/BFb0055731
The two faces of lattices in cryptology, CaLC, pp.146-180, 2001. ,
Adapting Density Attacks to Low-Weight Knapsacks, Advances in Cryptology -ASIACRYPT 2005, 11th International Conference on the Theory and Application of Cryptology and Information Security, pp.41-58, 2005. ,
DOI : 10.1007/11593447_3
The LLL Algorithm : Survey and Applications, 2009. ,
DOI : 10.1007/978-3-642-02295-1
URL : https://hal.archives-ouvertes.fr/hal-01141414
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
An ecient and parallel Gaussian sampler for lattices, CRYPTO (2010), pp.80-97 ,
On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications, ACM SIGSAM Bulletin, vol.15, issue.1, pp.37-44, 1981. ,
DOI : 10.1145/1089242.1089247
On lattices, learning with errors, random linear codes, and cryptography, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing STOC '05, pp.84-93, 2005. ,
Lattice-Based Cryptography, CRYPTO, pp.131-141, 2006. ,
DOI : 10.1007/11818175_8
A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, vol.26, issue.1, pp.96-99, 1983. ,
DOI : 10.1145/357980.358017
A hierarchy of polynomial time lattice basis reduction algorithms, Theoretical Computer Science, vol.53, issue.2-3, pp.2-3, 1987. ,
DOI : 10.1016/0304-3975(87)90064-8
Factoring Integers and Computing Discrete Logarithms via Diophantine Approximation, Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques EUROCRYPT'91, pp.281-293, 1991. ,
DOI : 10.1007/3-540-46416-6_24
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
Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction, Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques EUROCRYPT'95, pp.1-12, 1995. ,
DOI : 10.1007/3-540-49264-X_1
A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem, FOCS, pp.145-152, 1982. ,
Algorithms for quantum computation: discrete logarithms and factoring, Proceedings 35th Annual Symposium on Foundations of Computer Science, pp.124-134, 1994. ,
DOI : 10.1109/SFCS.1994.365700
Lectures on the Geometry of Numbers, 1989. ,
DOI : 10.1007/978-3-662-08287-4
Making NTRU as Secure as Worst-Case Problems over Ideal Lattices, Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques : advances in cryptologyCité pages 54 et 60.) [107] Vallée, B. Opérateurs de Ruelle-Mayer généralisés et analyse en moyenne des algorithmes d'Euclide et de Gauss, pp.27-47, 1997. ,
DOI : 10.1007/978-3-642-20465-4_4
Gauss' algorithm revisited, Journal of Algorithms, vol.12, issue.4, pp.556-572, 1991. ,
DOI : 10.1016/0196-6774(91)90033-U
Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators, Algorithmica, vol.22, issue.4, pp.660-685, 1998. ,
DOI : 10.1007/PL00009246
The lattice reduction algorithm of Gauss: an average case analysis, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, pp.830-839, 1990. ,
DOI : 10.1109/FSCS.1990.89606
How to guess ???-th roots modulo n by reducing lattice bases, Lectures Notes in Computer Science, vol.357, pp.427-442, 1988. ,
DOI : 10.1007/3-540-51083-4_78
Lattice reduction in two dimensions : analyses under realistic probabilistic models, DMTCS Proceedings, vol.0, issue.146, pp.66-126, 2008. ,
Probabilistic Analyses of Lattice Reduction Algorithms ,
DOI : 10.1007/978-3-642-02295-1_3
Another NP-complete partition problem and the complexity of computing short vectors in a lattice Available at author's home page, 1981. ,
Cryptanalysis of 'Less Short' RSA Secret Exponents, Applicable Algebra in Engineering, Communication and Computing, vol.8, issue.5, pp.425-435, 1997. ,
DOI : 10.1007/s002000050082
Cryptanalysis of short RSA secret exponents, IEEE Transactions on Information Theory, vol.36, issue.3, pp.553-558, 1990. ,
DOI : 10.1109/18.54902