-
1
-
-
0029719917
-
Generating hard instances of lattice problems
-
Full version available from ECCC as TR96-007
-
M. Ajtai. Generating hard instances of lattice problems. In Proc. 28th ACM Symposium on the Theory of Computing, 1996, 99-108. Full version available from ECCC as TR96-007.
-
(1996)
Proc. 28th ACM Symposium on the Theory of Computing
, pp. 99-108
-
-
Ajtai, M.1
-
2
-
-
0031644084
-
2 is NP-hard for randomized reductions
-
Full version available from ECCC as TR97-047
-
2 is NP-hard for randomized reductions. In Proc. 30th ACM Symposium on the Theory of Computing, 1998, 10-19. Full version available from ECCC as TR97-047.
-
(1998)
Proc. 30th ACM Symposium on the Theory of Computing
, pp. 10-19
-
-
Ajtai, M.1
-
3
-
-
0030679849
-
A public-key cryptosystem with worst-case/average-case equivalence
-
Full version available from ECCC as TR96-065
-
M. Ajtai and C. Dwork. A public-key cryptosystem with worst-case/average-case equivalence. In Proc. 29th ACM Symposium on the Theory of Computing, 1997, 284-293. Full version available from ECCC as TR96-065.
-
(1997)
Proc. 29th ACM Symposium on the Theory of Computing
, pp. 284-293
-
-
Ajtai, M.1
Dwork, C.2
-
5
-
-
0027795348
-
The hardness of approximate optima in lattices, codes, and systems of linear equations
-
S. Arora, L. Babai, J. Stern, and Z. Sweedyk. The hardness of approximate optima in lattices, codes, and systems of linear equations. In Proc. 34th IEEE Symposium on Foundations of Computer Science, 1993, 724-733.
-
(1993)
Proc. 34th IEEE Symposium on Foundations of Computer Science
, pp. 724-733
-
-
Arora, S.1
Babai, L.2
Stern, J.3
Sweedyk, Z.4
-
6
-
-
51249173801
-
On Lovász’ lattice reduction and the nearest lattice point problem
-
L. Babai. On Lovász’ lattice reduction and the nearest lattice point problem. Combinatorica, 6: 1-13, 1986.
-
(1986)
Combinatorica
, vol.6
, pp. 1-13
-
-
Babai, L.1
-
8
-
-
26444586741
-
Polar Lattices from the point of view of nuclear spaces
-
special issue
-
W. Banaszczyk. Polar Lattices from the point of view of nuclear spaces. Rev. Mat. Univ. Complutense Madr. 2 (special issue): 35-46, 1989.
-
(1989)
Rev. Mat. Univ. Complutense Madr
, Issue.2
, pp. 35-46
-
-
Banaszczyk, W.1
-
9
-
-
0000303291
-
New Bounds in Some Transference Theorems in the Geometry of Numbers
-
W. Banaszczyk. New Bounds in Some Transference Theorems in the Geometry of Numbers. Mathematische Annalen, 296: 625-635, 1993.
-
(1993)
Mathematische Annalen
, vol.296
, pp. 625-635
-
-
Banaszczyk, W.1
-
10
-
-
0032653013
-
On the complexity of computing short linearly independent vectors and short bases in a lattice
-
pp711-720
-
J. Blömer and J-P. Seifert. On the complexity of computing short linearly independent vectors and short bases in a lattice. Proc. 31st ACM Symposium on Theory of Computing, pp711-720, 1999.
-
(1999)
Proc. 31st ACM Symposium on Theory of Computing
-
-
Blömer, J.1
Seifert, J.-P.2
-
14
-
-
84957801215
-
A New Transference Theorem in the Geometry of Numbers
-
COCOON, Tokyo, Japan. Lecture Notes in Computer Science, 1627
-
J.-Y. Cai. A New Transference Theorem in the Geometry of Numbers. The 5th International Computing and Combinatorics Conference, 113-122, (COCOON) 1999, Tokyo, Japan. Lecture Notes in Computer Science, 1627.
-
(1999)
The 5th International Computing and Combinatorics Conference
, pp. 113-122
-
-
Cai, J.-Y.1
-
16
-
-
0004489099
-
A Relation of Primal-Dual Lattices and the Complexity of Shortest Lattice Vector Problem
-
J.-Y. Cai. A Relation of Primal-Dual Lattices and the Complexity of Shortest Lattice Vector Problem. Theoretical Computer Science 207: 105-116, 1998.
-
(1998)
Theoretical Computer Science
, vol.207
, pp. 105-116
-
-
Cai, J.-Y.1
-
18
-
-
48049110260
-
On routing in circulant graphs
-
COCOON, Tokyo, Japan. Lecture Notes in Computer Science, 1627
-
J.-Y. Cai, G. Havas, B. Mans, A. Nerurkar, J-P. Seifert and I. Shparlinski. On routing in circulant graphs. The 5th International Computing and Combinatorics Conference, 360-369, (COCOON) 1999, Tokyo, Japan. Lecture Notes in Computer Science, 1627.
-
(1999)
The 5th International Computing and Combinatorics Conference
, pp. 360-369
-
-
Cai, J.-Y.1
Havas, G.2
Mans, B.3
Nerurkar, A.4
Seifert, J.-P.5
Shparlinski, I.6
-
22
-
-
84946872297
-
A note on the non-NP-hardness of approximate lattice problems under general Cook reductions
-
Submitted to
-
J.-Y. Cai and A. Nerurkar. A note on the non-NP-hardness of approximate lattice problems under general Cook reductions. Submitted to Information Processing Letters.
-
Information Processing Letters
-
-
Cai, J.-Y.1
Nerurkar, A.2
-
25
-
-
0001494997
-
Small solutions to polynomial equations, and low exponent RSA vulnerabilities
-
D. Coppersmith. Small solutions to polynomial equations, and low exponent RSA vulnerabilities. Journal of Cryptology, 10: 233-260, 1997.
-
(1997)
Journal of Cryptology
, vol.10
, pp. 233-260
-
-
Coppersmith, D.1
-
27
-
-
84941433641
-
Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen
-
P. G. L. Dirichlet. Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. Journal für die Reine und Angewandte Mathematik, 40: 209-227, 1850.
-
(1850)
Journal für die Reine und Angewandte Mathematik
, vol.40
, pp. 209-227
-
-
Dirichlet, P.G.L.1
-
28
-
-
0346903950
-
Sur le nombre de divisions à effectuer pour obtenir le plus grande commun diviseur entre deux nombres entiers
-
A. Dupré. Sur le nombre de divisions à effectuer pour obtenir le plus grande commun diviseur entre deux nombres entiers. Journal de Mathématiques, 11: 41-74, 1846.
-
(1846)
Journal de Mathématiques
, vol.11
, pp. 41-74
-
-
Dupré, A.1
-
29
-
-
0021420540
-
The Complexity of Promise Problems with Applications to Public-key Cryptography
-
S. Even, A. L. Selman and Y. Yacobi. The Complexity of Promise Problems with Applications to Public-key Cryptography. Information and Control 61: 159-173, 1984.
-
(1984)
Information and Control
, vol.61
, pp. 159-173
-
-
Even, S.1
Selman, A.L.2
Yacobi, Y.3
-
31
-
-
0000377057
-
Highly resilient correctors for polynomials
-
P. Gemmell and M. Sudan. Highly resilient correctors for polynomials. Information Processing Letters, 43: 169-174, 1992.
-
(1992)
Information Processing Letters
, vol.43
, pp. 169-174
-
-
Gemmell, P.1
Sudan, M.2
-
34
-
-
84958655849
-
Public-key cryptosystems from lattice reduction problems
-
Burto S. Kaliski Jr. (Ed.), Lecture Notes in Computer Science, Springer-Verlag
-
O. Goldreich, S. Goldwasser, and S. Halevi. Public-key cryptosystems from lattice reduction problems. In Advances in Cryptology - CRYPTO '97, Burto S. Kaliski Jr. (Ed.), Lecture Notes in Computer Science, 1294: 112-131, Springer-Verlag, 1997.
-
(1997)
Advances in Cryptology - CRYPTO '97
, vol.1294
, pp. 112-131
-
-
Goldreich, O.1
Goldwasser, S.2
Halevi, S.3
-
35
-
-
84958598719
-
Eliminating decryption errors in the Ajtai-Dwork cryptosystem
-
Burto S. Kaliski Jr. (Ed.), Lecture Notes in Computer Science, Springer-Verlag
-
O. Goldreich, S. Goldwasser, and S. Halevi. Eliminating decryption errors in the Ajtai-Dwork cryptosystem. In Advances in Cryptology - CRYPTO '97, Burto S. Kaliski Jr. (Ed.), Lecture Notes in Computer Science, 1294: 105-111, Springer-Verlag, 1997.
-
(1997)
Advances in Cryptology - CRYPTO '97
, vol.1294
, pp. 105-111
-
-
Goldreich, O.1
Goldwasser, S.2
Halevi, S.3
-
40
-
-
0342349222
-
Dual Vectors and Lower Bounds for the Nearest Lattice Point Problem
-
J. Håstad. Dual Vectors and Lower Bounds for the Nearest Lattice Point Problem. Combinatorica, 8: 75-81, 1988.
-
(1988)
Combinatorica
, vol.8
, pp. 75-81
-
-
Håstad, J.1
-
41
-
-
0005319167
-
Extraits de lettres de M. Ch. Hermite à M. Jacobi sur di érents objets de la théorie des nombres
-
C. Hermite. Extraits de lettres de M. Ch. Hermite à M. Jacobi sur di érents objets de la théorie des nombres. Journal für die Reine und Angewandte Mathematik, 40: 261-278, 279-290, 291-307, 308-315, 1850.
-
(1850)
Journal für die Reine und Angewandte Mathematik
, vol.40
-
-
Hermite, C.1
-
43
-
-
85030534310
-
Polynomial factorization 1987-1991
-
Simon (Ed.), Lecture Notes in Computer Science, Springer
-
E. Kaltofen. Polynomial factorization 1987-1991. LATIN '92, Simon (Ed.), Lecture Notes in Computer Science, 583: 294-313, Springer, 1992.
-
(1992)
LATIN '92
, vol.583
, pp. 294-313
-
-
Kaltofen, E.1
-
44
-
-
0000126406
-
Minkowski’s convex body theory and integer programming
-
R. Kannan. Minkowski’s convex body theory and integer programming. Mathematics of Operations Research, 12: 415-440, 1987.
-
(1987)
Mathematics of Operations Research
, vol.12
, pp. 415-440
-
-
Kannan, R.1
-
46
-
-
0003262982
-
Sur les formes quadratiques positives quaternaires
-
A. Korkin and G. Zolotarev. Sur les formes quadratiques positives quaternaires. Mathematische Annalen, 5: 581-583, 1872.
-
(1872)
Mathematische Annalen
, vol.5
, pp. 581-583
-
-
Korkin, A.1
Zolotarev, G.2
-
47
-
-
0022012583
-
The computational complexity of simultaneous diophantine approximation problems
-
J. C. Lagarias. The computational complexity of simultaneous diophantine approximation problems. SIAM Journal of Computing, 14: 196-209, 1985.
-
(1985)
SIAM Journal of Computing
, vol.14
, pp. 196-209
-
-
Lagarias, J.C.1
-
48
-
-
34249953865
-
Korkin-Zolotarev Bases and Successive Minima of a Lattice and its Reciprocal Lattice
-
J. C. Lagarias, H. W. Lenstra, and C. P. Schnorr. Korkin-Zolotarev Bases and Successive Minima of a Lattice and its Reciprocal Lattice. Combinatorica, 10(4): 333-348, 1990.
-
(1990)
Combinatorica
, vol.10
, Issue.4
, pp. 333-348
-
-
Lagarias, J.C.1
Lenstra, H.W.2
Schnorr, C.P.3
-
51
-
-
0020845921
-
Integer programming with a fixed number of variables
-
H. W. Lenstra, Jr. Integer programming with a fixed number of variables. Mathematics of Operations Research, 8: 538-548, 1983.
-
(1983)
Mathematics of Operations Research
, vol.8
, pp. 538-548
-
-
Lenstra, H.W.1
-
53
-
-
0000336772
-
The generalized basis reduction algorithm
-
L. Lovász and H. Scarf. The generalized basis reduction algorithm. Mathematics of Operations Research, 17(3): 751-764, 1992.
-
(1992)
Mathematics of Operations Research
, vol.17
, Issue.3
, pp. 751-764
-
-
Lovász, L.1
Scarf, H.2
-
54
-
-
0002097530
-
Ein Übertragungsprinzip für konvexe Körper
-
K. Mahler. Ein Übertragungsprinzip für konvexe Körper. Čas. Pěstoväní Mat. Fys. 68: 93-102, 1939.
-
(1939)
Čas. Pěstoväní Mat. Fys
, vol.68
, pp. 93-102
-
-
Mahler, K.1
-
57
-
-
52649088417
-
Über die positiven quadratischen Formen und über kettenbruchähnliche Algorithmen
-
H. Minkowski. Über die positiven quadratischen Formen und über kettenbruchähnliche Algorithmen. Crelles Journal für die Reine und Angewandte Mathematik, 107: 278-297, 1891.
-
(1891)
Crelles Journal für die Reine und Angewandte Mathematik
, vol.107
, pp. 278-297
-
-
Minkowski, H.1
-
62
-
-
0009807286
-
A hierarchy of polynomial time basis reduction algorithms
-
C. P. Schnorr. A hierarchy of polynomial time basis reduction algorithms. Theory of Algorithms, 375-386, 1985.
-
(1985)
Theory of Algorithms
, pp. 375-386
-
-
Schnorr, C.P.1
-
63
-
-
33846200465
-
Lattice basis reduction: Improved practical algorithms and solving subset sum problems
-
C. P. Schnorr and M. Euchner. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Mathematical Programming, 66: 181-199, 1994.
-
(1994)
Mathematical Programming
, vol.66
, pp. 181-199
-
-
Schnorr, C.P.1
Euchner, M.2
-
65
-
-
4244009888
-
Un problème central en géométrie algorithmique des nombres: La réduction des réseaux;atour de l’algorithme LLL
-
English transl. by E. Kranakis, CWI Quart 3: 95-120, 1990
-
B. Vallée. Un problème central en géométrie algorithmique des nombres: la réduction des réseaux;atour de l’algorithme LLL. Inform. Théor. Appl., 345-376, 1989. English transl. by E. Kranakis, CWI Quart 3: 95-120, 1990.
-
(1989)
Inform. Théor. Appl
, pp. 345-376
-
-
Vallée, B.1
|