-
2
-
-
10044239059
-
klog2 - O(k)"
-
klog2 - O(k)," Journal of the AMS, vol. 17, no. 4, pp. 947-973, 2004.
-
(2004)
Journal of the AMS
, vol.17
, Issue.4
, pp. 947-973
-
-
Achlioptas, D.1
Peres, Y.2
-
4
-
-
27344461174
-
"Lattice Problems in NP∩coNP"
-
Preliminary version in Proceedings of FOCS 2004
-
D. Aharonov and O. Regev, "Lattice Problems in NP∩coNP," Journal of the ACM, vol. 52, no. 5, pp. 749-765, Preliminary version in Proceedings of FOCS 2004, 2005.
-
(2005)
Journal of the ACM
, vol.52
, Issue.5
, pp. 749-765
-
-
Aharonov, D.1
Regev, O.2
-
8
-
-
0034826416
-
"A sieve algorithm for the shortest lattice vector problem"
-
M. Ajtai, R. Kumar, and D. Sivakumar, "A sieve algorithm for the shortest lattice vector problem," in Proceedings of the 33rd ACM Symposium on Theory of Computing, pp. 601-610, 2001.
-
(2001)
Proceedings of the 33rd ACM Symposium on Theory of Computing
, pp. 601-610
-
-
Ajtai, M.1
Kumar, R.2
Sivakumar, D.3
-
9
-
-
33748114891
-
"On basing one-way functions on NP-hardness"
-
A. Akavia, O. Goldreich, S. Goldwasser, and D. Moshkovitz, "On basing one-way functions on NP-hardness," in Proceedings of the 38th ACM Symposium on Theory of Computing, 2006.
-
(2006)
Proceedings of the 38th ACM Symposium on Theory of Computing
-
-
Akavia, A.1
Goldreich, O.2
Goldwasser, S.3
Moshkovitz, D.4
-
10
-
-
0001338853
-
"BPP has subexponential time simulations unless EXPTIME has publishable proofs"
-
L. Babai, L. Fortnow, N. Nisan, and A. Wigderson, "BPP has subexponential time simulations unless EXPTIME has publishable proofs," Computational Complexity, vol. 3, no. 4, pp. 307-318, 1993.
-
(1993)
Computational Complexity
, vol.3
, Issue.4
, pp. 307-318
-
-
Babai, L.1
Fortnow, L.2
Nisan, N.3
Wigderson, A.4
-
11
-
-
0031639853
-
"On the complexity of unsatisfiability proofs for random k-CNF formulas"
-
P. Beame, R. Karp, T. Pitassi, and M. Saks, "On the complexity of unsatisfiability proofs for random k-CNF formulas," in Proceedings of the 30th ACM Symposium on Theory of Computing, 1998.
-
(1998)
Proceedings of the 30th ACM Symposium on Theory of Computing
-
-
Beame, P.1
Karp, R.2
Pitassi, T.3
Saks, M.4
-
12
-
-
0026853668
-
"On the theory of average case complexity"
-
S. Ben-David, B. Chor, O. Goldreich, and M. Luby, "On the theory of average case complexity," Journal of Computer and System Sciences, vol. 44, no. 2, pp. 193-219, 1992.
-
(1992)
Journal of Computer and System Sciences
, vol.44
, Issue.2
, pp. 193-219
-
-
Ben-David, S.1
Chor, B.2
Goldreich, O.3
Luby, M.4
-
13
-
-
0000802475
-
"Short proofs are narrow: Resolution made simple"
-
E. Ben-Sasson and A. Wigderson, "Short proofs are narrow: Resolution made simple," Journal of the ACM, vol. 48, no. 2, 2001.
-
(2001)
Journal of the ACM
, vol.48
, Issue.2
-
-
Ben-Sasson, E.1
Wigderson, A.2
-
14
-
-
0021522644
-
"How to generate cryptographically strong sequences of pseudorandom bits"
-
Preliminary version in Proceedings of FOCS'82
-
M. Blum and S. Micali, "How to generate cryptographically strong sequences of pseudorandom bits," SIAM Journal on Computing, vol. 13, no. 4, pp. 850-864, Preliminary version in Proceedings of FOCS'82, 1984.
-
(1984)
SIAM Journal on Computing
, vol.13
, Issue.4
, pp. 850-864
-
-
Blum, M.1
Micali, S.2
-
18
-
-
0024090265
-
"Many hard examples for resolution"
-
V. Chvatal and E. Szemeredi, "Many hard examples for resolution," Journal of the ACM, vol. 35, no. 4, pp. 759-768, 1998.
-
(1998)
Journal of the ACM
, vol.35
, Issue.4
, pp. 759-768
-
-
Chvatal, V.1
Szemeredi, E.2
-
19
-
-
35248862079
-
"Certifying unsatisfiability of random 2k-SAT formulas using approximation techniques"
-
in LNCS 2751
-
A. Coja-Oghlan, A. Goerdt, A. Lanka, and F. Schdlich, "Certifying unsatisfiability of random 2k-SAT formulas using approximation techniques," in Proceedings of 14th Symposium on Foundations of Computation Theory, pp. 15-26, LNCS 2751, 2003.
-
(2003)
Proceedings of 14th Symposium on Foundations of Computation Theory
, pp. 15-26
-
-
Coja-Oghlan, A.1
Goerdt, A.2
Lanka, A.3
Schdlich, F.4
-
20
-
-
0017018484
-
"New directions in cryptography"
-
W. Diffie and M. E. Hellman, "New directions in cryptography," IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644-654, 1976.
-
(1976)
IEEE Transactions on Information Theory
, vol.22
, Issue.6
, pp. 644-654
-
-
Diffie, W.1
Hellman, M.E.2
-
21
-
-
0021420540
-
"The complexity of promise problems with applications to public-key cryptography"
-
S. Even, A. Selman, and Y. Yacobi, "The complexity of promise problems with applications to public-key cryptography," Information and Computation, vol. 61, no. 2, pp. 159-173, 1984.
-
(1984)
Information and Computation
, vol.61
, Issue.2
, pp. 159-173
-
-
Even, S.1
Selman, A.2
Yacobi, Y.3
-
22
-
-
85009782374
-
"Cryptography and NP-completeness"
-
in Springer-Verlag
-
S. Even and Y. Yacobi, "Cryptography and NP-completeness," in Proceedings of the 7th International Colloquium on Automata, Languages and Programming, pp. 195-207, Springer-Verlag, 1980.
-
(1980)
Proceedings of the 7th International Colloquium on Automata, Languages and Programming
, pp. 195-207
-
-
Even, S.1
Yacobi, Y.2
-
27
-
-
0027684980
-
"Random-self-reducibility of complete sets"
-
J. Feigenbaum and L. Fortnow, "Random-self-reducibility of complete sets," SIAM Journal on Computing, vol. 22, pp. 994-1005, 1993.
-
(1993)
SIAM Journal on Computing
, vol.22
, pp. 994-1005
-
-
Feigenbaum, J.1
Fortnow, L.2
-
28
-
-
0033458154
-
"Necessary and sufficient conditions for sharp thresholds of graph properties and the k-SAT problem"
-
E. Friedgut, "Necessary and sufficient conditions for sharp thresholds of graph properties and the k-SAT problem," Journal of the AMS, vol. 12, pp. 1017-1054, 1999.
-
(1999)
Journal of the AMS
, vol.12
, pp. 1017-1054
-
-
Friedgut, E.1
-
33
-
-
0342349223
-
"On the possibility of basing Cryptography on the assumption that P ≠ NP"
-
Unpublished manuscript
-
O. Goldreich and S. Goldwasser, "On the possibility of basing Cryptography on the assumption that P ≠ NP," 1998. Unpublished manuscript.
-
(1998)
-
-
Goldreich, O.1
Goldwasser, S.2
-
34
-
-
2442638659
-
"On Yao's XOR Lemma"
-
O. Goldreich, N. Nisan, and A. Wigderson, "On Yao's XOR Lemma," Tech. Rep. TR95-50, Electronic Colloquium on Computational Complexity, 1995.
-
(1995)
Tech. Rep. TR95-50, Electronic Colloquium on Computational Complexity
-
-
Goldreich, O.1
Nisan, N.2
Wigderson, A.3
-
35
-
-
0021409284
-
"Probabilistic encryption"
-
Preliminary Version in Proceedings of STOC'82
-
S. Goldwasser and S. Micali, "Probabilistic encryption," Journal of Computer and System Sciences, vol. 28, no. 2, pp. 270-299, Preliminary Version in Proceedings of STOC'82, 1984.
-
(1984)
Journal of Computer and System Sciences
, vol.28
, Issue.2
, pp. 270-299
-
-
Goldwasser, S.1
Micali, S.2
-
38
-
-
0000844603
-
"Some optimal inapproximability results"
-
J. Håstad, "Some optimal inapproximability results," Journal of the ACM, vol. 48, no. 4, pp. 798-859, 2001.
-
(2001)
Journal of the ACM
, vol.48
, Issue.4
, pp. 798-859
-
-
Håstad, J.1
-
39
-
-
0345253860
-
"A pseudorandom generator from any one-way function"
-
J. Håstad, R. Impagliazzo, L. Levin, and M. Luby, "A pseudorandom generator from any one-way function," SIAM Journal on Computing, vol. 28, no. 4, pp. 1364-1396, 1999.
-
(1999)
SIAM Journal on Computing
, vol.28
, Issue.4
, pp. 1364-1396
-
-
Håstad, J.1
Impagliazzo, R.2
Levin, L.3
Luby, M.4
-
40
-
-
4544286907
-
"Using nondeterminism to amplify hardness"
-
A. Healy, S. Vadhan, and E. Viola, "Using nondeterminism to amplify hardness," in Proceedings of the 36th ACM Symposium on Theory of Computing, pp. 192-201, 2004.
-
(2004)
Proceedings of the 36th ACM Symposium on Theory of Computing
, pp. 192-201
-
-
Healy, A.1
Vadhan, S.2
Viola, E.3
-
46
-
-
0017523323
-
"Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane"
-
R. Karp, "Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane," Mathematics of Operations Research, vol. 2, no. 3, pp. 209-224, 1977.
-
(1977)
Mathematics of Operations Research
, vol.2
, Issue.3
, pp. 209-224
-
-
Karp, R.1
-
47
-
-
0342650348
-
"Probabilistic analysis"
-
in (M. O'hEigeartaigh, J. Lenstra, and A. R. Kan, eds.), Wiley
-
R. Karp, J. Lenstra, C. McDiarmid, and A. R. Kan, "Probabilistic analysis," in Combinatorial Optimization: An Annotated Bibliography, (M. O'hEigeartaigh, J. Lenstra, and A. R. Kan, eds.), pp. 52-88, Wiley, 1985.
-
(1985)
Combinatorial Optimization: An Annotated Bibliography
, pp. 52-88
-
-
Karp, R.1
Lenstra, J.2
McDiarmid, C.3
Kan, A.R.4
-
48
-
-
34047186406
-
"Hardness of approximating the shortest vector problem in lattices"
-
Manuscript
-
S. Khot, "Hardness of approximating the shortest vector problem in lattices," 2004. Manuscript.
-
(2004)
-
-
Khot, S.1
-
50
-
-
0041384096
-
"On polynomial-factor approximations to the shortest lattice vector length"
-
Preliminary version in Proceedings of SODA 2001
-
R. Kumar and D. Sivakumar, "On polynomial-factor approximations to the shortest lattice vector length," SIAM Journal on Discrete Mathematics, vol. 16, no. 3, pp. 422-425, Preliminary version in Proceedings of SODA 2001, 2003.
-
(2003)
SIAM Journal on Discrete Mathematics
, vol.16
, Issue.3
, pp. 422-425
-
-
Kumar, R.1
Sivakumar, D.2
-
51
-
-
34047147028
-
"Cryptography in transition"
-
A. Lempel, "Cryptography in transition," Computing Surveys, vol. 11, no. 4, pp. 215-220, 1979.
-
(1979)
Computing Surveys
, vol.11
, Issue.4
, pp. 215-220
-
-
Lempel, A.1
-
52
-
-
34250244723
-
"Factoring polynomials with rational coefficients"
-
A. Lenstra, H. Lenstra, and L. Lovasz, "Factoring polynomials with rational coefficients," Mathematische Annalen, vol. 261, pp. 515-534, 1982.
-
(1982)
Mathematische Annalen
, vol.261
, pp. 515-534
-
-
Lenstra, A.1
Lenstra, H.2
Lovasz, L.3
-
53
-
-
0022663555
-
"Average case complete problems"
-
L. Levin, "Average case complete problems," SIAM Journal on Computing, vol. 15,no. 1, pp. 285-286, 1986.
-
(1986)
SIAM Journal on Computing
, vol.15
, Issue.1
, pp. 285-286
-
-
Levin, L.1
-
54
-
-
51249173191
-
"One-Way Functions and Pseudorandom Generators"
-
L. Levin, "One-Way Functions and Pseudorandom Generators," Combinatorica, vol. 7, no. 4, pp. 357-363, 1987.
-
(1987)
Combinatorica
, vol.7
, Issue.4
, pp. 357-363
-
-
Levin, L.1
-
55
-
-
0010786255
-
"Average case complexity under the universal distribution equals worst-case complexity"
-
M. Li and P. M. B. Vitányi, "Average case complexity under the universal distribution equals worst-case complexity," IPL, vol. 42, no. 3, pp. 145-149, 1992.
-
(1992)
IPL
, vol.42
, Issue.3
, pp. 145-149
-
-
Li, M.1
Vitányi, P.M.B.2
-
56
-
-
0035707359
-
"The shortest vector problem is NP-hard to approximate to within some constant"
-
D. Micciancio, "The shortest vector problem is NP-hard to approximate to within some constant," SIAM Journal on Computing, vol. 30, no. 6, pp. 2008-2035, 2001.
-
(2001)
SIAM Journal on Computing
, vol.30
, Issue.6
, pp. 2008-2035
-
-
Micciancio, D.1
-
57
-
-
16244401113
-
"Almost perfect lattices, the covering radius problem, and applications to Ajtai's connection factor"
-
D. Micciancio, "Almost perfect lattices, the covering radius problem, and applications to Ajtai's connection factor," SIAM Journal on Computing, vol. 34, no. 1, pp. 118-169, 2004.
-
(2004)
SIAM Journal on Computing
, vol.34
, Issue.1
, pp. 118-169
-
-
Micciancio, D.1
-
60
-
-
0028516244
-
"Hardness vs randomness"
-
Preliminary version in Proc. of FOCS'88
-
N. Nisan and A. Wigderson, "Hardness vs randomness," Journal of Computer and System Sciences, vol. 49, pp. 149-167, Preliminary version in Proc. of FOCS'88, 1994.
-
(1994)
Journal of Computer and System Sciences
, vol.49
, pp. 149-167
-
-
Nisan, N.1
Wigderson, A.2
-
62
-
-
34047174131
-
"One-way functions, hard on average problems and statistical zero-knowledge proofs"
-
R. Ostrovsky, "One-way functions, hard on average problems and statistical zero-knowledge proofs," in STRUCTURES91, pp. 51-59, 1991.
-
(1991)
STRUCTURES91
, pp. 51-59
-
-
Ostrovsky, R.1
-
64
-
-
33745571012
-
"On lattices, learning with errors, random linear codes, and cryptography"
-
O. Regev, "On lattices, learning with errors, random linear codes, and cryptography," in Proceedings of the 37th ACM Symposium on Theory of Computing, pp. 84-93, 2005.
-
(2005)
Proceedings of the 37th ACM Symposium on Theory of Computing
, pp. 84-93
-
-
Regev, O.1
-
67
-
-
0023532388
-
"A hierarchy of polynomial time lattice basis reduction algorithms"
-
C. Schnorr, "A hierarchy of polynomial time lattice basis reduction algorithms," Theoretical Computer Science, vol. 53, pp. 201-224, 1987.
-
(1987)
Theoretical Computer Science
, vol.53
, pp. 201-224
-
-
Schnorr, C.1
-
69
-
-
0035276434
-
"Pseudorandom generators without the XOR Lemma"
-
M. Sudan, L. Trevisan, and S. Vadhan, "Pseudorandom generators without the XOR Lemma," Journal of Computer and System Sciences, vol. 62, no. 2, pp. 236-266, 2001.
-
(2001)
Journal of Computer and System Sciences
, vol.62
, Issue.2
, pp. 236-266
-
-
Sudan, M.1
Trevisan, L.2
Vadhan, S.3
-
71
-
-
33748588052
-
"Some Applications of coding theory in computational complexity"
-
arXiv:cs.CC/0409044
-
L. Trevisan, "Some Applications of coding theory in computational complexity," Quaderni di Matematica, vol. 13, pp. 347-424, arXiv:cs.CC/0409044, 2004.
-
(2004)
Quaderni Di Matematica
, vol.13
, pp. 347-424
-
-
Trevisan, L.1
-
74
-
-
15244355932
-
"The Complexity of constructing pseudorandom generators from hard functions"
-
E. Viola, "The Complexity of constructing pseudorandom generators from hard functions," Computational Complexity, vol. 13, no. 3-4, pp. 147-188, 2004.
-
(2004)
Computational Complexity
, vol.13
, Issue.3-4
, pp. 147-188
-
-
Viola, E.1
|