M.J. Coster, B.A. LaMacchia, A.M. Odlyzko, C.P. Schnorr  Home/Search
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Abstract: The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum problems of density ! 0:6463 : : : in polynomial time if it could invoke a polynomial-time algorithm... (Update)
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38: Solving low-density subset sum problems (context) - Lagarias, Odlyzko - 1985
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BibTeX entry: (Update)
M. J. Coster, B. A. LaMacchia, A. M. Odlyzko and C. P. Schnorr, An improved low-density subset sum algorithm, Proc. Advances in Cryptology - Eurocrypt'91, Springer Verlag, 1991, pp. 54--67. http://citeseer.ist.psu.edu/coster91improved.html More
@article{ coster91improved,
author = "Matthijs J. Coster and B. A. LaMacchia and Andrew M. Odlyzko and Claus P. Schnorr",
title = "An Improved Low-Density Subset Sum Algorithm",
journal = "Lecture Notes in Computer Science",
volume = "547",
pages = "54--??",
year = "1991",
url = "citeseer.ist.psu.edu/coster91improved.html" }
Citations (may not include all citations):4212 Computers and Intractability: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
227 Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
60 Solving low-density subset sum problems (context) - Lagarias, Odlyzko - 1985
51 A hierarchy of polynomial time lattice basis reduction algor.. (context) - Schnorr - 1987
38 A knapsack-type public key cryptosystem based on arithmetic .. - Chor, Rivest - 1988
33 Polynomial time algorithms for finding integer relations amo.. (context) - Hastad, Just et al. - 1989
23 Cryptanalysis: a survey of recent results (context) - Brickell, Odlyzko - 1988
23 the Lagarias-Odlyzko algorithm for the subset sum problem (context) - Frieze - 1986
19 Solving low density knapsacks (context) - Brickell - 1984 DBLP
18 A more efficient algorithm for lattice basis reduction (context) - Schnorr - 1988
14 Lattice points in high-dimensional spheres - Mazo, Odlyzko - 1990
13 Cryptology and Computational Number Theory (context) - Odlyzko, rise et al. - 1990 ACM
13 What happened with knapsack cryptographic schemes (context) - Desmedt - 1988
12 Succinct certificates for almost all subset sum problems (context) - Furst, Kannan - 1989 ACM DBLP
10 The cryptanalysis of knapsack cryptosystems (context) - Brickell - 1988
10 Simultaneous reduction of a lattice basis and its reciprocal.. (context) - Seysen
6 Basis Reduction Algorithms and Subset Sum Problems - LaMacchia - 1991
4 Another NP-complete partition problem and the complexity of .. (context) - Boas - 1981
4 Solving subset sum problems with the L 3 algorithm (context) - Radziszowski, Kreher - 1988
3 Approximating integer lattices by lattices with cyclic facto.. (context) - Paz, Schnorr - 1987 ACM DBLP
The graph only includes citing articles where the year of publication is known.
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Short Proofs for Nondivisibility of Sparse Polynomials.. - Grigoriev, Karpinski.. (1996) (Correct)
Lattice Points in High-Dimensional Spheres - Mazo, Odlyzko (1990) (Correct)
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