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Improved Low-Density Subset Sum Algorithms (1991)  (Make Corrections)  (49 citations)
Matthijs J. Coster, Antoine Joux, Brian A. LaMacchia, Andrew M. Odlyzko, Claus-Peter Schnorr, Jacques Stern
Lecture Notes in Computer Science



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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 nonzero 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
30:   Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
23:   Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Pr.. - Schnorr, Euchner - 1991

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/article/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/article/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
60   Lattice Basis Reduction: Improved Practical Algorithms and S.. - Schnorr, Euchner - 1991
51   A hierarchy of polynomial time lattice basis reduction algor.. (context) - Schnorr - 1987
49   An improved low-density subset sum algorithm - Coster, LaMacchia et al. - 1991
38   A knapsack-type public key cryptosystem based on arithmetic .. - Chor, Rivest - 1988
33   Polynomial time algorithms for finding integer relations amo.. (context) - astad, Just et al. - 1989
23   the Lagarias-Odlyzko algorithm for the subset sum problem (context) - Frieze - 1986
23   Cryptanalysis: a survey of recent results (context) - Brickell, Odlyzko - 1988
19   Solving low density knapsacks (context) - Brickell - 1984
18   A more efficient algorithm for lattice basis reduction (context) - Schnorr - 1988
16   The rise and fall of knapsack cryptosystems - Odlyzko - 1990
14   Another NP-complete partition problem and the complexity of .. (context) - Boas - 1981
14   Lattice points in high-dimensional spheres - Mazo, Odlyzko - 1990
13   What happened with knapsack cryptographic schemes (context) - Desmedt - 1988
12   Succinct certificates for almost all subset sum problems (context) - Furst, Kannan - 1989
10   Simultaneous reduction of a lattice basis and its reciprocal.. (context) - Seysen
10   The cryptanalysis of knapsack cryptosystems (context) - Brickell - 1988
6   Basis Reduction Algorithms and Subset Sum Problems - LaMacchia - 1991
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
2   Improving the critical density of the Lagarias-Odlyzko attac.. (context) - Joux, Stern - 1991



The graph only includes citing articles where the year of publication is known.


Documents on the same site (http://www.mi.informatik.uni-frankfurt.de/research/papers.html):   More
Lattice Basis Reduction: Improved Practical Algorithms and.. - Schnorr, Euchner (1993)   (Correct)
Factoring Integers and Computing Discrete Logarithms via.. - Schnorr (1993)   (Correct)
Breaking Knapsack Cryptosystems by l_infinity norm Enumeration - Ritter (1996)   (Correct)

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