A. Joux and J. Stern, Improving the critical density of the Lagarias-Odlyzko attack against subset sum problems, to be published. Home/Search Document Not in Database Summary Related Articles Check |
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Basis Reduction Algorithms and Subset Sum Problems - LaMacchia (1991) (3 citations) (Correct)
....: 85 vii viii LIST OF FIGURES Introduction In 1985 Lagarias and Odlyzko [26] developed a general attack on knapsack cryptosystems which reduces solving subset sum problems to the problem of finding the Euclidean norm shortest nonzero vector in a point lattice. Recent improvements to this attack [12, 19] have stimulated interest in finding lattice basis reduction algorithms well suited to the lattices associated with subset sum problems. This thesis studies a new approach to lattice basis reduction originally developed by M. Seysen [38] Seysen s reduction algorithm was initially developed to ....
....larger and denser subset sum problems. Given the existence of a lattice oracle, the analysis in [26] shows that it is possible to solve almost all subset sum problems of density d 0:6463 : in polynomial time. Recently, Coster, LaMacchia, Odlyzko and Schnorr [12] and Joux and Stern [19] independently demonstrated via different techniques that this bound could be improved to d 0:9408. In fact, if we assume the existence of a sup norm lattice oracle instead of a Euclidean norm lattice oracle, 12] showed that the density bound then becomes d 1. The Lagarias Odlyzko attack ....
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A. Joux and J. Stern, Improving the critical density of the Lagarias-Odlyzko attack against subset sum problems, to be published.
Improved Low-Density Subset Sum Algorithms - Coster, Joux, LaMacchia.. (1991) (34 citations) Self-citation (Joux Stern) (Correct)
....of the same problem. The modification of the Lagarias Odlyzko attack described in Section 3 is due to Coster, LaMacchia, Odlyzko and Schnorr, and an extended abstract of it appears in [5] The other modification, outlined in Section 4, is due to Joux and Stern, and was presented earlier in [12]. 2. Previous results In [13] Lagarias and Odlyzko show that if the density is bounded by 0:6463 : the lattice oracle is guaranteed to find the solution vector with high probability. This section derives the 0:6463 : bound using simpler techniques due to Frieze [8] Our presentation ....
A. Joux and J. Stern, Improving the critical density of the Lagarias-Odlyzko attack against subset sum problems, Proceedings of Fundamentals of Computation Theory '91, L. Budach, ed., Lecture Notes in Computer Science 529, Springer-Verlag, New York, 1991, 258-264.
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