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Revision #1 to TR97-047 | 11th November 1997 00:00

The Shortest Vector Problem in L_2 is NP-hard for Randomized Reductions.

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Revision #1 Authors: Miklos Ajtai
Accepted on: 11th November 1997 00:00
Downloads: 3713
Keywords: 


Abstract:

We show that the shortest vector problem in lattices
with L_2 norm is NP-hard for randomized reductions. Moreover we
also show that there is a positive absolute constant c, so that to
find a vector which is longer than the shortest non-zero vector by no
more than a factor of 1+2^{-n^c} (with respect to the L_{2} norm) is
also NP-hard for randomized reductions. The corresponding decision
problem is NP-complete for randomized reductions.

Revision of: TR97-047


Paper:

TR97-047 | 20th October 1997 00:00

The Shortest Vector Problem in L_2 is NP-hard for Randomized Reductions.





TR97-047 Authors: Miklos Ajtai
Publication: 21st October 1997 09:51
Downloads: 2276
Keywords: 


Abstract:

We show that the shortest vector problem in lattices
with L_2 norm is NP-hard for randomized reductions. Moreover we
also show that there is a positive absolute constant c, so that to
find a vector which is longer than the shortest non-zero vector by no
more than a factor of 1+2^{-n^c} (with respect to the L_{2} norm) is
also NP-hard for randomized reductions. The corresponding decision
problem is NP-complete for randomized reductions.


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