Paper 2012/620

Solving Subset Sum Problems of Densioty close to 1 by "randomized" BKZ-reduction

Claus P. Schnorr and Taras Shevchenko

Abstract

Subset sum or Knapsack problems of dimension $n$ are known to be hardest for knapsacks of density close to 1.These problems are NP-hard for arbitrary $n$. One can solve such problems either by lattice basis reduction or by optimized birthday algorithms. Recently Becker, Coron, Jou } [BCJ10] present a birthday algorithm that follows Schroeppel, Shamir [SS81], and Howgrave-Graham, Joux [HJ10]. This algorithm solves 50 random knapsacks of dimension 80 and density close to 1 in roughly 15 hours on a 2.67 GHz PC. We present an optimized lattice basis reduction algorithm that follows Schnorr, Euchne} [SE03] using pruning of Schnorr, Hörner [SH95] that solves such random knapsacks of dimension 80 on average in less than a minute, and 50 such problems all together about 9.4 times faster and using much less space than [BCJ10] on another 2.67 GHz PC.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
BKZblock reduction of lattice basessubset sum problem
Contact author(s)
scjhnorr @ cs uni-frankfurt de
History
2012-11-05: received
Short URL
https://ia.cr/2012/620
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/620,
      author = {Claus P.  Schnorr and Taras Shevchenko},
      title = {Solving Subset Sum Problems of Densioty close to 1 by "randomized" BKZ-reduction},
      howpublished = {Cryptology ePrint Archive, Paper 2012/620},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/620}},
      url = {https://eprint.iacr.org/2012/620}
}
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