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
-
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},
url = {https://eprint.iacr.org/2012/620}
}
