Improved Generic Algorithms for Hard Knapsacks

Anja Becker, Jean-Sébastien Coron, and Antoine Joux

Abstract

At Eurocrypt 2010, Howgrave-Graham and Joux described an algorithm for solving hard knapsacks of density close to 1 in time O(2^0.337n) and memory O(2^0.256n), thereby improving a 30-year old algorithm by Shamir and Schroeppel. In this paper we extend the Howgrave-Graham Joux technique to get an algorithm with running time down to O(2^0.291n). An implementation shows the practicability of the technique. Another challenge is to reduce the memory requirement. We describe a constant memory algorithm based on cycle finding with running time O(2^0.72n); we also show a time-memory tradeoff.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. An extended abstract of this paper appeared at Eurocrypt 2011. This is the full version.
Contact author(s)
jean-sebastien coron @ uni lu
History
Short URL
https://ia.cr/2011/474

CC BY

BibTeX

@misc{cryptoeprint:2011/474,
author = {Anja Becker and Jean-Sébastien Coron and Antoine Joux},
title = {Improved Generic Algorithms for Hard Knapsacks},
howpublished = {Cryptology ePrint Archive, Paper 2011/474},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/474}},
url = {https://eprint.iacr.org/2011/474}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.