Paper 2011/474

Improved Generic Algorithms for Hard Knapsacks

Anja Becker, Jean-Sébastien Coron, and Antoine Joux


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)
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
2011-09-06: received
Short URL
Creative Commons Attribution


      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{}},
      url = {}
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