Improved Generic Algorithms for Hard Knapsacks

Anja Becker (1) , Jean-Sébastien Coron (2) , Antoine Joux (1)

1 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
2 Uni.lu - Université du Luxembourg

At Eurocrypt 2010, Howgrave-Graham and Joux described an algorithm for solving hard knapsacks of density close to 1 in time (20337n) and memory (20256n), 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 (20291n). 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 (2072n); we also show a time-memory tradeoff.

Domaines: Cryptographie et sécurité [cs.CR]

Anja Becker, Jean-Sébastien Coron, Antoine Joux. Improved Generic Algorithms for Hard Knapsacks. Eurocrypt 2011, May 2011, Tallinn, Estonia. pp.364-385, ⟨10.1007/978-3-642-20465-4_21⟩. ⟨hal-00664332⟩