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Improved Generic Algorithms for Hard Knapsacks

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00664332
Contributor : Isabelle Moudenner Cohen <>
Submitted on : Monday, January 30, 2012 - 1:11:11 PM
Last modification on : Friday, January 10, 2020 - 3:42:21 PM

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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⟩

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