Improved Generic Algorithms for Hard Knapsacks

At Eurocrypt 2010, Howgrave-Graham and Joux described an algorithm for solving hard knapsacks of density close to 1 in time ˜O(20.337n ) and memory ˜O(20.256n ), 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(20.291n ). 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(20.72n ); we also show a time-memory tradeoff.

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Anja Becker, Jean-Sébastien Coron, Antoine Joux
• Keywords: IACR 2011, Memory Requirement, Schroeppel, Time Memory