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 script O(2 0.337n) and memory script 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 script 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 script O(20.072n); we also show a time-memory tradeoff. © 2011 International Association for Cryptologic Research.