[Resource Topic] 2010/189: New generic algorithms for hard knapsacks

Welcome to the resource topic for 2010/189

Title:
New generic algorithms for hard knapsacks

Authors: Nick Howgrave-Graham, Antoine Joux

Abstract:

In this paper, we study the complexity of solving hard knapsack problems, i.e., knapsacks with a density close to 1 where lattice-based low density attacks are not an option. For such knapsacks, the current state-of-the-art is a 31-year old algorithm by Schroeppel and Shamir which is based on birthday paradox techniques and yields a running time of \TildeOh(2^{n/2}) for knapsacks of n elements and uses \TildeOh(2^{n/4}) storage. We propose here two new algorithms which improve on this bound, finally lowering the running time down to \TildeOh (2^{0.3113\, n}) for almost all knapsacks of density 1. We also demonstrate the practicality of these algorithms with an implementation.

ePrint: https://eprint.iacr.org/2010/189

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