Faster algorithm for solving hard knapsacks for moderate message length

Authors:
Yuji Nagashima;Noboru Kunihiro
Affiliations:
The University of Tokyo, Japan;The University of Tokyo, Japan
Venue:
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Year:
2012

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Abstract

At Eurocrypt2011, Becker, Coron and Joux proposed an algorithm for solving hard knapsacks, i.e., knapsacks with a density close to 1. Their algorithm solves hard knapsacks in time $\tilde{O}(2^{0.2909n})$. In this paper, we evaluate their algorithm by O notation and prove that the running time is O(n3.5 ·20.2909n). Furthermore, we extend their algorithm and propose the algorithm of which running time is O(n3 ·20.2919n). Asymptotic running time of our algorithm is not faster. However, when n