Faster Algorithm for Solving Hard Knapsacks for Moderate Message Length

  • Yuji Nagashima
  • Noboru Kunihiro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7372)


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(n 3.5 ·20.2909n ). Furthermore, we extend their algorithm and propose the algorithm of which running time is O(n 3 ·20.2919n ). Asymptotic running time of our algorithm is not faster. However, when n < 6312, our algorithm can solve subset sum problem faster than algorithm of Becker, Coron and Joux.


knapsack cryptosystem subset sum problem hard knapsacks 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yuji Nagashima
    • 1
  • Noboru Kunihiro
    • 1
  1. 1.The University of TokyoJapan

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