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Subset Sum Quantumly in 1.17^n

Authors Alexander Helm, Alexander May

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Author Details

Alexander Helm
  • Horst Görtz Institute for IT-Security, Ruhr University Bochum, Germany
Alexander May
  • Horst Görtz Institute for IT-Security, Ruhr University Bochum, Germany

Funding

  • Helm, Alexander: Founded by NRW Research Training Group SecHuman.

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Alexander Helm and Alexander May. Subset Sum Quantumly in 1.17^n. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.TQC.2018.5

Abstract

We study the quantum complexity of solving the subset sum problem, where the elements a_1, ..., a_n are randomly chosen from Z_{2^{l(n)}} and t = sum_i a_i in Z_{2^{l(n)}} is a sum of n/2 elements. In 2013, Bernstein, Jeffery, Lange and Meurer constructed a quantum subset sum algorithm with heuristic time complexity 2^{0.241n}, by enhancing the classical subset sum algorithm of Howgrave-Graham and Joux with a quantum random walk technique. We improve on this by defining a quantum random walk for the classical subset sum algorithm of Becker, Coron and Joux. The new algorithm only needs heuristic running time and memory 2^{0.226n}, for almost all random subset sum instances.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Subset sum
  • Quantum walk
  • Representation technique

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