Space–Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm

  • Per Austrin
  • Petteri Kaski
  • Mikko Koivisto
  • Jussi Määttä
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)


The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the Subset Sum problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the recently discovered dissection method of Dinur et al. (CRYPTO 2012) yields a significantly improved space–time tradeoff curve for instances with strong randomness properties. Our main result is that these strong randomness assumptions can be removed, obtaining the same space–time tradeoffs in the worst case. We also show that for small space usage the dissection algorithm can be almost fully parallelized. Our strategy for dealing with arbitrary instances is to instead inject the randomness into the dissection process itself by working over a carefully selected but random composite modulus, and to introduce explicit space–time controls into the algorithm by means of a “bailout mechanism”.


Internal Node Recursive Call Time Tradeoff Randomized Algorithm Tradeoff Curve 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Per Austrin
    • 1
    • 2
  • Petteri Kaski
    • 3
  • Mikko Koivisto
    • 4
  • Jussi Määttä
    • 3
  1. 1.Aalto Science InstituteAalto UniversityFinland
  2. 2.KTH Royal Institute of TechnologySweden
  3. 3.HIIT & Department of Information and Computer ScienceAalto UniversityFinland
  4. 4.HIIT & Department of Computer ScienceUniversity of HelsinkiFinland

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