Abstract
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”.
P.A. supported by the Aalto Science Institute, the Swedish Research Council grant 621-2012-4546, and ERC Advanced Investigator grant 226203. P.K. supported by the Academy of Finland, grants 252083 and 256287. M.K. supported by the Academy of Finland, grants 125637, 218153, and 255675. A full version of the present conference abstract is available at: http://arxiv.org/abs/1303.0609
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Austrin, P., Kaski, P., Koivisto, M., Määttä, J. (2013). Space–Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_5
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