Space---Time tradeoffs for subset sum: an improved worst case algorithm

Authors:
Per Austrin;Petteri Kaski;Mikko Koivisto;Jussi Määttä
Affiliations:
Aalto Science Institute, Aalto University, Finland,KTH Royal Institute of Technology, Sweden;HIIT & Department of Information and Computer Science, Aalto University, Finland;HIIT & Department of Computer Science, University of Helsinki, Finland;HIIT & Department of Information and Computer Science, Aalto University, Finland
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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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".