An improved multi-set algorithm for the dense subset sum problem

Authors:
Andrew Shallue
Affiliations:
University of Calgary, Calgary, AB, Canada
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

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Abstract

Given sets L1, . . . , Lk of elements from Z/mZ, the k-setbirthday problem is to find an element from each list such that theirsum is 0 modulo m. We give a new analysis of the algorithm in [16],proving that it returns a solution with high probability. By the workof Lyubashevsky [10], we get as an immediate corollary an improvedalgorithm for the random modular subset sum problem. Assuming themodulus m = 2nƐ for Ɛ nƐ/(1-Ɛ)log n).