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- W2279841002 abstract "Given positive integers a1,...,an,t, the fixed weight subset sum problem is to find a subset of the ai that sum to t, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern knapsack cryptosystems, and solving the problem results directly in a message attack. We present new exponential algorithms that do not rely on lattices, and hence will be applicable when lattice basis reduction algorithms fail. These algorithms rely on a generalization of the notion of splitting system given by Stinson (18). In particular, if the problem has length n and weight l then for constant k a power of two less than n we apply a k-set birthday algorithm to the splitting system of the problem. This randomized algorithm has time and space complexity that satisfies T · S log k = e O( n l � ) (where the" @default.
- W2279841002 created "2016-06-24" @default.
- W2279841002 creator A5065298061 @default.
- W2279841002 date "2012-01-13" @default.
- W2279841002 modified "2023-09-27" @default.
- W2279841002 title "DIVISION ALGORITHMS FOR THE FIXED WEIGHT SUBSET SUM PROBLEM" @default.
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