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The largest super-increasing subset of a random set

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2 Author(s)

It is shown that the longest super-increasing sequence which can be constructed from a set of n independent uniformly distributed random variables is almost surely asymptotic to \log _{2}n . Some extensions of this result, as well as the implications for the security of knapsack-based cryptographic systems, are discussed.

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Information Theory, IEEE Transactions on  (Volume:29 ,  Issue: 1 )