Generalized Compact Knapsacks are Collision Resistant

@article{Lyubashevsky2005GeneralizedCK,
  title={Generalized Compact Knapsacks are Collision Resistant},
  author={Vadim Lyubashevsky and Daniele Micciancio},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2005}
}
The generalized knapsack problem is the following: given m random elements a1, . . . , am in a ring R, and a target t ∈ R, find z1, . . . , zm ∈ D such that P aizi = t, where D is some fixed subset of R. In (Micciancio, FOCS 2002) it was proved that for appropriate choices of R and D, solving the generalized compact knapsack problem on the average is as hard as solving certain worst-case problems for cyclic lattices, even for almost constant values of m. This result immediately yields very… CONTINUE READING
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