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# 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} }

- Published 2005 in Electronic Colloquium on Computational Complexity
DOI:10.1007/11787006_13

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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