Quantum Algorithm for the Collision Problem

@article{Brassard1997QuantumAF,
  title={Quantum Algorithm for the Collision Problem},
  author={G. Brassard and P. H{\o}yer and A. Montreal and Odense University},
  journal={arXiv: Quantum Physics},
  year={1997}
}
In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a… Expand
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