On the Circuit Complexity of Perfect Hashing

@inproceedings{Goldreich1996OnTC,
  title={On the Circuit Complexity of Perfect Hashing},
  author={Oded Goldreich and Avi Wigderson},
  booktitle={Studies in Complexity and Cryptography},
  year={1996}
}
We consider the size of circuits that perfectly hash an arbitrary subset S⊂{0, 1} of cardinality 2 into {0, 1}. We observe that, in general, the size of such circuits is exponential in 2k−m, and provide a matching upper bound. 

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