On the circuit complexity of perfect hashing

Authors:
Oded Goldreich;Avi Wigderson
Affiliations:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Israel;School of Mathematics of the Institute, Princeton
Venue:
Studies in complexity and cryptography
Year:
2011

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Abstract

We consider the size of circuits that perfectly hash an arbitrary subset S⊂{0, 1}n of cardinality 2k into {0, 1}m. We observe that, in general, the size of such circuits is exponential in 2k -m, and provide a matching upper bound.