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On the circuit complexity of perfect hashing. (English) Zbl 1343.94057
Goldreich, Oded (ed.), Studies in complexity and cryptography. Miscellanea on the interplay between randomness and computation. In collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman. Berlin: Springer (ISBN 978-3-642-22669-4/pbk). Lecture Notes in Computer Science 6650, 26-29 (2011).
Summary: We consider the size of circuits that perfectly hash an arbitrary subset \(S \subset \{0,1\}^{n }\) of cardinality \(2^{k }\) 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.
For the entire collection see [Zbl 1220.68005].
MSC:
94A60 Cryptography
68R05 Combinatorics in computer science
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