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The Exact Multiplicative Complexity of the Hamming Weight Function

Published

Author(s)

Rene C. Peralta, Joan Boyar

Abstract

We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for addition and multiplication modulo 2 (alternatively, XOR and conjunction gates) only. The number of multiplications necessary and sufficient to build such a circuit is called the multiplicative complexity of the Hamming weight function. We prove the exact multiplicative complexity of the Hamming weight function on n variables is n minus the Hamming weight of the binary representation of n.
Proceedings Title
Proceedings published by Springer-Verlag
Conference Dates
September 13, 2005
Conference Title
Latin American Theoretical Informatics Symposium

Keywords

circuit complexity, complexity, concrete complexity, cryptographic proofs, Hamming weight, multiplicative, symmetric functions

Citation

Peralta, R. and Boyar, J. (2005), The Exact Multiplicative Complexity of the Hamming Weight Function, Proceedings published by Springer-Verlag (Accessed April 22, 2024)
Created September 13, 2005, Updated February 19, 2017