On the Complexity of Computing Two Nonlinearity Measures

Magnus Gausdal Find

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arXiv · 1403.0417

On the Complexity of Computing Two Nonlinearity Measures

Magnus Gausdal Find

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Abstract

We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time $2^{O(n)}$ given the truth table of length $2^n$, in fact under the same assumption it is impossible to approximate the multiplicative complexity within a factor of $(2-\epsilon)^{n/2}$. When given a circuit, the problem of determining the multiplicative complexity is in the second level of the polynomial hierarchy. For nonlinearity, we show that it is #P hard to compute given a function represented by a circuit.

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BibTeX RIS

Magnus Gausdal Find. 2014-03-03. On the Complexity of Computing Two Nonlinearity Measures. https://arxiv.org/abs/1403.0417

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