论文信息 - When Six Gates are Not Enough

When Six Gates are Not Enough

We apply the pigeonhole principle to show that there must exist Boolean functions on 7 inputs with a multiplicative complexity of at least 7, i.e., that cannot be computed with only 6 multiplications in the Galois field with two elements.

Michael Frank | Peter Schneider-Kamp | Luís Cruz-Filipe | Michael Codish

[1] Joan Boyar,et al. On the multiplicative complexity of Boolean functions over the basis (cap, +, 1) , 2000, Theor. Comput. Sci..

[2] Michael Frank,et al. Twenty-Five Comparators Is Optimal When Sorting Nine Inputs (and Twenty-Nine for Ten) , 2014, 2014 IEEE 26th International Conference on Tools with Artificial Intelligence.

[3] René Peralta,et al. The Multiplicative Complexity of Boolean Functions on Four and Five Variables , 2014, LightSec.

[4] Joan Boyar,et al. Tight bounds for the multiplicative complexity of symmetric functions , 2008, Theor. Comput. Sci..

[5] Martin Hirt,et al. Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation , 2005, ASIACRYPT.

[6] J. Boyar,et al. On the multiplicative complexity of Boolean functions over the basis ∧,⊕,1 , 1998 .