Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The multiplicative complexity of quadratic boolean forms
Theoretical Computer Science
On the multiplicative complexity of Boolean functions over the basis ∧,⊕,1
Theoretical Computer Science - Selected papers in honor of Manuel Blum
The Multiplicative Complexity of Boolean Functions
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A 2.5 n-lower bound on the combinational complexity of Boolean functions
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Algebraic Complexity Theory
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Faster secure two-party computation with less memory
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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The multiplicative complexity of a Boolean function f is defined as the minimum number of binary conjunction (AND) gates required to construct a circuit representing f, when only exclusive-or, conjunction and negation gates may be used. This article explores in detail the multiplicative complexity of symmetric Boolean functions. New techniques that allow such exploration are introduced. They are powerful enough to give exact multiplicative complexities for several classes of symmetric functions. In particular, the multiplicative complexity of computing the Hamming weight of n bits is shown to be exactly n−Hℕ(n), where Hℕ(n) is the Hamming weight of the binary representation of n. We also show a close relationship between the complexity of symmetric functions and fractals derived from the parity of binomial coefficients.