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The dictatorship function can be evaluated after examining only a single bit of the input, but that bit must always be examined. Benjamini, Schramm, and Wilson describe a more complex example based on
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can compute the function exactly while ensuring that the probability of reading any particular input bit is small, roughly inversely proportional to the square root of the number of bits.
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311:; Wilson, David Bruce (2005), "Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read", in Gabow, Harold N.; Fagin, Ronald (eds.),
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268:, where being balanced is one of "the most important criteria for cryptographically strong Boolean functions". If a function is not balanced, it will have a
375:; Zhang, Xian-Mo; Zheng, Yuliang (1993), "Nonlinearly balanced Boolean functions and their propagation characteristics", in Stinson, Douglas R. (ed.),
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Advances in
Cryptology – CRYPTO '93, 13th Annual International Cryptology Conference, Santa Barbara, California, USA, August 22–26, 1993, Proceedings
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is balanced. The bent functions are exactly the functions for which this is true, for all nonzero choices of
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Proceedings of the 37th Annual ACM Symposium on Theory of
Computing, Baltimore, MD, USA, May 22–24, 2005
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260:Application
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115:bits, and
351:(1): 52,
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398:Category
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