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- W1746229377 abstract "For a Boolean function f , define Δ f (α)=∑ x f ̂ (x) f ̂ (x⊕α) , f ̂ (x)=(−1) f(x) , the absolute indicator Δ f = max α≠0 |Δ f (α)| , and the sum-of-squares indicator σ f =∑ α Δ f 2 (α) . We construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics, namely we show that 2 2n (1+p)⩽σ f ⩽2 3n−2 ,Δ f =2 n , where p is the number of linear structures (with even Hamming weight) of the first half of a strict avalanche criterion balanced Boolean function f . We also derive some bounds for the nonlinearity of such functions. It improves upon the results of Son et al. (Inform. Process. Lett. 65 (3) (1998) 139) and Sung et al. (Inform. Process. Lett. 69 (1) (1999) 21). In our second result we construct a class of highly nonlinear balanced functions with good local and global avalanche characteristics. We show that for these functions, 2 2n+2 ⩽σ f ⩽2 2n+2+ε ( ε=0 for n even and ε=1 for n odd)." @default.
- W1746229377 created "2016-06-24" @default.
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- W1746229377 date "2002-04-01" @default.
- W1746229377 modified "2023-10-03" @default.
- W1746229377 title "Nonlinearity, local and global avalanche characteristics of balanced Boolean functions" @default.
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- W1746229377 doi "https://doi.org/10.1016/s0012-365x(01)00193-5" @default.
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