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Propagation characteristics of Boolean functions. (English) Zbl 0764.94024
Advances in Cryptology, Proc. Workshop, EUROCRYPT ’90, Aarhus/Denm. 1990, Lect. Notes Comput. Sci. 473, 161-173 (1991).
Summary: [For the entire collection see Zbl 0755.00009.]
The relation between the Walsh-Hadamard transform and the autocorrelation function of Boolean functions is used to study propagation characteristics of these functions. The Strict Avalanche Criterion and the Perfect Nonlinearity Criterion are generalized in a Propagation Criterion of degree \(k\). New properties and constructions for Boolean bent functions are given and also the extension of the definition to odd values of \(n\) is discussed. New properties of functions satisfying higher order SAC are derived. Finally a general framework is established to classify functions according to their propagation characteristics if a number of bits is kept constant.

94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
94A60 Cryptography