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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.

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