Elsevier

Information Processing Letters

Volume 65, Issue 3, 13 February 1998, Pages 139-144
Information Processing Letters

Global avalanche characteristics and nonlinearity of balanced Boolean functions

https://doi.org/10.1016/S0020-0190(98)00009-XGet rights and content

Abstract

The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such as, propagation characteristic, in a global manner. The two indicators σf and Δf related to GAC are introduced. However, an important problem to compute lower bounds of two indicators for balanced Boolean functions was not solved yet. In this paper, we derive lower bounds on the two indicators for balanced Boolean functions: σf ⩾ 22n + 2n + 3 and Δf ⩾ 8. Moreover, we obtain an upper bound on nonlinearity for balanced Boolean functions: Nf ⩽ 2n−1 122 − n2 √σf, which improves the previously known results.

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Research supported by The Basic Research Grants (97-01-00-13-01-5), Korea Science and Engineering Foundation, 1997.

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