The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such ... more The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such as, propagation characteristic, in a global manner. The two indicators af and Af 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: af 2 2'" + 2n+3 and Af 2 8. Moreover, we obtain an upper bound on nonlinearity for balanced Boolean functions: Nf < 2"-' -~2-"iz,/Z7, which improves the previously known results.
The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such ... more The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such as, propagation characteristic, in a global manner. The two indicators af and Af 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: af 2 2'" + 2n+3 and Af 2 8. Moreover, we obtain an upper bound on nonlinearity for balanced Boolean functions: Nf < 2"-' -~2-"iz,/Z7, which improves the previously known results.
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