Global avalanche characteristics and nonlinearity of balanced Boolean functions

Jung Je Son; Jong In Lim; Seongtaek Chee; Soo Hak Sung

doi:10.1016/s0020-0190(98)00009-x

Global avalanche characteristics and nonlinearity of balanced Boolean functions

Jung Je Son, Jong In Lim, Seongtaek Chee, Soo Hak Sung

School of Cybersecurity

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

The GAC (global avalanche characteristic) was introduced to measure cryptographic behavior, such as, propagation characteristic, in a global manner. The two indicators σ_f and Δ_f 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: σ_f ≥ 2²ⁿ + 2ⁿ⁺³ and Δ_f ≥ 8. Moreover, we obtain an upper bound on nonlinearity for balanced Boolean functions: N_f ≤ 2^n-1 -1/22^-n/2 √σ_f, which improves the previously known results.

Original language	English
Pages (from-to)	139-144
Number of pages	6
Journal	Information Processing Letters
Volume	65
Issue number	3
DOIs	https://doi.org/10.1016/s0020-0190(98)00009-x
Publication status	Published - 1998 Feb 13

Keywords

Balancedness
Boolean function
Cryptography
Global avalanche characteristic
Nonlinearity

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/s0020-0190(98)00009-x

Cite this

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AU - Son, Jung Je

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AU - Chee, Seongtaek

AU - Sung, Soo Hak

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AB - 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 -1/22-n/2 √σf, which improves the previously known results.

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KW - Global avalanche characteristic

KW - Nonlinearity

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Global avalanche characteristics and nonlinearity of balanced Boolean functions

Abstract

Keywords

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