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ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH σf = 22n + 2n+3(n ≥ 3).
- Source :
-
International Journal of Foundations of Computer Science . Apr2014, Vol. 25 Issue 3, p343-353. 11p. - Publication Year :
- 2014
-
Abstract
- The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n ≥ 5). We conclude that there does not exist a m(m ≥ 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n ≥ 7. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01290541
- Volume :
- 25
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- International Journal of Foundations of Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 97193414
- Full Text :
- https://doi.org/10.1142/S0129054114500178