On Relationships among Avalanche, Nonlinearity, and Correlation Immunity
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Connections among nonlinearity, avalanche and correlation immunity
Theoretical Computer Science - Algorithms,automata, complexity and games
New construction of resilient functions with satisfying multiple cryptographic criteria
InfoSecu '04 Proceedings of the 3rd international conference on Information security
Construction of Resilient Functions with Multiple Cryptographic Criteria
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
A Generalization of the Bent-Function Sequence Construction
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
The Rayleigh Quotient of Bent Functions
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
International Journal of Information and Coding Theory
Some results concerning cryptographically significant mappings over GF(2n)
Designs, Codes and Cryptography
A construction of weakly and non-weakly regular bent functions
Journal of Combinatorial Theory Series A
On the value distributions of Walsh spectrums of quadratic Plateaued functions
Computers and Electrical Engineering
The kth-order quasi-generalized bent functions over ring Zp
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Geometric and design-theoretic aspects of semibent functions II
Designs, Codes and Cryptography
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Note: Nonexistence of certain types of plateaued functions
Discrete Applied Mathematics
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The focus of this article is on nonlinear characteristics of cryptographic Boolean functions. First, we introduce the notion of plateaued functions that have many cryptographically desirable properties. Second, we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria, including nonlinearity, avalanche, and correlation immunity, and prove that critical cases of the inequalities coincide with characterizations of plateaued functions. We then proceed to prove that plateaued functions include as a proper subset all partially bent functions that were introduced earlier by Claude Carlet (1993). This solves an interesting problem that arises naturally from previously known results on partially bent functions. In addition, we construct plateaued, but not partially bent, functions that have many properties useful in cryptography