Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Designs, Codes and Cryptography
On constructions and nonlinearity of correlation immune functions
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Nonlinearity and propagation characteristics of balanced Boolean functions
Information and Computation
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
New Results on Correlation Immunity
ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Construction of DES-like S-boxes Based on Boolean Functions Satisfyieng the SAC
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Auto-correlations and new bounds on the nonlinearity of boolean functions
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Cryptographically resilient functions
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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Nonlinear Boolean functions play an important role in the design of block ciphers, stream ciphers and one-way hash functions. Over the years researchers have identified a number of indicators that forecast nonlinear properties of these functions. Studying the relationships among these indicators has been an area that has received extensive research. The focus of this paper is on the interplay of three notable nonlinear indicators, namely nonlinearity, avalanche and correlation immunity. We establish, for the first time, an explicit and simple lower bound on the nonlinearity Nf of a Boolean function f of n variables satisfying the avalanche criterion of degree p, namely, Nf ≥ 2n-1 -2n-1-(1/2)p. We also identify all the functions whose nonlinearity attains the lower bound. As a further contribution of this paper, we prove that except for very few cases, the sum of the degree of avalanche and the order of correlation immunity of a Boolean function of n variables is at most n-2. The new results obtained in this work further highlight the significance of the fact that while avalanche property is in harmony with nonlinearity, both go against correlation immunity.