Asymptotic Nonlinearity of Boolean Functions
Designs, Codes and Cryptography
On the Distribution of Boolean Function Nonlinearity
SIAM Journal on Discrete Mathematics
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
On the construction of highly nonlinear permutations
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Finite Fields and Their Applications
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The nonlinearity of a Boolean function $F: \mathbb{F}_{2}^{m}\rightarrow \mathbb{F}_{2}$ is the minimum Hamming distance between f and all affine functions. The nonlinearity of a S-box $f: \mathbb{F}_{2}^{m}\rightarrow \mathbb{F}_{2}^{n}$ is the minimum nonlinearity of its component (Boolean) functions $v\cdot f,\, v\in \mathbb{F}_{2}^{n}\,\backslash \{0\}$ . This notion quantifies the level of resistance of the S-box to the linear attack. In this paper, the distribution of the nonlinearity of (m, n)-functions is investigated. When n驴=驴1, it is known that asymptotically, almost all m-variable Boolean functions have high nonlinearities. We extend this result to (m, n)-functions.