Constructing Two Classes of Boolean Functions With Good Cryptographic Properties

Wu et al. proposed a generalized Tu-Deng conjecture over \mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}} , and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open. Based on Wu's work and assuming that the conjecture is true, we com...

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Bibliographic Details
Published in:IEEE access 2019, Vol.7, p.149657-149665
Main Authors: Chen, Yindong, Zhang, Liu, Gong, Zhangquan, Cai, Weihong
Format: Article
Language:English
Subjects:
1-resilient
Additives
Algebra
Algebraic immunity
Artificial intelligence
Boolean
Boolean algebra
Boolean function
Boolean functions
Codes
Cryptography
FAA
fast algebraic attacks
nonlinearity
Properties (attributes)
Resists
Tu-Deng conjecture
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Summary:Wu et al. proposed a generalized Tu-Deng conjecture over \mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}} , and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open. Based on Wu's work and assuming that the conjecture is true, we come up with a new class of balanced Boolean functions which has optimal algebraic degree, high nonlinearity and optimal algebraic immunity. The Boolean function also behaves well against fast algebraic attacks. Meanwhile we construct another class of Boolean functions by concatenation, which is 1-resilient and also has other good cryptographic properties.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2947367