Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Upper bound for algebraic immunity on a subclass of Maiorana McFarland class of bent functions
Information Processing Letters
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
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In Gupta et al. (2011) [5], the authors proved that the algebraic immunity of a subclass of Maiorana-McFarland functions is at most @?n4@?+2 and claimed that this bound is tight. The main theorem of the upper bound is correct. However, their proof is incomplete and the bound is not tight. We will prove a more general theorem of a much larger subclass of Maiorana-McFarland functions and find that its algebraic immunity cannot achieve the optimum value. However, we find an 8-variable Maiorana-McFarland function which is not in that larger subclass of Maiorana-McFarland functions achieving the optimum algebraic immunity (this is the first time that a nontrivial Maiorana-McFarland function with the optimum algebraic immunity is given). Hence, this shows that there exist the Maiorana-McFarland functions achieving the optimum algebraic immunity.