On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions
Brajesh Kumar Singh · International Journal of Engineering Mathematics · 2014
The r th-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the r th-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the r th-order nonlinearity of a Boolean function is very complicated problem, especially when r>1 . This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form Tr1nλxd for all x∈𝔽2n , λ∈𝔽2n* , where a d=2i+2j+2k+1 , where i , j , and k are integers such that i>j>k≥1 and n>2i , and b d=23ℓ+22ℓ+2ℓ+1 , where ℓ is a positive integer such that gcdℓ,𝓃=1 and n>6 .