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The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. In this paper we investigate the lower bound of the higher-order nonlinearity of Niho Boolean functions f(x) = tr(λxd) over F2n, where... [formula]
The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. By investigating the lower bound of the nonlinearity of the derivative of the function f, this paper tightens the lower bound of the second-order nonlinearity...
The rth order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed–Muller codes. This paper tightens the lower bounds of the second order nonlinearity of three classes of Boolean functions in the form f(x)=tr(xd) in n variables, where...
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