Aperiodic propagation criteria for Boolean functions

Nega–Hadamard Transform, Bent and Negabent Functions

“…In the nega-Hadamard transform context, the basic idea of this result is explained in [5] and equation (15) of [13]. In Lemma 2 we are able to use Hadamard transform because unlike the definition in [5,13] our negacrosscorrelation does not include the factor (−1) wt(u) .…”

One and Two-Variable Interlace Polynomials: A Spectral Interpretation

“…{I, H, N } n , where a is now an affine function from GF(2) |R H |+|R N | → Z 4 . Q can also be used to assess the block cipher attack scenario where one has full read/write access to a subset of plaintext bits and access to all ciphertext bits [9]. Using similar arguments, Q HN summarises all possible Z 4 -linear approximations to a Boolean function, i.e.…”

Close Encounters with Boolean Functions of Three Different Kinds

“…Constructions of Boolean functions with good aperiodic properties is not a welldeveloped area of research in cryptography [12,9].…”

“…We then focus on the construction of bipolar arrays in C n 2 , which can be described by generalised Boolean functions, where these functions have good aperiodic properties [9]. By re-expressing the autocorrelation and Fourier properties of these functions using unitary matrix terminology, we view our problem within a wider context, where the multidimensional continuous discrete Fourier transform is a tensor product of members of an infinite-size set of 2 × 2 unitary matrices [25,19,28].…”

“…Type-I, II, and III properties relate to the action of the Heisenberg-Weyl group under some restrictions. Moreover, those quadratic Boolean functions which represent one-dimensional quantum codes with good distance [9,4] also have good properties with respect to the action of the Heisenberg-Weyl group.…”