No abstract

No abstract

Abstract. In this paper we start developing a detailed theory of negaHadamard transforms. Consequently, we derive several results on negabentness of concatenations, and partially-symmetric functions. We also obtain a characterization of bent-negabent functions in a subclass of Maiorana-McFarland set. As a by-product of our results we obtain simple proofs of several existing facts.

While performing cryptanalysis, it is of interest to approximate a Boolean function in n variables f : F n 2 → F 2 by affine functions. Usually, it is assumed that all the input vectors to a Boolean function are equiprobable while mounting affine approximation attack or fast correlation attacks. In this paper we consider a more general case when each component of the input vector to f is independent and identically distributed Bernoulli variates with the parameter p. Since our scope is within the area of cryptography, we initiate an analysis of cryptographic Boolean functions under the previous considerations and derive expression of the analogue of Walsh-Hadamard transform and nonlinearity in the case under consideration. We observe that if we allow p to take up complex values then a framework involving quantum Boolean functions can be introduced, which provides a connection between Walsh-Hadamard transform, nega-Hadamard transform and Boolean functions with biased inputs.

No abstract