Cryptographic Boolean functions with biased inputs
Gangopadhyay, Aditi Kar
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While performing cryptanalysis, it is of interest to approximate a Boolean function in n variables f : Fn → F2 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.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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