Cryptographic Boolean functions with biased inputs
Gangopadhyay, Aditi Kar
MetadataShow full item record
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.
Showing items related by title, author, creator and subject.
Correlation immunity, avalanche features, and other cryptographic properties of generalized Boolean functions Martinsen, Thor (Monterey, California: Naval Postgraduate School, 2017-09);This dissertation investigates correlation immunity, avalanche features, and the bent cryptographic properties for generalized Boolean functions defined on Vn with values in Zԛ. We extend the concept of correlation immunity ...
Chung, Jong Ho (Monterey, California: Naval Postgraduate School, 2013-09);In this thesis, we study a type of affine equivalence for the monomial rotation-symmetric (MRS) Boolean func-tions and two new construction techniques for cryptographic Boolean functions based on the affine equivalence of ...
O'Dowd, Timothy R. (Monterey, California. Naval Postgraduate School, 2010-12);Linear cryptanalysis attacks are a threat against cryptosystems. These attacks can be defended against by using combiner functions composed of highly nonlinear Boolean functions. Bent functions, which have the highest ...