Welcome to the resource topic for 2002/049
Title:
Tensor Transform of Boolean Functions and Related Algebraic and Probabilistic Properties
Authors: Alexander Kholosha, Henk C. A. van Tilborg
Abstract:We introduce a tensor transform for Boolean functions that covers
the algebraic normal and Walsh transforms but which also allows
for the definition of new, probabilistic and weight transforms,
relating a function to its bias polynomial and to the weights of
its subfunctions respectively. Our approach leads to easy proofs
for some known results and to new properties of the aforecited
transforms. Several new results about algebraic and correlation
properties that depend on the weight transform of Boolean
functions are proved. Finally, we present a new probabilistic
characteristic of a Boolean function that is defined by its
algebraic normal and probabilistic transforms over the reals.
ePrint: https://eprint.iacr.org/2002/049
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