Paper 2002/049

Tensor Transform of Boolean Functions and Related Algebraic and Probabilistic Properties

Alexander Kholosha and 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.

Note: Updated version

Metadata
Available format(s)
PDF PS
Publication info
Published elsewhere. Unknown where it was published
Keywords
key-stream generatorBoolean functiontensor transformWalsh transformcorrelationprobabilistic properties
Contact author(s)
A Kholosha @ tue nl
History
2002-09-27: revised
2002-04-19: received
See all versions
Short URL
https://ia.cr/2002/049
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2002/049,
      author = {Alexander Kholosha and Henk C. A.  van Tilborg},
      title = {Tensor Transform of Boolean Functions and Related Algebraic and Probabilistic Properties},
      howpublished = {Cryptology ePrint Archive, Paper 2002/049},
      year = {2002},
      note = {\url{https://eprint.iacr.org/2002/049}},
      url = {https://eprint.iacr.org/2002/049}
}
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