By considering a new metric, we generalize cryptographic properties of Boolean functions such as resiliency and propagation characteristics. These new definitions result in a better understanding of the properties of Boolean functions and provide a better insight in the space defined by this metric. This approach leads to the construction of {"}hand-made{"} Boolean functions, i.e., functions for which the security with respect to some specific monotone sets of inputs is considered, instead of the security with respect to all possible monotone sets with the same cardinality, as in the usual definitions. This approach has the advantage that some trade-offs between important properties of Boolean functions can be relaxed.
Braeken, A, Nikov, V, Nikova, S & Preneel, B 2004, 'On Boolean functions with generalized cryptographic properties', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3348, pp. 120-135. https://doi.org/10.1007/978-3-540-30556-9_11
Braeken, A., Nikov, V., Nikova, S., & Preneel, B. (2004). On Boolean functions with generalized cryptographic properties. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3348, 120-135. https://doi.org/10.1007/978-3-540-30556-9_11
@article{619cb59fc5c94f3f856237e8c21d669f,
title = "On Boolean functions with generalized cryptographic properties",
abstract = "By considering a new metric, we generalize cryptographic properties of Boolean functions such as resiliency and propagation characteristics. These new definitions result in a better understanding of the properties of Boolean functions and provide a better insight in the space defined by this metric. This approach leads to the construction of {"}hand-made{"} Boolean functions, i.e., functions for which the security with respect to some specific monotone sets of inputs is considered, instead of the security with respect to all possible monotone sets with the same cardinality, as in the usual definitions. This approach has the advantage that some trade-offs between important properties of Boolean functions can be relaxed.",
author = "An Braeken and Ventzislav Nikov and Svetla Nikova and Bart Preneel",
note = "Funding Information: ★ The work described in this paper has been supported in part by the European Com-mission through the IST Programme under Contract IST-2002-507932 ECRYPT and Concerted Research Action GOA-MEFISTO-666 of the Flemish Government. Funding Information: ★★★The author was partially supported by IWT STWW project on Anonymity and Privacy in Electronic Services.",
year = "2004",
doi = "10.1007/978-3-540-30556-9_11",
language = "English",
volume = "3348",
pages = "120--135",
journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
issn = "0302-9743",
publisher = "Springer Verlag",
}