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Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Date
2014-09-28
Author
Sertkaya, Isa
Doğanaksoy, Ali
Uzunkol, Osmanbey
Kiraz, Mehmet Sabir
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphism group of bijective mappings as a subgroup of the symmetric group of the 2(n) dimensional F-2-vector space due to the existence of non-affine mapping classes.
Subject Keywords
Cryptographic boolean functions
,
Affine equivalence
,
Nonlinearity preserving mappings
,
Sylvester hadamard matrices
URI
https://hdl.handle.net/11511/48751
DOI
https://doi.org/10.1007/978-3-319-16277-5_7
Collections
Department of Mathematics, Conference / Seminar