Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2

Date

2014-09-28

Author

Sertkaya, Isa
Doğanaksoy, Ali
Uzunkol, Osmanbey
Kiraz, Mehmet Sabir

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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

Collections

Department of Mathematics, Conference / Seminar