On verification of restricted extended affine equivalence of vectorial boolean functions

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2012

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Sınak, Ahmet

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Vectorial Boolean functions are used as S-boxes in cryptosystems. To design inequivalent vectorial Boolean functions resistant to known attacks is one of the challenges in cryptography. Verifying whether two vectorial Boolean functions are equivalent or not is the final step in this challenge. Hence, finding a fast technique for determining whether two given vectorial Boolean functions are equivalent is an important problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this thesis. We study the verification complexity of REA-equivalence of two vectorial Boolean functions for some types, namely types I to VI. We first review the verification of the REA-equivalence types I to IV given in the recent work of Budaghyan and Kazymyrov (2012). Furthermore, we present the complexities of the verification of REA-equivalence types I and IV in the case basic simultaneous Gaussian elimination method is used. Next, we present two new REA-equivalence types V and VI with their complexities. Finally, we give the algorithms of each type I to VI with their MAGMA codes.

Subject Keywords

Vector analysis., Algebra, Boolean., Differential equations, Linear., Cryptography.

URI

http://etd.lib.metu.edu.tr/upload/12615191/index.pdf
https://hdl.handle.net/11511/22180

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

A. Sınak, “On verification of restricted extended affine equivalence of vectorial boolean functions,” M.S. - Master of Science, Middle East Technical University, 2012.