In this thesis, we examine a family of vectorial boolean functions on F22m inspired by Kim function, in order to find new APN permutations on F22m for m > 2. The functions of this family are defined as F(X) = X3 + bX3q + cX2q+1 + dXq+2 , where parameters b, c and d are from F2m . Necessary and sufficient conditions for this functions to be APN or equivalent to a permutation are presented in this thesis. To find conditions for being APN, Trace-0/Trace-1 decomposition method is used. A method using exponential sums is used to deduce which functions of this family is CCZ-equivalent to a certain type of permutation. These results were then used to search for APN permutations on F26 and F210 . 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:352724 |
| Date | January 2016 |
| Creators | Krasnayová, Dáša |
| Contributors | Göloglu, Faruk, Lisoněk, Petr |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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