Almost perfect nonlinear functions
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Almost perfect nonlinear (APN) functions, or differentially 2-uniform functions, are optimally resistant to differential cryptanalysis. As such, the study of APN functions particularly over fields of characteristic two, has important applications in cryptography. We cover the known results on APN functions over both odd and even characteristic fields. We also explore differentially 1-uniform functions, or perfect nonlinear (PN) functions over odd characteristic fields, and almost bent (AB) functions over even characteristic fields. AB functions are a subset of APN functions that have high nonlinearity, making them resistant to linear cryptanalysis. In addition, we explore equivalence classes of APN functions, and what it means for a class of APN functions to be "new", or inequivalent to previously known classes. Finally, we present some new examples of APN functions over the field F53.
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This work is available on request. You can request a copy at https://library.carleton.ca/forms/request-pdf-copy-thesis
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Copyright © 2008 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2008
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