The c-differential uniformity and boomerang uniformity of two classes of permutation polynomials
| Autor: | Mohit Pal, Sartaj Ul Hasan, Pantelimon Stanica |
|---|---|
| Přispěvatelé: | Cyber Academic Group, Naval Postgraduate School (U.S.), Applied Mathematics (MA) |
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Differential cryptanalysis Distribution (number theory) Substitution (logic) permutation polynomials Function (mathematics) Library and Information Sciences Type (model theory) perfect and almost perfect c-nonlinearity Computer Science Applications Permutation Finite field Finite fields c- differential uniformity boomerang uniformity Information Systems Block cipher Mathematics |
| Popis: | The article of record as published may be found at http://dx.doi.org/10.1109/TIT.2021.3123104 The Difference Distribution Table (DDT) and the differential uniformity play a major role for the design of substitution boxes in block ciphers, since they indicate the func- tion’s resistance against differential cryptanalysis. This concept was extended recently to c-DDT and c-differential uniformity, which have the potential of extending differential cryptanalysis. Recently, a new theoretical tool, the Boomerang Connectivity Table (BCT) and the corresponding boomerang uniformity were introduced to quantify the resistance of a block cipher against boomerang-style attacks. Here we concentrate on two classes (introduced recently) of permutation polynomials over finite fields of even characteristic. For one of these, which is an involution used to construct a 4-uniform permutation, we explicitly determine the c-DDT entries and BCT entries. For the second type of function, which is a differentially 4-uniform function, we give bounds for its c-differential and boomerang uniformities. The research of Sartaj Ul Hasan is partially supported by MATRICS grant MTR/2019/000744 from the Science and Engineering Research Board, Government of India. Pantelimon Stănică acknowledges the sabbatical support from Naval Postgraduate School from September 2020 to July 2021. |
| Databáze: | OpenAIRE |
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