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A new method to investigate the CCZ-equivalence between functions with low differential uniformity.
- Source :
-
Finite Fields & Their Applications . Nov2016, Vol. 42, p165-186. 22p. - Publication Year :
- 2016
-
Abstract
- Recently, many new classes of differentially 4-uniform permutations have been constructed. However, it is difficult to decide whether they are CCZ-inequivalent or not. In this paper, we propose a new notion called “Projected Differential Spectrum”. By considering the properties of the projected differential spectrum, we find several relations that should be satisfied by CCZ-equivalent functions. Based on these results, we mathematically prove that any differentially 4-uniform permutation constructed in [11] by C. Carlet, D. Tang, X. Tang, et al., is CCZ-inequivalent to the inverse function. We also get two interesting results with the help of computer experiments. The first one is a proof that any permutation constructed in [11] is CCZ-inequivalent to a function which is the summation of the inverse function and any Boolean function on F 2 2 k when 4 ≤ k ≤ 7 . The second one is a differentially 4-uniform permutation on F 2 6 which is CCZ-inequivalent to any function in the aforementioned two classes. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 42
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 118344211
- Full Text :
- https://doi.org/10.1016/j.ffa.2016.07.007