Differentially 4-uniform permutations
Functions | Conditions | References |
---|---|---|
and t is odd | [1][2] | |
and t is odd | [3] | |
(inverse) | [2][4] | |
and t is odd | [5] | |
is odd, and is a primitive element in | [6] | |
is even | [7] | |
and | [7] | |
is a quadratic APN permutation on |
[8] | |
t is odd | [9] | |
is even or are odd, | [10] | |
are odd, | [11] | |
is even is function |
[12] |
- ↑ R. Gold. Maximal recursive sequences with 3-valued recursive cross-correlation functions. IEEE Trans. Inf. Theory, 14, pp. 154-156, 1968. https://doi.org/10.1109/TIT.1968.1054106
- ↑ 2.0 2.1 K. Nyberg. Differentially uniform mappings for cryptography. Advances in Cryptography, EUROCRYPT’93, Lecture Notes in Computer Science 765, pp. 55-64, 1994. Lecture Notes in Computer Science, vol 765. Springer, Berlin, Heidelberg https://doi.org/10.1007/3-540-48285-7_6
- ↑ T. Kasami. The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes. Inform. and Control, 18, pp. 369-394, 1971. https://doi.org/10.1016/S0019-9958(71)90473-6
- ↑ G. Lachaud, J. Wolfmann. The weights of the orthogonals of the extended quadratic binary Goppa codes. IEEE Trans. Inf. Theory, vol. 36, no. 3, pp. 686-692, 1990. https://doi.org/10.1109/18.54892
- ↑ C. Bracken, G. Leander. A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree. Finite Fields and Their Applications, vol. 16, no. 4, pp. 231-242, 2010. https://doi.org/10.1016/j.ffa.2010.03.001
- ↑ C. Bracken, C. H. Tan, Y. Tan. Binomial differentially 4 uniform permutations with high nonlinearity. Finite Fields and Their Applications, vol. 18, no. 3, pp. 537-546, 2012. https://doi.org/10.1016/j.ffa.2011.11.006
- ↑ 7.0 7.1 Y. Tan, L. Qu, C. H. Tan, C. Li. New Families of Differentially 4-Uniform Permutations over F(22k). In: T. Helleseth, J. Jedwab (eds) Sequences and Their Applications - SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol. 7280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30615-0_3
- ↑ Y. Li, M. Wang. Constructing differentially 4-uniform permutations over GF(22m) from quadratic APN permutations over GF(22m+1). Designs, Codes and Cryptography, vol. 72, pp. 249-264, 2014. https://doi.org/10.1007/s10623-012-9760-9
- ↑ Y. Yu, M. Wang, Y. Li. Constructing Differentially 4 Uniform Permutations from Known Ones. Chinese Journal of Electronics, vol. 22, no. 3, pp. 495-499, 2013.
- ↑ Z. Zha, L. Hu, S. Sun. Constructing new differentially 4-uniform permutations from the inverse function. Finite Fields and Their Applications, vol. 25, pp. 64-78, 2014. https://doi.org/10.1016/j.ffa.2013.08.003
- ↑ Xu G, Cao X, Xu S. Constructing new differentially 4-uniform permutations and APN functions over finite fields. Cryptography and Communications-Discrete Structures, Boolean Functions and Sequences. Pre-print. 2014.
- ↑ C. Carlet, D. Tang, X. Tang, Q. Liao. New Construction of Differentially 4-Uniform Bijections. In: D. Lin, S. Xu, M. Yung (eds) Information Security and Cryptology. Inscrypt 2013. Lecture Notes in Computer Science, vol. 8567, Springer, Cham. https://doi.org/10.1007/978-3-319-12087-4_2