, As a prelude of this conclusion, we want to recall the main conjecture concerning crooked functions: Conjecture: Let : F 2 ? F 2 be a crooked function, as defined by Definition 3. Then is quadratic or
Crooked functions, bent functions, and distance regular graphs, Electronic Journal of Combinatorics, vol.5, issue.1 ,
On almost perfect nonlinear functions, IEEE Trans. Inform. Theory, vol.52, issue.9, pp.4160-4170, 2006. ,
A family of crooked funcions, Designs, Codes and Cryptography, vol.50, pp.235-241, 2009. ,
Crooked binomials, Des. Codes Cryptogr, vol.46, pp.269-301, 2008. ,
On the non-existence of quadratic APN and crooked functions on finite fields, Proc. of the Workshop on Coding and Cryptography, pp.316-324, 2004. ,
On cryptographic properties of the cosets of (1, ), IEEE Transactions on Information Theory, vol.47, issue.4, pp.1494-1513, 2001. ,
Decomposing bent functions, IEEE Trans. Inform. Theory, vol.49, issue.8, pp.2004-2023, 2003. ,
Structural weaknesses of permutations with a low differential uniformility and generalized crooked functions, Finite Fields: Theory and Applications -FQ9 -Contemporary Mathematics, vol.518, pp.55-71, 2010. ,
Partially-bent functions. Designs, Codes and Cryptography, pp.135-145, 1993. ,
Codes, bent functions and permutations suitable for DES-like cryptosystems. Designs, Codes and Cryptography, vol.15, pp.125-156, 1998. ,
Special issue on Applications of discrete mathematics in secure communication, Subhamoy Maitra Ed, Advances in Mathematics of Communications, vol.13, issue.4, pp.579-600, 2019. ,
Uniformly packed codes and more distance regular graphs from crooked functions, J. Algebraic Combin, vol.12, issue.2, 2000. ,
Codes, graphs, and schemes from nonlinear functions, European J. Combin, vol.24, issue.1, pp.85-98, 2003. ,
Near bent functions on a hyperplane, Finite Fields Appl, vol.14, issue.3, p.720, 2008. ,
Two characterization of crooked functions, IEEE Trans. Inform. Theory, vol.54, issue.2, p.866, 2008. ,
The only crooked power functions are 2 +2, European J. Combin, vol.28, pp.1345-1350, 2007. ,
Crooked maps in 2, Finite Fields Appl, vol.13, issue.3, pp.713-726, 2007. ,
Construction of bent functions from near-bent functions, Journal of Combinatorial Theory, Series A, vol.116, p.970, 2009. ,
On the maximum number of bent component of vectorial functions, IEEE Transactions on Information Theory, vol.64, issue.1, pp.403-411, 2018. ,
On plateaued functions, IEEE Trans. Inform. Theory, vol.47, issue.3, pp.1215-1223, 2001. ,