Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the unifo...Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.展开更多
In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that t...In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).展开更多
This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almos...This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.展开更多
文摘Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.
基金supported by National Natural Science Foundation of China(Grant Nos.61070172,10990011 and 61170257)the External Science and Technology Cooperation Program of Hubei Province(Grant No.2012IHA01402)+1 种基金National Key Basic Research Program of China(Grant No.2013CB834203)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA06010702)
文摘In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).
基金supported by the National Basic Research Program of China under Grant No.2011CB302400
文摘This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.
