Title :
On the Walsh Transform of a Class of Functions From Niho Exponents
Author :
Nian Li ; Helleseth, Tor ; Kholosha, A. ; Xiaohu Tang
Author_Institution :
Inf. Security & Nat. Comput. Grid Lab., Southwest Jiaotong Univ., Chengdu, China
Abstract :
In this paper, a class of functions from Niho exponents with four-valued Walsh transform is obtained for any prime by a uniform method, and the distribution of the Walsh transform values is also completely determined. In particular, this class of functions is proven to be bent for a special case. Although it is shown that the obtained bent functions are equivalent to the Leander-Kholosha´s class of bent functions, a direct and much simpler proof for the bentness of this kind of Niho functions is provided.
Keywords :
Walsh functions; cryptography; transforms; Leander-Kholosha class; Niho exponents; bent functions; cryptographic functions; cryptographic properties; four-valued Walsh transform; functions class; Correlation; Cryptography; Educational institutions; Informatics; Information theory; Transforms; Distribution; Niho exponent; Parseval´s equation; Walsh transform;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2252053
